"Theoretically, there are more than 3,000 possible ratio values in one-player guessing games." "The optimal choices... maximizes the player’s payoff by continually halving each choice until both reach zero." "Fig. 1 illustrates the full set of possible ratios and their frequencies under random play, ...." "The frequent occurrence of specific ratios, particularly 0.5 and 1, may reflect the use of boundedly rational decision-making strategies."

"The ordinal logistic regression analysis, summarized in Table 1, shows a significant positive relationship between Cognitive Reflection Test (CRT) scores and rationality levels. The coefficient for CRT scores ( 𝛽 = 0.7563, 𝑧 = 7.886, 𝑝 < .001) suggests that each unit increase in CRT score more than doubles the odds of moving to a higher rationality level (odds ratio of 2.13). The thresholds indicate moderate to substantial increases in the likelihood of advancing from irrational to bounded rational ( 𝛽 = 0.4071, 𝑝 < .05) and from bounded rational to optimal decision-making ( 𝛽 = 1.8457, 𝑝 < .001)."