The independent chip model (ICM) forms a cornerstone of all modern poker tournament strategy. However, despite its prominence, the ICM's performance in the real world has not been sufficiently scrutinized, especially at a large scale. In this paper, we introduce our new dataset of poker tournaments, consisting of results of over ten thousand events. Then, using this dataset, we perform two experiments as part of a large-scale empirical validation of the ICM. First, we verify that the ICM performs more accurately than a baseline we propose. Second, we obtain empirical evidence of the ICM underestimating the performances of players with larger stacks while overestimating those who are short-stacked. Our contributions may be useful to future researchers developing new algorithms for estimating a player's value in poker tournaments.
This paper introduces the Poker Hand History (PHH) file format, designed to standardize the recording of poker hands across different game variants. Despite poker's widespread popularity in the mainstream culture as a mind sport and its prominence in the field of artificial intelligence (AI) research as a benchmark for imperfect information AI agents, it lacks a consistent format that humans can use to document poker hands across different variants that can also easily be parsed by machines. To address this gap in the literature, we propose the PHH format which provides a concise human-readable machine-friendly representation of hand history that comprehensively captures various details of the hand, ranging from initial game parameters and actions to contextual parameters including but not limited to the venue, players, and time control information. In the supplementary, we provide 10,088 hands covering 11 different variants in the PHH format. The latest standard is available on GitHub: https://github.com/uoftcprg/phh-std
PokerKit is an open-source Python library designed to overcome the restrictions of existing poker game simulation and hand evaluation tools, which typically support only a handful of poker variants and lack flexibility in game state control. In contrast, PokerKit significantly expands this scope by supporting an extensive array of poker variants and it provides a flexible architecture for users to define their custom games. This paper details the design and implementation of PokerKit, including its intuitive programmatic API, multi-variant game support, and a unified hand evaluation suite across different hand types. The flexibility of PokerKit allows for applications in diverse areas, such as poker AI development, tool creation, and online poker casino implementation. PokerKit's reliability has been established through static type checking, extensive doctests, and unit tests, achieving 99% code coverage. The introduction of PokerKit represents a significant contribution to the field of computer poker, fostering future research and advanced AI development for a wide variety of poker games. The source code is available at https://github.com/uoftcprg/pokerkit