To 3D or not to 3D? Cognitive demands of 2D and 3D online chess

To 3D or not to 3D? 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Cognitive demands of 2D and 3D online chess Jana Schneider, Wilfried Kunde, Annika L. Klaffehn This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7766269/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Chess is a universally known game of logic and strategy and has served as a hallmark not only for human, but also artificial intelligence. However, transitioning the game to the digital age has introduced multiple options and opinions on how a chess board should be displayed on computer screens. Here, we ask whether presenting a chess layout from above in 2D or from a player’s perspective in 3D impacts perception and comprehension of the displayed positions. In a high-powered online study we found that check and non-check positions were discriminated faster when presented in 2D rather than in 3D mode. As participants overwhelmingly reported more familiarity with 2D settings, we argue that this advantage is based on training effects. Moreover, this advantage was largely independent of the temporal overlap with performing another unrelated reaction task, which suggests that the 3D disadvantage arises from a lengthening of capacity-limited information processing stages. Yet, we show in a more fine-grained analysis based on the Reverse Impact Overadditivity (RIO) logic we introduce here, that a superior perceptual (precentral) processing of 3D layouts may explain the data pattern. Chess 2D/3D Multitasking Psychological Refractory Period Reverse Impact Overadditivity Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Chess may be one of the oldest board games, yet it is more popular than ever. A multitude of active players come together daily to battle it out. This has especially been made possible by internet platforms that offer real time chess games against opponents across the globe online (Khandekar, 2020; McClain, 2010). Whether or not these online games have quite the same properties as an old fashioned chess battle over the board (otb) is questionable, however. The Covid-19 pandemic, and resulting online-held competitive tournaments have given us opportunity to compare performance. Künn et al. ( 2021 ) showed that in the online event Magnus Carlsen Invitational players had a lower quality of play than the same players had in the offline held Rapid World Championship in the same year. He noted possible reasons for this, including missing peer effects in online playing environments as players did not see each other before, during and after the game. Another factor that conceivably contributes to such performance differences is the mode of visual presentation of the chess setup. In online chess most players use a 2D interface, while in otb chess, players can not only touch the pieces but also perceive the board in 3D. Strikingly, the option to transform classically 2D online chess setups into 3D already exists in most modern online chess applications (examples: lichess.org, chess.com). One could assume that the opportunity to make the online experience more closely resemble the one otb should be well received. Surprisingly however, there seems to be very little use of this option, as evident from the current dataset, but also personal experience, the comments of chess streamers (Rosen, 2020), as well as live commentaries of tournaments. In order to assess the differences in cognitive performance depending on the board setup, we performed an online experiment with volunteer chess players. They encountered a check/ non-check discrimination task (binary decision on whether one of the kings is checked), as proposed by Reingold et al. ( 2001 ), with a 2D or 3D board presentation. We expect that discrimination performance differs between presentation modes, for instance because one of these modes is inherently easier to process, or just more familiar to the participants. To delve deeper into the cognitive processes that could drive such performance differences between 2D and 3D chess layouts, we measured the check/ no check discrimination performance in the context of a psychological refractory period (PRP) paradigm. PRP paradigms are characterized by performing two tasks (T1 and T2) in response to two separate stimuli (S1 and S2). The presentation of S2 is systematically delayed following S1 by a certain stimulus onset asynchrony (SOA; e.g., McCann & Johnston, 1992 ; Pashler, 1993 ; Pashler, 1994 ; Telford, 1931). We integrated the check/ no check discrimination task as Task 2 into a PRP setting, employing the so-called locus-of-slack logic (Schweickert, 1978 ). With this logic it is possible to determine whether an experimental factor impacts capacity-limited stages of information processing (e.g., response selection) or other processes that can occur in parallel in two tasks (such as certain perceptual processes). The basic approach has been documented in several previous works (e.g., Janczyk & Kunde, 2020 ; Kunde, Janczyk, & Pfister, 2012; Pashler, 1993 ). Briefly, the idea is based upon varying the experimental factor, which in our case is the 2D vs 3D presentation mode of the chess layout, in Task 2 of a PRP-setup. If this factor affects RTs by extending a central, capacity-limited stage or any stage after that (postcentral), it should do so irrespective of the temporal overlap with another primary Task T1 (additive influence). However, the crucial factor may also impact another, non capacity-limited process, before the central stage. In this case, it should impact RTs when the temporal overlap with another task is low (long SOA), but less so when the temporal overlap is high (short SOA). Thus, an underadditive interaction between the crucial experimental factor and SOA should occur. This expectation is based on the notion that additional, non-capacity-limited processing caused by the experimental factor, can occur while the secondary task is waiting for capacity-limited processing in Task 1 to be completed. This study therefore offers not only insights into the relative efficiency with which 2D and 3D representations of chess boards can be perceived and processed but can help disentangle the stages of information processing, especially automatic perceptual and capacity limited, that may drive these discrepancies. Methods Participants A priori power analyses with the pwr package (version 1.3-0) for R suggested a minimum sample size of 34 participants, to detect effect sizes d z ≥ 0.5 with a power of 0.8 (two-tailed), greatly sufficient to detect classical PRP effects (e.g., d ≥ 4.72, Klaffehn et al., 2018 ). However, since comparisons between 2D and 3D had no precedent to estimate effect sizes from, and we also planned to correlate performance with demographics and chess experience, we strove for a sample size of N ≥ 128 participants (power of 0.8 to detect d z ≥ 0.25 in two-tailed paired t -test and correlations of r ≥ 0.24). Based on these criteria, we collected data online for two weeks in the year of 2022 and advertised on various chess platforms, among them the English and German homepage of the German chess company Chessbase (Chessbase, 2022). We planned to prolong the data collection period for a week if the goal of N ≥ 128 had not been met and explore other data collection possibilities if after 3 weeks fewer than 34 people participated. The first 300 participants could take part in a raffle to win one of ten coupons for the chess company Euroschach , so a minimum winning probability of 3% was guaranteed. Instead, participants could also opt for 0.5 participant hour credits as partial course credit (University of Wuerzburg). This form of reimbursement as well as all other elements of this study was deemed unproblematic from an ethical standpoint by the local ethics committee (GZEK 2022-40). After two weeks, we had collected complete data sets of N = 457 participants. Of them 92.3% were male and 7.5% female 1 . One person identified the own gender as diverse. The mean age of the participants was 45.01 years (18–85; SD = 14.95) years. Instructions were offered in English or German. 71% completed the experiment in German language, while 29% preferred English. No further demographic data was collected as we expected no influence onto basic cognitive functioning. Stimuli and Apparatus The experiment was programmed to be run on participants browsers at home using the programming languages JavaScript, HTML and CSS. Additionally, plugins from open-source projects jsPsych (de Leeuw, 2015 ) and jspsych psyschophysics (Kuroki, 2021 ) were used. The experiment was published and accessed via the free mindprobe server https://jatos.mindprobe.eu/ ; provided by the European Society for Cognitive Psychology), which is also where data was stored using JATOS ( https://www.jatos.org/ ). All trials consisted of a color identification task and a check detection task. Stimuli for the color identification task were colored frames of 120 px width and 550 x 550 px at the outer end of the outline. Frames were either blue (HexColor #4472C4) or orange (HexColor #FFC000). Chess diagrams for the check detection task were created using the chess program Chessbase 16. Of these 100 possible positions, 50 featured a checked king and 50 did not. All positions were taken from the 30th World Championship Match between grandmasters Anatoli Karpov and Garry Kasparov that lasted 48 games (Ftacnik et al., 2022 ). Check and no check positions had the same number of pieces. All positions were shown from White’s point of view. Images in 2D were presented centrally on the screen, covering 310 x 310 px. Settings for 3D pictures were adapted to cover approximately the same space, with the bottom of the picture being bigger and the top smaller than the 2D version. All stimuli as well as the program to run the experiment online are provided on the OSF ( https://osf.io/63q2c/ ). Procedure Participants first viewed an informed consent form detailing their rights, data usage and protection, as well as eligibility criteria (knowledge of chess rules, 18 years or older, normal color vision), their chance to win a voucher, and contact information. Only those who consented could proceed. Prior to the experimental phase, participants