2017/03/05 by Urban Larsson, Larsson, Urban, Johan Wästlund +1 · 1 voice
Computer Science · Mathematics · Psychology · Social Sciences · #91A46 #Artificial Intelligence in Games #Combinatorics (math.CO) #Digital Games and Media #FOS: Mathematics #Gambling Behavior and Treatments #math.CO #msc:91A46
paper · pdf · doi:10.48550/arxiv.1703.01624
22 pages, 13 figures
arxiv created 2017/03/05 · openalex publication_date 2017/03/05 · arxiv published 2017/03/05 · arxiv updated 2017/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Bidding chess is a chess variant where instead of alternating play, players bid for the opportunity to move. Generalizing a known result on so-called Richman games, we show that for a natural class of games including bidding chess, each position can be assigned rational upper and lower values corresponding to the limit proportion of money that Black (say) needs in order to force a win and to avoid losing, respectively. We have computed these values for all three-piece endgames, and in all cases, the upper and lower values coincide. Already with three pieces, the game is quite complex, and the values have denominators of up to 138 digits.