# Imperfect-information games

In imperfect-information games with ordered state spaces, cumulative regrets are no longer stored cell by cell for every information set; they are transformed into Haar wavelet coefficients and only the largest are kept. Tabular CFR+ previously grew memory linearly with the game tree under fine discretization, while Deep CFR traded memory for neural inference latency. On Deep-Stack Kuhn poker, growing the state count from one thousand to ten million raised memory only from 0.6 MB to 2.1 MB, a compression ratio above 99.9%; on Flop Hold'em, reaching comparable exploitability took about one-sixth the wall-clock time of Deep CFR.

In imperfect-information games with ordered state spaces, cumulative regrets are no longer stored cell by cell for every information set; they are transformed into Haar wavelet coefficients and only the largest are kept. Tabular CFR+ previously grew memory linearly with the game tree under fine discretization, while Deep CFR traded memory for neural inference latency. On Deep-Stack Kuhn poker, growing the state count from one thousand to ten million raised memory only from 0.6 MB to 2.1 MB, a compression ratio above 99.9%; on Flop Hold'em, reaching comparable exploitability took about one-sixth the wall-clock time of Deep CFR.