were queried on their demographic data (gender, age) and their chess expertise and preferences for 2D or 3D settings. Measures for chess expertise included chess experience in years, number of played games online, Elo rating (e.g. FIDE International Chess Federation, 2023; Chess, 2023), online rating (e.g. Chess, 2023), and online puzzle rating (e.g. Chess, 2023). Regarding participant’s preferences, they were asked to report the relative frequency with which they used 2D or 3D settings for online chess games on a 5-item scale. If they did not report equal shares of both settings, they were additionally asked to choose from different possible reasons for their preference (“I did not know 2D/3D settings were possible.”; “I tried 2D/3D settings, but I did not like it.”; “I knew [the other option] was possible, but I never tried it.”; “Other reason”). A free text field allowed to enter specific reasons for disliking 2D/ 3D settings. All of the questionnaire items were mandatory, but each included a “no comment” option. Note ITI: inter stimulus interval; SOA: stimulus onset asynchrony. Stimuli are scaled up for better visibility. Participants encountered each combination of Position x SOA x Representation Mode exactly once. A random half of each combination was paired with a blue, and the other with an orange frame. Check and No Check positions were parallelized regarding number of pieces. Above the colored frame, the respective key assignments appeared. Keypairs for the two tasks were “A”/“S” and “K”/”L”. Key pairing was random for each participant. In the experimental phase, participants encountered 100 positions (50 with and 50 without a check). Each position was combined with each of the SOA (0 ms, 1000 ms) and representation mode (2D, 3D) conditions exactly once during the experiment, resulting in 400 combinations. A random half of each combination was paired with a blue, the other half with an orange frame as S1. Each trial started with the presentation of the colored frame and, either simultaneously or with a delay of 1000 ms, the presentation of the chessboard. Participants were instructed to always identify the color first and press the corresponding key and then perform the check detection task. Participants received error feedback, if they misidentified the frame color or when they responded first with the keys assigned to the check detection task. They did not receive error feedback on performance in the check detection task to minimize memory effects. Every 10 trials, they received a summary statistic on their performance, including percentage of correct trials and their mean reaction time in these trials. They were reminded to try and respond as correctly and as quickly as possible. The trials were divided into 4 blocks (50 trials each), at the end of which participants could take a short break and continue by pressing a button on the screen. SOA was blocked with either the two 0 ms blocks or the two 1000 ms blocks being presented first. Within these blocks, all combinations of color, representation mode and check were presented in random order. At the end of the experiment participants were shown their own overall rate of correct trials as well as their average reaction time in correct trials. Also, the differences in their mean reaction times and accuracies between 2D and 3D condition were shown. Participants needed on average 45 minutes to complete the experiment (M = 44.6 min, SD = 15.8 min) when excluding 13 persons who took more than 2.5 hours for this calculation. Exclusions & Analysis Plan Data of participants were excluded if their overall error rate was above 40%, as preregistered. It is likely that participants with such error rates resorted to guesswork, either out of noncompliance or because of insufficient knowledge of chess rules. Based on this criterion, data of four participants were not further considered. Single trials were excluded from analysis if the reaction time was above 2.5 standard deviations from each participants’ mean in each condition or below zero seconds. A reaction time below zero seconds was only possible if participants responded to the chess stimulus, before it appeared (in the SOA 1000 condition). Trials in which the color was identified incorrectly or where participants performed more than two keystrokes were also excluded. These were not construed as error trials, even if the chess position was also misidentified and not included in the accuracy analysis. For the analysis of mean reaction times, only correct response trials were included. All data exclusions followed our preregistration. We planned to primarily analyze reaction times and error rates pertaining to T2 (chess stimulus) and show (a) a performance benefit for 2D or 3D representation and (b) that this difference is based on a perceptual benefit, as evident in larger differences between 2D and 3D representation in the SOA 1000 than in the SOA 0 condition. Considering the chess position’s unusual complexity as a second stimulus (S2) in a PRP paradigm, we anticipated the possibility of reduced or absent PRP effects. This may diminish the chance to observe the expected interaction effect. Our contingency plan for this problem involved a median split over PRP effect strength, repeating the interaction analysis only on the subset of participants, that showed the greatest PRP effect. With a remaining sample size of 453 participants, the study had greater than 99% power to detect small paired contrasts (Cohen’s d = 0.2) and small correlations ( r = 0.2). Even when the sample was halved ( n = 227), statistical power remained above 90% for detecting small paired contrasts, as estimated using the pwr package (version 1.3-0) in R. Transparency and Openness Prior to data collection, the main hypotheses, data acquisition plans and power analyses were preregistered on the OSF (osf.io/5s9uj). In accordance with academic standards, we report in full how we determined our sample size, all data exclusions, all manipulations, and all measures in the study. Raw data and analysis script are available online (osf.io/63q2c). Data were analyzed using SPSS 28.0.1.0 Results Task 2 performance For the main analysis, we assessed reaction times and accuracy of the check detection task (RT2). Mean RTs and error rates were subjected to a repeated measures analysis of variance (rmANOVA) with the factors, SOA (0 ms vs. 1000 ms) and presentation mode (2D vs. 3D). For clarity, all following t -tests are reported two-tailed, regardless of whether they were preregistered. Reaction times showed a clear PRP effect, F (1,452) = 354.53, p < .001, η p ² = .440, displaying shorter RT2s with SOA 1000 as compared to trials with simultaneous stimulus onset (SOA 0) both, in the 2D setting, t (452) = 19.56, p < .001, d = 0.92, and in the 3D setting, t (452) = 17.63, p < .001, d = 0.83. Participants showed a clear speed performance benefit for 2D over 3D settings F (1,452) = 1055.44, p < .001, η p ² = .700. The speed performance benefit of 2D over 3D data was not moderated by SOA, F (1,452) = 1.17, p = .281, η p ² = .003. Accuracy of responses did not depend on SOA F (1,452) = 0.08, p = .785, η p ² < .001, and there was also no advantage of 2D or 3D presentation mode, F (1,452) = 1.62, p = .204, η p ² = .004. The interaction term was nonsignificant, F (1,452) = 0.20, p = .658, η p ² < .001. Upon performing the pre-registered median split and including only those participants, that showed above average PRP effects, we detected an overadditive effect of presentation mode on RT2 data. The speed performance benefit of 2D over 3D displays was larger in the SOA 0 condition, than in the SOA 1000 condition, F (1,226) = 15.97, p < .001, η p ² = .066. This subset of participants naturally showed a main effect of SOA, F (1,226) = 2290.80, p < .001, η p ² = .910 and they also showed a strong effect of presentation mode, F (1,226) = 491.69, p .450, all η p ² < .003). Note CI PD s compare the RTs to the same stimuli in the same SOA condition between board representations (2D vs. 3D). Check Analyses Participants were faster in detecting check (M = 2970 ms, SD = 425 ms) than no check positions (M = 3797 ms, SD = 315 ms), F (1,452) = 1023.67, p < .001, η p 2 = .694. This effect was more pronounced in the 3D presentation mode, F (1,452) = 142.24, p < .001, η p 2 = .239, but did not significantly interact with SOA, F (1,452) = 3.30, p = .070, η p 2 = .007. At the same time, participants showed worse accuracy for positions with check (M = 0.88, SD = 0.07) than without check (M = 0.98, SD = 0.03), F (1,452) = 1130.14, p < .001, η p 2 = .714. This effect was more pronounced in the SOA 1000 condition, F (1,452) = 5.90, p = .015, η p 2 = .013, and in 2D presentation mode mode, F (1,452) = 18.80, p < .001, η p 2 = .040. We additionally analyzed other features of the chess stimulus regarding performance data. Find these results in Appendix A. Task 1 performance Reaction times of the color identification task, T1 of the PRP paradigm were subjected to a 2 (SOA) x 2 (presentation mode) repeated measures ANOVA. RT1 was lower with an SOA of 0 ms than of 1000 ms, F (1,452) = 48.88, p < .001, η p 2 = 0.10, and with 2D compared to 3D presentation, F (1,452) = 125.15, p < .001, η p 2 = 0.22. The two main effects interacted, F (1,452) = 35.47, p < .001, η p 2 = 0.07 with a stronger influence of the chess stimulus’ presentation mode, when it was presented simultaneously with the color frame (∆=94ms) than with an SOA of 1000 ms (∆=61 ms). Correlational and quasi experimental analyses We probed for relationships between performance in the PRP task and self reported participant data. Participants who chose the ‘no comment’ option were removed from each analysis. We found no significant benefit of one gender over another regarding speed, r s (448) = − .03, p = .602, or accuracy, r s (448) = − .08, p = .087, in the check detection task. One person who self-identified as diverse was excluded from this analysis. Age was positively correlated to RT2s r (441) = .51, p < .001. Older participants needed more time to react to the positions than younger participants. This effect remained also after controlling for FIDE rating, r (438) = .55, p < .001, and chess experience in years, r (443) = .63, p < .001. Notably, age and accuracy were weakly correlated, r (441) = .10, p = .032. The PRP effect (the difference in reaction times between SOA 0 and SOA 1000 conditions) was not correlated with chess experience, r s = − .01, p = .790, or FIDE rating, r s (445) = − .01, p = .906 Table 1 Correlations of performance measures with expertise reports Response times Accuracies Measure N r s p r s p Chess Experience 452 − .15 .001 .24 < .001 FIDE Rating 444 − .39 < .001 .28 < .001 Online Rating 417 − .53 < .001 .17 < .001 Online Puzzles Rating 375 − .37 < .001 .12 .021 Number Online Games 453 − .40 < .001 .06 .175 Note. Participants that chose the ‘no comment’ option were excluded from the respective test, leading to different sample sizes for each analysis. Qualitative data on 2D vs. 3D preferences A large majority of participants indicated to only use 2D boards online, which left us with a negligible sample of participants who had more, or even any tangible experience with 3D boards. Figure 3 provides a summary of the participants responses regarding their preferences. Note Represented is the percentage an option has been selected or mentioned in a free text field. Responses from the free text field (bottom panel) have been categorized by hand. Discussion Among our sample, participants were faster to correctly detect check positions in 2D chess boards than 3D chess boards. This finding has likely to do with the fact, that our cohort was greatly biased regarding prior experience. In fact, they had overwhelmingly reported to prefer, or only use 2D stimuli when playing online chess. The performance benefit could therefore be readily attributed to familiarity rather than being an innate property of 2D presentations. Notably, the performance benefit of the 2D display occurred at both levels of temporal overlap with another task. Additionally, our analysis revealed that participants were quicker to decide for the presence of a check than for its absence. This effect also was independent of temporal overlap. According to the tried-and-tested locus of slack logic such additive effects suggest that the benefit of the 2D presentation as well as the benefit of detecting a check resulted from shortening of a capacity-limited stage of processing. This notion is further supported by the finding that presence of a check and the presentation mode did interact with each other, resulting in the longest reaction times for deciding against a check in 3D displays. It should be noted that participants took longer to decide on no check positions but also made fewer mistakes. This is reminiscent of a speed accuracy trade-off. Most likely, however, the main effects may reflect methodological confounds. The detection of a check position should prompt participants to abandon any further search, leading to shorter reaction times. At the same time, overlooking a check position is much more likely than mistakenly detecting one, leading to the observed difference in accuracy ratings. To allow us to detect any interaction effects, that may otherwise be masked by extraordinarily long and varied reaction times to the rather complex chess stimulus, we further split our sample regarding the size of their PRP effect. Interestingly, for those participants that showed the most substantial PRP effects, the speed performance benefit of 2D over 3D displays was reduced at an SOA of 1000 ms compared to 0 ms. This was mirrored in RT data of Task 1. Such overadditive effects are typically associated with manipulations on the Task 1 level (Maquestiaux, Hartley, & Bertsch, 2004 ; Tombu, & Jolicœr, 2002) or interactions between Task 1 and Task 2 processing (Lien, & Proctor, 2002 ; Ulrich, & Miller 2008 ). Both accounts are unlikely in our case, as Task 1 remained constant over all trials. Instead, we suggest that more than one processing stage is affected by the manipulation of presentation mode. Indeed, an overadditive effect can be explained by assuming that a manipulation shortens the precentral stage of processing while simultaneously lengthening the central, capacity limited stage. Following this Reverse Impact Overadditivity (RIO) logic, in the current dataset 2D stimuli should be marked by a shortened capacity limited stage, but slower perceptual processing than 3D stimuli (see Fig. 4 for a graphical representation of the RIO logic in the current dataset). This is a speculative though fascinating notion requiring further investigation for consolidation. Note This possible configuration of action stages following the here introduced Reverse Impact Overadditivity (RIO) logic could explain a larger performance benefit for 2D over 3D stimuli under the SOA 0 condition by assuming a shorter perceptual stage for 3D than 2D stimuli. Our post-hoc analysis of reaction times to the color identification task (T1) showed, that RT1s were not independent of SOA or board representation. This is a common finding in PRP paradigms (Strobach et al., 2015 ) and questions the strict sequential processing of different tasks and stages. The findings could indicate partial response grouping (Ulrich & Miller, 2008 ) with Stimulus 1 being processed first, but a response is sometimes withheld until also Stimulus 2 had been processed. More relevant with regards to reaction times to the chess stimulus, the effects on RT1 could be interpreted as bottleneck switching, e.g., a switching back and forth between tasks while the two central stages are being processed, or resource sharing, where central stages can be processed in parallel, albeit with reduced efficiency (e.g., Mittelstädt et al, 2022 ). Upon a qualitative analysis of response times to the color stimulus in our dataset, a pattern of response grouping emerges (See Appendix B for a graphical representation), with many participants exhibiting a peak of very short with some very long RT1s. Additionally, the data pattern suggests that in a condition where not all stimuli are presented from the start (e.g., SOA1000), some participants withheld Task 1 responses, until the second stimulus was presented. Both of these explanations represent response biases, that should exert no influence on processing time of the chess stimulus. Nevertheless, it cannot be excluded, that bottleneck switching and/ or resource sharing also impacted the data. Please note, capacity sharing models make the same predictions as serial models regarding the influence of perceptual vs central factors on RT2 (Tombu & Jolicouer, 2002). Moreover, it should be noted, that the RT1 data pattern closely mirrors results for RT2. Not only did participants take longer to react to the color identification task, when Stimulus 2 featured a 3D chess board, but they also had longer reaction times and a larger influence of presentation mode in the SOA 0 condition, similar to RT2s of our high PRP-effect subgroup. Effects found in RT2 data can thus not be explained by a redistribution of resources towards Task 1. In fact, it is plausible that the true effects may be more pronounced if participants were able to prioritize Task 1 more efficiently. Our additional correlation analyses revealed that participants with more experience were generally faster in differentiating between check and non-check positions and, regarding most experience measures, also did so with higher accuracy. However, experience did not impact the PRP effect. On the one hand, these results do not support the theory of automatic and parallel processing of experts in chess. Central processing of the chess positions was still highly dependent on resources, even for chess experts. However, this also showcases, that chess experts do not experience faster precentral (perceptual) processing of the chess stimuli than less experienced players. In alignment with our previous conjectures, training effects most likely shortened the central stage of the check detection task. Regarding the debate on whether to 3D or not to 3D, this has important implications. If 3D stimuli can indeed be perceived more efficiently than 2D stimuli, the speed benefit of 2D representation may be based on training effects. In this case, an equally intense training of 3D stimuli could possibly yield the most remarkable performance enhancements. Conclusions Most online chess players seem to prefer and use a 2D rather than 3D representation of the board. Notwithstanding of whether this preference is a cause or a consequence, they are faster at distinguishing check vs. non-check positions if they are presented on 2D boards. Our data shows that this speed performance benefit of the 2D presentation mode is most likely due to shortening of capacity-limited processing. Considering the large differences in familiarity regarding board presentation, we assume that this benefit may largely be a result of training effects rather than an innate advantage of 2D over 3D representations. In fact, we argue that following a Reversed Impact Overadditivity (RIO) logic, even within our participant pool, which had very limited exposure to 3D stimuli, it is possible that this form of presentation is more easily perceptible than the common and preferred 2D chess displays. This hypothesis presents an intriguing avenue for future research. It would be particularly fascinating to explore whether intense training with 3D board representations would yield even better performance benefits. Declarations Open Practices Statement Prior to data collection, the main hypotheses, data acquisition plans and power analyses were preregistered on the OSF (link not anonymisable). Raw data, analysis scripts and experimental code are available on the OSF (https://osf.io/63q2c/?view_only=deec10b34a8c40c7a30874d3da7684f9). Funding: J.S. received 300€ to compensate participants from the Institute of Psychology, University of Wuerzburg to support her bachelor thesis. Conflicts of interest/Competing interests: the authors have no competing interests to disclose. Ethics approval: The form of reimbursement as well as all other elements of this study was deemed unproblematic from an ethical standpoint by the local ethics committee (GZEK 2022-40). Consent to participate: Informed consent was obtained from all individual participants included in the study. Consent for publication: Each individual participant consented to have their data published anonymously and were given the chance to have their data deleted at the end of the experiment. Availability of data and materials: Data and analysis scripts are available at on the OSF (https://osf.io/63q2c/) Code availability: All stimuli as well as the program to run the experiment online are provided on the OSF (https://osf.io/63q2c/) Authors contribution: J.S.: Conceptualization, Methodology, Software, Investigation, Formal analysis, Writing - Original Draft, Writing - Review & Editing, Visualization, Funding acquisition. W.K. : Resources, Writing - Review & Editing, Supervision, Funding acquisition. A.L.K. : Conceptualization, Methodology, Software, Formal analysis, Writing - Original Draft, Writing - Review & Editing, Visualization, Supervision References Broadbent, D. E. (1958). The effects of noise on behaviour. In D. E. Broadbent (Ed.), Perception and communication (pp. 81–107). Pergamon. https://doi.org/10.1037/10037-005 Chess. 