Discrepancies between empirical and theoretical probability in human binary choices within the game of Go

To make a decision or determine the order of things, people commonly use binary choices such as tossing a coin, with an assumption that the empirical probability equals to the theoretical probability. However, recent understanding on empirical coin-toss probability is contrasting, i.e., even or uneven by quantic or deterministic mechanism, wherein such discrepancies yet remain to be resolved. Here, we investigated whether the probability of stone selection in the game of Go is equal for both parties across Go games to establish the stone selection as a binary choice model for studying the discrepancy between theoretical and empirical probability. The stone selection process is considered as a sequential strategic interaction similar to other binary choice games such as matching pennies. The large-scale data analyses of professional Go matches (n = 21,212 among 311 Go masters) showed that the black stone selection was significantly higher for higher-ranked players compared with lower-ranked players. Moreover, in situ stone selection games between amateur Go players (the number of participants: n = 293, 2 games each) demonstrated that the amateur players with upper master levels had significantly higher chances for selecting black stones than players with lower master levels. The results support that actual chance for human binary choice may not be equal to theoretical odds, unlike usual expectations. The present study may contribute to providing input or insights to expand its discussion regarding the discrepancy between theoretical and empirical probability in binary choices, including strategy in game theory and elucidating the underlying mechanisms.