Unsound Search with Policy and Value Networks in Legends of Code and Magic

Abstract

Decision-time search in perfect and imperfect information games with enumerable belief states are effective methods for game AI. Collectible card games are imperfect information games with large belief states. Legends of Code and Magic is a collectible card game competition where the belief states are $2^{101}$. The Legends of Code and Magic (LoCM) champion, ByteRL, plays with no search. Other works claim sound enumeration-based search is unusable in the genre due to the number of belief states. We measured three previously defined properties that predict where theoretically unsound perfect information Monte Carlo's defects are cheap and found LoCM sits in the favorable region. Starting with imitation learning of the runner-up policy, NeteaseOPD, we created a policy and value feed-forward network. Our agent searches over worlds sampled from a prior over the opponent's deck built from the runner-up's drafts. Using our strictest configuration in the battle phase we beat ByteRL with a win percentage of 51.35% 95% CI [50.37, 52.33], over 10,000 pre-registered games using the LoCM official referee and time limit. Search is not a minor factor on the matchup between our agent and ByteRL. Without search this agent scores 26.8% and adding search adds +24.6 points. Unsound search in imperfect information games could be exploitable. We replicate a published best-response attack against ByteRL. We then apply the same attack protocol to two search configurations of our agent, and each one resists it better than ByteRL at every iteration. In LoCM unsound search gives us a stronger and more resilient agent.