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(2022). Evidence of resource sharing in the psychological refractory period (PRP) paradigm. Journal of Experimental Psychology: Human Perception & Performance , 48 (11), 1279–1293. https://doi.org/10.1037/xhp0001052 Pashler, H. (1993). Dual-task interference and elementary mental mechanisms. In D. E. Meyer, & S. Kornblum (Eds.), Attention and performance 14: Synergies in experimental psychology, artificial intelligence, and cognitive neuroscience (pp. 245–264). The MIT Press. Pashler, H. (1994). Dual-task interference in simple tasks: Data and theory. Psychological Bulletin , 116 (2), 220–244. https://doi.org/10.1037/0033-2909.116.2.220 Reingold, E. M., Charness, N., Schultetus, R. S., & Stampe, D. M. (2001). Perceptual automaticity in expert chess players: Parallel encoding of chess relations. Psychonomic Bulletin & Review , 8 (3), 504–510. https://doi.org/10.3758/BF03196185 Rosen, E. (2020, May 20). 3D Blitz chess [Video]. YouTube. https://www.youtube.com/watch?v=KslZZd6cjRg Schweickert, R. (1978). A critical path generalization of the additive factor method: Analysis of a Stroop task. Journal of Mathematical Psychology , 18 (2), 105–139. https://doi.org/10.1016/0022-2496 (78)90059-Smerdon, D. (2022). Facts and myths about gender in chess [PowerPoint presentation]. FIDE International Chess Federation. https://www.fide.com/docs/presentations/2022%20FIDE%20Exchange%20Forum%20-%20Smerdon.pdf Strobach, T., Schütz, A., & Schubert, T. (2015). On the importance of Task 1 and error performance measures in PRP dual-task studies. Frontiers In Psychology . https://doi.org/10.3389/fpsyg.2015.00403 Tombu, M., & Jolicoeur, P. (2002). All-or-none bottleneck versus capacity sharing accounts of the psychological refractory period phenomenon. Psychological Research Psychologische Forschung , 66 (4), 274–286. https://doi.org/10.1007/s00426-002-0101-x Ulrich, R., & Miller, J. (2008). Response grouping in the psychological refractory period (PRP) paradigm: Models and contamination effects. Cognitive Psychology , 57 (2), 75–121. https://doi.org/10.1016/j.cogpsych.2007.06.004 Welford, A. T. (1952). The psychological refractory period and the timing of high-speed performance - a review and a theory. British Journal of Psychology , 43 (1), 2–19. https://doi.org/10.1111/j.2044-8295.1952.tb00322.x Footnotes The percentage of women of all FIDE rated chess players is only 11% (Smerdon, 2022). Additional Declarations No competing interests reported. Supplementary Files Appendices.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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16:13:52","extension":"xml","order_by":21,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":99264,"visible":true,"origin":"","legend":"","description":"","filename":"c86d3654f61d4301899e9c63ffa636a71structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7766269/v1/a0a769deefa66dfaa2cf65e8.xml"},{"id":94481110,"identity":"43b5967c-8cc7-4140-9e38-ad5db683511d","added_by":"auto","created_at":"2025-10-27 16:12:40","extension":"html","order_by":22,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":110167,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7766269/v1/f6ca3e994f61cf174c0f05ee.html"},{"id":94481686,"identity":"48bfcf7d-3660-4419-94ed-d9df3e3723c1","added_by":"auto","created_at":"2025-10-27 16:14:24","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":141854,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of experimental phase\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote.\u003c/em\u003e ITI: inter stimulus interval; SOA: stimulus onset asynchrony. Stimuli are scaled up for better visibility. Participants encountered each combination of Position x SOA x Representation Mode exactly once. A random half of each combination was paired with a blue, and the other with an orange frame. Check and No Check positions were parallelized regarding number of pieces. Above the colored frame, the respective key assignments appeared. Keypairs for the two tasks were “A”/“S” and “K”/”L”. Key pairing was random for each participant.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7766269/v1/cbc270e15f1014806d814337.png"},{"id":94481687,"identity":"d1a319c1-b1b8-4b95-82f3-2c77e2f07daf","added_by":"auto","created_at":"2025-10-27 16:14:24","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":45423,"visible":true,"origin":"","legend":"\u003cp\u003eMean reaction times for the chess task (RT2) and the color task (RT1)\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote.\u003c/em\u003e CI\u003csub\u003ePD\u003c/sub\u003es compare the RTs to the same stimuli in the same SOA condition between board representations (2D vs. 3D).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7766269/v1/01990ef8c4f050c75fc21f3d.png"},{"id":94481078,"identity":"82861fc7-4e33-46c0-b2c4-fdae296afa3a","added_by":"auto","created_at":"2025-10-27 16:12:35","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":171267,"visible":true,"origin":"","legend":"\u003cp\u003eSelf reported preference data.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote.\u003c/em\u003e Represented is the percentage an option has been selected or mentioned in a free text field. Responses from the free text field (bottom panel) have been categorized by hand.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7766269/v1/8fb1543286a4107b2a1f753e.png"},{"id":94481533,"identity":"455674a1-f47d-4f11-a174-2140206bed86","added_by":"auto","created_at":"2025-10-27 16:13:35","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":163551,"visible":true,"origin":"","legend":"\u003cp\u003ePossible configuration of action stages.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eNote.\u003c/em\u003e This possible configuration of action stages following the here introduced Reverse Impact Overadditivity (RIO) logic could explain a larger performance benefit for 2D over 3D stimuli under the SOA 0 condition by assuming a shorter perceptual stage for 3D than 2D stimuli.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7766269/v1/394f86d75ea42b33e42944cc.png"},{"id":94489879,"identity":"5ed1e51a-b158-47da-bba5-fe926623ee7a","added_by":"auto","created_at":"2025-10-27 17:06:21","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1094936,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7766269/v1/1fb94255-e215-47f0-b84d-1fc5b0ae186a.pdf"},{"id":94481068,"identity":"3ff7f4ff-5cdc-47a9-b811-33bfac9141f7","added_by":"auto","created_at":"2025-10-27 16:12:33","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":737780,"visible":true,"origin":"","legend":"","description":"","filename":"Appendices.docx","url":"https://assets-eu.researchsquare.com/files/rs-7766269/v1/3bf86f244da4718df56f8e67.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"To 3D or not to 3D? Cognitive demands of 2D and 3D online chess","fulltext":[{"header":"Introduction","content":"\u003cp\u003eChess may be one of the oldest board games, yet it is more popular than ever. A multitude of active players come together daily to battle it out. This has especially been made possible by internet platforms that offer real time chess games against opponents across the globe online (Khandekar, 2020; McClain, 2010). Whether or not these online games have quite the same properties as an old fashioned chess battle over the board (otb) is questionable, however. The Covid-19 pandemic, and resulting online-held competitive tournaments have given us opportunity to compare performance. K\u0026uuml;nn et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) showed that in the online event \u003cem\u003eMagnus Carlsen Invitational\u003c/em\u003e players had a lower quality of play than the same players had in the offline held Rapid World Championship in the same year. He noted possible reasons for this, including missing peer effects in online playing environments as players did not see each other before, during and after the game.\u003c/p\u003e\u003cp\u003eAnother factor that conceivably contributes to such performance differences is the mode of visual presentation of the chess setup. In online chess most players use a 2D interface, while in otb chess, players can not only touch the pieces but also perceive the board in 3D. Strikingly, the option to transform classically 2D online chess setups into 3D already exists in most modern online chess applications (examples: lichess.org, chess.com). One could assume that the opportunity to make the online experience more closely resemble the one otb should be well received. Surprisingly however, there seems to be very little use of this option, as evident from the current dataset, but also personal experience, the comments of chess streamers (Rosen, 2020), as well as live commentaries of tournaments. In order to assess the differences in cognitive performance depending on the board setup, we performed an online experiment with volunteer chess players. They encountered a check/ non-check discrimination task (binary decision on whether one of the kings is checked), as proposed by Reingold et al. (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2001\u003c/span\u003e), with a 2D or 3D board presentation. We expect that discrimination performance differs between presentation modes, for instance because one of these modes is inherently easier to process, or just more familiar to the participants.\u003c/p\u003e\u003cp\u003eTo delve deeper into the cognitive processes that could drive such performance differences between 2D and 3D chess layouts, we measured the check/ no check discrimination performance in the context of a psychological refractory period (PRP) paradigm. PRP paradigms are characterized by performing two tasks (T1 and T2) in response to two separate stimuli (S1 and S2). The presentation of S2 is systematically delayed following S1 by a certain stimulus onset asynchrony (SOA; e.g., McCann \u0026amp; Johnston, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e1992\u003c/span\u003e; Pashler, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1993\u003c/span\u003e; Pashler, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1994\u003c/span\u003e; Telford, 1931). We integrated the check/ no check discrimination task as Task 2 into a PRP setting, employing the so-called locus-of-slack logic (Schweickert, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1978\u003c/span\u003e). With this logic it is possible to determine whether an experimental factor impacts capacity-limited stages of information processing (e.g., response selection) or other processes that can occur in parallel in two tasks (such as certain perceptual processes). The basic approach has been documented in several previous works (e.g., Janczyk \u0026amp; Kunde, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Kunde, Janczyk, \u0026amp; Pfister, 2012; Pashler, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1993\u003c/span\u003e). Briefly, the idea is based upon varying the experimental factor, which in our case is the 2D vs 3D presentation mode of the chess layout, in Task 2 of a PRP-setup. If this factor affects RTs by extending a central, capacity-limited stage or any stage after that (postcentral), it should do so irrespective of the temporal overlap with another primary Task T1 (additive influence). However, the crucial factor may also impact another, non capacity-limited process, before the central stage. In this case, it should impact RTs when the temporal overlap with another task is low (long SOA), but less so when the temporal overlap is high (short SOA). Thus, an underadditive interaction between the crucial experimental factor and SOA should occur. This expectation is based on the notion that additional, non-capacity-limited processing caused by the experimental factor, can occur while the secondary task is waiting for capacity-limited processing in Task 1 to be completed. This study therefore offers not only insights into the relative efficiency with which 2D and 3D representations of chess boards can be perceived and processed but can help disentangle the stages of information processing, especially automatic perceptual and capacity limited, that may drive these discrepancies.\u003c/p\u003e"},{"header":"Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003eParticipants\u003c/h2\u003e\u003cp\u003eA priori power analyses with the pwr package (version 1.3-0) for R suggested a minimum sample size of 34 participants, to detect effect sizes \u003cem\u003ed\u003c/em\u003e\u003csub\u003ez\u003c/sub\u003e \u0026ge; 0.5 with a power of 0.8 (two-tailed), greatly sufficient to detect classical PRP effects (e.g., \u003cem\u003ed\u003c/em\u003e\u0026thinsp;\u0026ge;\u0026thinsp;4.72, Klaffehn et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). However, since comparisons between 2D and 3D had no precedent to estimate effect sizes from, and we also planned to correlate performance with demographics and chess experience, we strove for a sample size of N\u0026thinsp;\u0026ge;\u0026thinsp;128 participants (power of 0.8 to detect \u003cem\u003ed\u003c/em\u003e\u003csub\u003ez\u003c/sub\u003e \u0026ge; 0.25 in two-tailed paired \u003cem\u003et\u003c/em\u003e-test and correlations of \u003cem\u003er\u003c/em\u003e\u0026thinsp;\u0026ge;\u0026thinsp;0.24).\u003c/p\u003e\u003cp\u003eBased on these criteria, we collected data online for two weeks in the year of 2022 and advertised on various chess platforms, among them the English and German homepage of the German chess company Chessbase (Chessbase, 2022). We planned to prolong the data collection period for a week if the goal of N\u0026thinsp;\u0026ge;\u0026thinsp;128 had not been met and explore other data collection possibilities if after 3 weeks fewer than 34 people participated. The first 300 participants could take part in a raffle to win one of ten coupons for the chess company \u003cem\u003eEuroschach\u003c/em\u003e, so a minimum winning probability of 3% was guaranteed. Instead, participants could also opt for 0.5 participant hour credits as partial course credit (University of Wuerzburg). This form of reimbursement as well as all other elements of this study was deemed unproblematic from an ethical standpoint by the local ethics committee (GZEK 2022-40).\u003c/p\u003e\u003cp\u003eAfter two weeks, we had collected complete data sets of N\u0026thinsp;=\u0026thinsp;457 participants. Of them 92.3% were male and 7.5% female\u003csup\u003e1\u003c/sup\u003e. One person identified the own gender as diverse. The mean age of the participants was 45.01 years (18\u0026ndash;85; SD\u0026thinsp;=\u0026thinsp;14.95) years. Instructions were offered in English or German. 71% completed the experiment in German language, while 29% preferred English. No further demographic data was collected as we expected no influence onto basic cognitive functioning.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eStimuli and Apparatus\u003c/h3\u003e\n\u003cp\u003eThe experiment was programmed to be run on participants browsers at home using the programming languages JavaScript, HTML and CSS. Additionally, plugins from open-source projects \u003cem\u003ejsPsych\u003c/em\u003e (de Leeuw, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) and \u003cem\u003ejspsych psyschophysics\u003c/em\u003e (Kuroki, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) were used. The experiment was published and accessed via the free mindprobe server \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://jatos.mindprobe.eu/\u003c/span\u003e\u003cspan address=\"https://jatos.mindprobe.eu/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e; provided by the European Society for Cognitive Psychology), which is also where data was stored using JATOS (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.jatos.org/\u003c/span\u003e\u003cspan address=\"https://www.jatos.org/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). All trials consisted of a color identification task and a check detection task. Stimuli for the color identification task were colored frames of 120 px width and 550 x 550 px at the outer end of the outline. Frames were either blue (HexColor #4472C4) or orange (HexColor #FFC000). Chess diagrams for the check detection task were created using the chess program Chessbase 16. Of these 100 possible positions, 50 featured a checked king and 50 did not. All positions were taken from the 30th World Championship Match between grandmasters Anatoli Karpov and Garry Kasparov that lasted 48 games (Ftacnik et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Check and no check positions had the same number of pieces. All positions were shown from White\u0026rsquo;s point of view. Images in 2D were presented centrally on the screen, covering 310 x 310 px. Settings for 3D pictures were adapted to cover approximately the same space, with the bottom of the picture being bigger and the top smaller than the 2D version. All stimuli as well as the program to run the experiment online are provided on the OSF (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://osf.io/63q2c/\u003c/span\u003e\u003cspan address=\"https://osf.io/63q2c/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e\n\u003ch3\u003eProcedure\u003c/h3\u003e\n\u003cp\u003eParticipants first viewed an informed consent form detailing their rights, data usage and protection, as well as eligibility criteria (knowledge of chess rules, 18 years or older, normal color vision), their chance to win a voucher, and contact information. Only those who consented could proceed. Prior to the experimental phase, participants were queried on their demographic data (gender, age) and their chess expertise and preferences for 2D or 3D settings. Measures for chess expertise included chess experience in years, number of played games online, Elo rating (e.g. FIDE International Chess Federation, 2023; Chess, 2023), online rating (e.g. Chess, 2023), and online puzzle rating (e.g. Chess, 2023). Regarding participant\u0026rsquo;s preferences, they were asked to report the relative frequency with which they used 2D or 3D settings for online chess games on a 5-item scale. If they did not report equal shares of both settings, they were additionally asked to choose from different possible reasons for their preference (\u0026ldquo;I did not know 2D/3D settings were possible.\u0026rdquo;; \u0026ldquo;I tried 2D/3D settings, but I did not like it.\u0026rdquo;; \u0026ldquo;I knew [the other option] was possible, but I never tried it.\u0026rdquo;; \u0026ldquo;Other reason\u0026rdquo;). A free text field allowed to enter specific reasons for disliking 2D/ 3D settings. All of the questionnaire items were mandatory, but each included a \u0026ldquo;no comment\u0026rdquo; option.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eNote\u003c/strong\u003e\u003cp\u003eITI: inter stimulus interval; SOA: stimulus onset asynchrony. Stimuli are scaled up for better visibility. Participants encountered each combination of Position x SOA x Representation Mode exactly once. A random half of each combination was paired with a blue, and the other with an orange frame. Check and No Check positions were parallelized regarding number of pieces. Above the colored frame, the respective key assignments appeared. Keypairs for the two tasks were \u0026ldquo;A\u0026rdquo;/\u0026ldquo;S\u0026rdquo; and \u0026ldquo;K\u0026rdquo;/\u0026rdquo;L\u0026rdquo;. Key pairing was random for each participant.\u003c/p\u003e\u003c/p\u003e\u003cp\u003eIn the experimental phase, participants encountered 100 positions (50 with and 50 without a check). Each position was combined with each of the SOA (0 ms, 1000 ms) and representation mode (2D, 3D) conditions exactly once during the experiment, resulting in 400 combinations. A random half of each combination was paired with a blue, the other half with an orange frame as S1. Each trial started with the presentation of the colored frame and, either simultaneously or with a delay of 1000 ms, the presentation of the chessboard. Participants were instructed to always identify the color first and press the corresponding key and then perform the check detection task. Participants received error feedback, if they misidentified the frame color or when they responded first with the keys assigned to the check detection task. They did not receive error feedback on performance in the check detection task to minimize memory effects. Every 10 trials, they received a summary statistic on their performance, including percentage of correct trials and their mean reaction time in these trials. They were reminded to try and respond as correctly and as quickly as possible. The trials were divided into 4 blocks (50 trials each), at the end of which participants could take a short break and continue by pressing a button on the screen. SOA was blocked with either the two 0 ms blocks or the two 1000 ms blocks being presented first. Within these blocks, all combinations of color, representation mode and check were presented in random order. At the end of the experiment participants were shown their own overall rate of correct trials as well as their average reaction time in correct trials. Also, the differences in their mean reaction times and accuracies between 2D and 3D condition were shown. Participants needed on average 45 minutes to complete the experiment (M\u0026thinsp;=\u0026thinsp;44.6 min, SD\u0026thinsp;=\u0026thinsp;15.8 min) when excluding 13 persons who took more than 2.5 hours for this calculation.\u003c/p\u003e\n\u003ch3\u003eExclusions \u0026 Analysis Plan\u003c/h3\u003e\n\u003cp\u003eData of participants were excluded if their overall error rate was above 40%, as preregistered. It is likely that participants with such error rates resorted to guesswork, either out of noncompliance or because of insufficient knowledge of chess rules. Based on this criterion, data of four participants were not further considered. Single trials were excluded from analysis if the reaction time was above 2.5 standard deviations from each participants\u0026rsquo; mean in each condition or below zero seconds. A reaction time below zero seconds was only possible if participants responded to the chess stimulus, before it appeared (in the SOA 1000 condition). Trials in which the color was identified incorrectly or where participants performed more than two keystrokes were also excluded. These were not construed as error trials, even if the chess position was also misidentified and not included in the accuracy analysis. For the analysis of mean reaction times, only correct response trials were included. All data exclusions followed our preregistration.\u003c/p\u003e\u003cp\u003eWe planned to primarily analyze reaction times and error rates pertaining to T2 (chess stimulus) and show (a) a performance benefit for 2D or 3D representation and (b) that this difference is based on a perceptual benefit, as evident in larger differences between 2D and 3D representation in the SOA 1000 than in the SOA 0 condition. Considering the chess position\u0026rsquo;s unusual complexity as a second stimulus (S2) in a PRP paradigm, we anticipated the possibility of reduced or absent PRP effects. This may diminish the chance to observe the expected interaction effect. Our contingency plan for this problem involved a median split over PRP effect strength, repeating the interaction analysis only on the subset of participants, that showed the greatest PRP effect. With a remaining sample size of 453 participants, the study had greater than 99% power to detect small paired contrasts (Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.2) and small correlations (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.2). Even when the sample was halved (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;227), statistical power remained above 90% for detecting small paired contrasts, as estimated using the \u003cem\u003epwr\u003c/em\u003e package (version 1.3-0) in R.\u003c/p\u003e\n\u003ch3\u003eTransparency and Openness\u003c/h3\u003e\n\u003cp\u003ePrior to data collection, the main hypotheses, data acquisition plans and power analyses were preregistered on the OSF (osf.io/5s9uj). In accordance with academic standards, we report in full how we determined our sample size, all data exclusions, all manipulations, and all measures in the study. Raw data and analysis script are available online (osf.io/63q2c). Data were analyzed using SPSS 28.0.1.0\u003c/p\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003eTask 2 performance\u003c/h2\u003e\u003cp\u003eFor the main analysis, we assessed reaction times and accuracy of the check detection task (RT2). Mean RTs and error rates were subjected to a repeated measures analysis of variance (rmANOVA) with the factors, SOA (0 ms vs. 1000 ms) and presentation mode (2D vs. 3D). For clarity, all following \u003cem\u003et\u003c/em\u003e-tests are reported two-tailed, regardless of whether they were preregistered.\u003c/p\u003e\u003cp\u003eReaction times showed a clear PRP effect, \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;354.53, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u003csub\u003ep\u003c/sub\u003e\u0026sup2; = .440, displaying shorter RT2s with SOA 1000 as compared to trials with simultaneous stimulus onset (SOA 0) both, in the 2D setting, \u003cem\u003et\u003c/em\u003e(452)\u0026thinsp;=\u0026thinsp;19.56, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.92, and in the 3D setting, \u003cem\u003et\u003c/em\u003e(452)\u0026thinsp;=\u0026thinsp;17.63, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.83. Participants showed a clear speed performance benefit for 2D over 3D settings \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;1055.44, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u003csub\u003ep\u003c/sub\u003e\u0026sup2; = .700. The speed performance benefit of 2D over 3D data was not moderated by SOA, \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;1.17, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.281, η\u003csub\u003ep\u003c/sub\u003e\u0026sup2; = .003.\u003c/p\u003e\u003cp\u003eAccuracy of responses did not depend on SOA \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;0.08, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.785, η\u003csub\u003ep\u003c/sub\u003e\u0026sup2; \u0026lt; .001, and there was also no advantage of 2D or 3D presentation mode, \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;1.62, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.204, η\u003csub\u003ep\u003c/sub\u003e\u0026sup2; = .004. The interaction term was nonsignificant, \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;0.20, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.658, η\u003csub\u003ep\u003c/sub\u003e\u0026sup2; \u0026lt; .001.\u003c/p\u003e\u003cp\u003eUpon performing the pre-registered median split and including only those participants, that showed above average PRP effects, we detected an overadditive effect of presentation mode on RT2 data. The speed performance benefit of 2D over 3D displays was larger in the SOA 0 condition, than in the SOA 1000 condition, \u003cem\u003eF\u003c/em\u003e(1,226)\u0026thinsp;=\u0026thinsp;15.97, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u003csub\u003ep\u003c/sub\u003e\u0026sup2; = .066. This subset of participants naturally showed a main effect of SOA, \u003cem\u003eF\u003c/em\u003e(1,226)\u0026thinsp;=\u0026thinsp;2290.80, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u003csub\u003ep\u003c/sub\u003e\u0026sup2; = .910 and they also showed a strong effect of presentation mode, \u003cem\u003eF\u003c/em\u003e(1,226)\u0026thinsp;=\u0026thinsp;491.69, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u003csub\u003ep\u003c/sub\u003e\u0026sup2; = .685. Just like in the full sample, no significant main effects or interactions regarding accuracies were detected (all \u003cem\u003ep\u003c/em\u003es\u0026thinsp;\u0026gt;\u0026thinsp;.450, all η\u003csub\u003ep\u003c/sub\u003e\u0026sup2; \u0026lt; .003).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eNote\u003c/strong\u003e\u003cp\u003eCI\u003csub\u003ePD\u003c/sub\u003es compare the RTs to the same stimuli in the same SOA condition between board representations (2D vs. 3D).\u003c/p\u003e\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eCheck Analyses\u003c/h3\u003e\n\u003cp\u003eParticipants were faster in detecting check (M\u0026thinsp;=\u0026thinsp;2970 ms, SD\u0026thinsp;=\u0026thinsp;425 ms) than no check positions (M\u0026thinsp;=\u0026thinsp;3797 ms, SD\u0026thinsp;=\u0026thinsp;315 ms), \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;1023.67, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u003csub\u003ep\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;.694. This effect was more pronounced in the 3D presentation mode, \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;142.24, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u003csub\u003ep\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;.239, but did not significantly interact with SOA, \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;3.30, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.070, η\u003csub\u003ep\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;.007. At the same time, participants showed worse accuracy for positions with check (M\u0026thinsp;=\u0026thinsp;0.88, SD\u0026thinsp;=\u0026thinsp;0.07) than without check (M\u0026thinsp;=\u0026thinsp;0.98, SD\u0026thinsp;=\u0026thinsp;0.03), \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;1130.14, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u003csub\u003ep\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;.714. This effect was more pronounced in the SOA 1000 condition, \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;5.90, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.015, η\u003csub\u003ep\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;.013, and in 2D presentation mode mode, \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;18.80, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u003csub\u003ep\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;.040.\u003c/p\u003e\u003cp\u003eWe additionally analyzed other features of the chess stimulus regarding performance data. Find these results in Appendix A.\u003c/p\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003eTask 1 performance\u003c/h2\u003e\u003cp\u003eReaction times of the color identification task, T1 of the PRP paradigm were subjected to a 2 (SOA) x 2 (presentation mode) repeated measures ANOVA. RT1 was lower with an SOA of 0 ms than of 1000 ms, \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;48.88, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u003csub\u003ep\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.10, and with 2D compared to 3D presentation, \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;125.15, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u003csub\u003ep\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.22. The two main effects interacted, \u003cem\u003eF\u003c/em\u003e(1,452)\u0026thinsp;=\u0026thinsp;35.47, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, η\u003csub\u003ep\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.07 with a stronger influence of the chess stimulus\u0026rsquo; presentation mode, when it was presented simultaneously with the color frame (∆=94ms) than with an SOA of 1000 ms (∆=61 ms).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003eCorrelational and quasi experimental analyses\u003c/h2\u003e\u003cp\u003eWe probed for relationships between performance in the PRP task and self reported participant data. Participants who chose the \u0026lsquo;no comment\u0026rsquo; option were removed from each analysis. We found no significant benefit of one gender over another regarding speed, \u003cem\u003er\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e(448)\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;.03, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.602, or accuracy, \u003cem\u003er\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e(448)\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;.08, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.087, in the check detection task. One person who self-identified as diverse was excluded from this analysis. Age was positively correlated to RT2s \u003cem\u003er\u003c/em\u003e(441)\u0026thinsp;=\u0026thinsp;.51, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001. Older participants needed more time to react to the positions than younger participants. This effect remained also after controlling for FIDE rating, \u003cem\u003er\u003c/em\u003e(438)\u0026thinsp;=\u0026thinsp;.55, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001, and chess experience in years, \u003cem\u003er\u003c/em\u003e(443)\u0026thinsp;=\u0026thinsp;.63, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001. Notably, age and accuracy were weakly correlated, \u003cem\u003er\u003c/em\u003e(441)\u0026thinsp;=\u0026thinsp;.10, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.032. The PRP effect (the difference in reaction times between SOA 0 and SOA 1000 conditions) was not correlated with chess experience, \u003cem\u003er\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;.01, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.790, or FIDE rating, \u003cem\u003er\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e(445)\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;.01, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.906\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eCorrelations of performance measures with expertise reports\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e\u003cp\u003eResponse times\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"3\" nameend=\"c8\" namest=\"c6\"\u003e\u003cp\u003eAccuracies\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMeasure\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eN\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cem\u003er\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cem\u003er\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eChess Experience\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e452\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e.001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e.24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFIDE Rating\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e444\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;.39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOnline Rating\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e417\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;.53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOnline Puzzles Rating\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e375\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;.37\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e.021\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNumber Online Games\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e453\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;.001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e.06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e.175\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"8\"\u003e\u003cem\u003eNote.\u003c/em\u003e Participants that chose the \u0026lsquo;no comment\u0026rsquo; option were excluded from the respective test, leading to different sample sizes for each analysis.\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003eQualitative data on 2D vs. 3D preferences\u003c/h2\u003e\u003cp\u003eA large majority of participants indicated to only use 2D boards online, which left us with a negligible sample of participants who had more, or even any tangible experience with 3D boards. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e provides a summary of the participants responses regarding their preferences.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eNote\u003c/strong\u003e\u003cp\u003eRepresented is the percentage an option has been selected or mentioned in a free text field. Responses from the free text field (bottom panel) have been categorized by hand.\u003c/p\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eAmong our sample, participants were faster to correctly detect check positions in 2D chess boards than 3D chess boards. This finding has likely to do with the fact, that our cohort was greatly biased regarding prior experience. In fact, they had overwhelmingly reported to prefer, or only use 2D stimuli when playing online chess. The performance benefit could therefore be readily attributed to familiarity rather than being an innate property of 2D presentations. Notably, the performance benefit of the 2D display occurred at both levels of temporal overlap with another task. Additionally, our analysis revealed that participants were quicker to decide for the presence of a check than for its absence. This effect also was independent of temporal overlap. According to the tried-and-tested locus of slack logic such additive effects suggest that the benefit of the 2D presentation as well as the benefit of detecting a check resulted from shortening of a capacity-limited stage of processing. This notion is further supported by the finding that presence of a check and the presentation mode did interact with each other, resulting in the longest reaction times for deciding against a check in 3D displays.\u003c/p\u003e\u003cp\u003eIt should be noted that participants took longer to decide on no check positions but also made fewer mistakes. This is reminiscent of a speed accuracy trade-off. Most likely, however, the main effects may reflect methodological confounds. The detection of a check position should prompt participants to abandon any further search, leading to shorter reaction times. At the same time, overlooking a check position is much more likely than mistakenly detecting one, leading to the observed difference in accuracy ratings.\u003c/p\u003e\u003cp\u003eTo allow us to detect any interaction effects, that may otherwise be masked by extraordinarily long and varied reaction times to the rather complex chess stimulus, we further split our sample regarding the size of their PRP effect. Interestingly, for those participants that showed the most substantial PRP effects, the speed performance benefit of 2D over 3D displays was reduced at an SOA of 1000 ms compared to 0 ms. This was mirrored in RT data of Task 1. Such overadditive effects are typically associated with manipulations on the Task 1 level (Maquestiaux, Hartley, \u0026amp; Bertsch, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Tombu, \u0026amp; Jolicœr, 2002) or interactions between Task 1 and Task 2 processing (Lien, \u0026amp; Proctor, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Ulrich, \u0026amp; Miller \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). Both accounts are unlikely in our case, as Task 1 remained constant over all trials. Instead, we suggest that more than one processing stage is affected by the manipulation of presentation mode. Indeed, an overadditive effect can be explained by assuming that a manipulation shortens the precentral stage of processing while simultaneously lengthening the central, capacity limited stage. Following this Reverse Impact Overadditivity (RIO) logic, in the current dataset 2D stimuli should be marked by a shortened capacity limited stage, but slower perceptual processing than 3D stimuli (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e for a graphical representation of the RIO logic in the current dataset). This is a speculative though fascinating notion requiring further investigation for consolidation.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eNote\u003c/strong\u003e\u003cp\u003eThis possible configuration of action stages following the here introduced Reverse Impact Overadditivity (RIO) logic could explain a larger performance benefit for 2D over 3D stimuli under the SOA 0 condition by assuming a shorter perceptual stage for 3D than 2D stimuli.\u003c/p\u003e\u003c/p\u003e\u003cp\u003eOur post-hoc analysis of reaction times to the color identification task (T1) showed, that RT1s were not independent of SOA or board representation. This is a common finding in PRP paradigms (Strobach et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) and questions the strict sequential processing of different tasks and stages. The findings could indicate partial response grouping (Ulrich \u0026amp; Miller, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) with Stimulus 1 being processed first, but a response is sometimes withheld until also Stimulus 2 had been processed. More relevant with regards to reaction times to the chess stimulus, the effects on RT1 could be interpreted as bottleneck switching, e.g., a switching back and forth between tasks while the two central stages are being processed, or resource sharing, where central stages can be processed in parallel, albeit with reduced efficiency (e.g., Mittelst\u0026auml;dt et al, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Upon a qualitative analysis of response times to the color stimulus in our dataset, a pattern of response grouping emerges (See Appendix B for a graphical representation), with many participants exhibiting a peak of very short with some very long RT1s. Additionally, the data pattern suggests that in a condition where not all stimuli are presented from the start (e.g., SOA1000), some participants withheld Task 1 responses, until the second stimulus was presented.\u003c/p\u003e\u003cp\u003eBoth of these explanations represent response biases, that should exert no influence on processing time of the chess stimulus. Nevertheless, it cannot be excluded, that bottleneck switching and/ or resource sharing also impacted the data. Please note, capacity sharing models make the same predictions as serial models regarding the influence of perceptual vs central factors on RT2 (Tombu \u0026amp; Jolicouer, 2002). Moreover, it should be noted, that the RT1 data pattern closely mirrors results for RT2. Not only did participants take longer to react to the color identification task, when Stimulus 2 featured a 3D chess board, but they also had longer reaction times and a larger influence of presentation mode in the SOA 0 condition, similar to RT2s of our high PRP-effect subgroup. Effects found in RT2 data can thus not be explained by a redistribution of resources towards Task 1. In fact, it is plausible that the true effects may be more pronounced if participants were able to prioritize Task 1 more efficiently.\u003c/p\u003e\u003cp\u003eOur additional correlation analyses revealed that participants with more experience were generally faster in differentiating between check and non-check positions and, regarding most experience measures, also did so with higher accuracy. However, experience did not impact the PRP effect. On the one hand, these results do not support the theory of automatic and parallel processing of experts in chess. Central processing of the chess positions was still highly dependent on resources, even for chess experts. However, this also showcases, that chess experts do not experience faster precentral (perceptual) processing of the chess stimuli than less experienced players. In alignment with our previous conjectures, training effects most likely shortened the central stage of the check detection task. Regarding the debate on whether to 3D or not to 3D, this has important implications. If 3D stimuli can indeed be perceived more efficiently than 2D stimuli, the speed benefit of 2D representation may be based on training effects. In this case, an equally intense training of 3D stimuli could possibly yield the most remarkable performance enhancements.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eMost online chess players seem to prefer and use a 2D rather than 3D representation of the board. Notwithstanding of whether this preference is a cause or a consequence, they are faster at distinguishing check vs. non-check positions if they are presented on 2D boards. Our data shows that this speed performance benefit of the 2D presentation mode is most likely due to shortening of capacity-limited processing. Considering the large differences in familiarity regarding board presentation, we assume that this benefit may largely be a result of training effects rather than an innate advantage of 2D over 3D representations. In fact, we argue that following a Reversed Impact Overadditivity (RIO) logic, even within our participant pool, which had very limited exposure to 3D stimuli, it is possible that this form of presentation is more easily perceptible than the common and preferred 2D chess displays. This hypothesis presents an intriguing avenue for future research. It would be particularly fascinating to explore whether intense training with 3D board representations would yield even better performance benefits.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eOpen Practices Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003ePrior to data collection, the main hypotheses, data acquisition plans and power analyses were preregistered on the OSF (link not anonymisable). Raw data, analysis scripts and experimental code are available on the OSF (https://osf.io/63q2c/?view_only=deec10b34a8c40c7a30874d3da7684f9).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e J.S. received 300\u0026euro; to compensate participants from the Institute of Psychology, University of Wuerzburg to support her bachelor thesis.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest/Competing interests:\u003c/strong\u003e the authors have no competing interests to disclose.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval:\u003c/strong\u003e The form of reimbursement as well as all other elements of this study was deemed unproblematic from an ethical standpoint by the local ethics committee (GZEK 2022-40).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to participate:\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eInformed consent was obtained from all individual participants included in the study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication:\u003c/strong\u003e Each individual participant consented to have their data published anonymously and were given the chance to have their data deleted at the end of the experiment.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials:\u003c/strong\u003e Data and analysis scripts are available at on the OSF (https://osf.io/63q2c/)\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode availability:\u003c/strong\u003e All stimuli as well as the program to run the experiment online are provided on the OSF (https://osf.io/63q2c/)\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors contribution:\u003c/strong\u003e \u003cstrong\u003eJ.S.:\u003c/strong\u003e Conceptualization, Methodology, Software, Investigation, Formal analysis, Writing - Original Draft, Writing - Review \u0026amp; Editing, Visualization, Funding acquisition. \u003cstrong\u003eW.K.\u003c/strong\u003e: Resources, Writing - Review \u0026amp; Editing, Supervision, Funding acquisition. \u003cstrong\u003eA.L.K.\u003c/strong\u003e: Conceptualization, Methodology, Software, Formal analysis, Writing - Original Draft, Writing - Review \u0026amp; Editing, Visualization, Supervision\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBroadbent, D. 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The psychological refractory period and the timing of high-speed performance - a review and a theory. \u003cem\u003eBritish Journal of Psychology\u003c/em\u003e, \u003cem\u003e43\u003c/em\u003e(1), 2\u0026ndash;19. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1111/j.2044-8295.1952.tb00322.x\u003c/span\u003e\u003cspan address=\"10.1111/j.2044-8295.1952.tb00322.x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Footnotes","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e The percentage of women of all FIDE rated chess players is only 11% (Smerdon, 2022).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Chess, 2D/3D, Multitasking, Psychological Refractory Period, Reverse Impact Overadditivity","lastPublishedDoi":"10.21203/rs.3.rs-7766269/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7766269/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eChess is a universally known game of logic and strategy and has served as a hallmark not only for human, but also artificial intelligence. However, transitioning the game to the digital age has introduced multiple options and opinions on how a chess board should be displayed on computer screens. Here, we ask whether presenting a chess layout from above in 2D or from a player\u0026rsquo;s perspective in 3D impacts perception and comprehension of the displayed positions. In a high-powered online study we found that check and non-check positions were discriminated faster when presented in 2D rather than in 3D mode. As participants overwhelmingly reported more familiarity with 2D settings, we argue that this advantage is based on training effects. Moreover, this advantage was largely independent of the temporal overlap with performing another unrelated reaction task, which suggests that the 3D disadvantage arises from a lengthening of capacity-limited information processing stages. Yet, we show in a more fine-grained analysis based on the Reverse Impact Overadditivity (RIO) logic we introduce here, that a superior perceptual (precentral) processing of 3D layouts may explain the data pattern.\u003c/p\u003e","manuscriptTitle":"To 3D or not to 3D? Cognitive demands of 2D and 3D online chess","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-27 15:25:39","doi":"10.21203/rs.3.rs-7766269/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ff4b7550-e5c4-46ee-8fb5-44729db2a7fa","owner":[],"postedDate":"October 27th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-29T01:08:20+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-27 15:25:39","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7766269","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7766269","identity":"rs-7766269","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}