Research Article

Superhuman AI for heads-up no-limit poker: Libratus beats top professionals

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Science  26 Jan 2018:
Vol. 359, Issue 6374, pp. 418-424
DOI: 10.1126/science.aao1733
  • Fig. 1 Subgame solving.

    (Top) A subgame (red) is reached during play. Blue and red indicate the blueprint strategy. The white path indicates the action sequence before the reached subgame. (Middle) A more-detailed strategy for that subgame is determined by solving an augmented subgame in which, on each iteration, the opponent is dealt a random poker hand and given the choice of taking the expected value of the old abstraction (red) or of playing in the new, finer-grained abstraction (green), where the strategy for both players can change. This forces Libratus to make the finer-grained strategy at least as good as that in the original abstraction against every opponent poker hand. (Bottom) The new strategy is substituted in place of the old one.

  • Fig. 2 A visualization of nested subgame solving.

    Every time a subgame is reached during play, a more detailed abstraction is constructed and solved just for that subgame while fitting its solution within the overarching blueprint strategy.

  • Fig. 3 Libratus performance against top humans.

    Shown are the results of the 2017 Brains vs. Artificial Intelligence: Upping the Ante competition. The 95% confidence intervals (if the games are treated as independent and identically distributed) are shown as dotted lines.

  • Table 1 Exploitability of subgame-solving techniques on smaller poker variants.

    Shown is the comparison in exploitability of safe subgame-solving and unsafe subgame-solving techniques to no subgame-solving techniques for three medium-sized poker variants. Exploitability measures performance against a worst-case adversary.

    Subgame-solving techniqueSmall two-round hold’em (mbb/game)Large two-round hold’em (mbb/game)Three-round hold’em (mbb/game)
    No subgame solving91.341.3346
    Unsafe subgame solving5.5139779.3
    Safe subgame solving22.69.8472.6
  • Table 2 Exploitability of nested subgame solving.

    Shown is the comparison to no nested subgame solving (which instead uses the leading action translation technique) in a small poker variant.

    Nested subgame-solving approachExploitability (mbb/game)
    No nested subgame solving1465
    Nested unsafe subgame solving148
    Nested safe subgame solving119
  • Table 3 Head-to-head performance of Libratus.

    Shown are results for the Libratus blueprint strategy as well as forms of nested subgame solving against Baby Tartanian8 in HUNL.

    Version of LibratusPerformance against Baby Tartanian8 (mbb/game)
    Blueprint–8 ± 15
    Blueprint with postprocessing18 ± 21
    On-tree nested subgame solving59 ± 28
    Full nested subgame solving63 ± 28

Supplementary Materials

  • Superhuman AI for heads-up no-limit poker: Libratus beats top professionals

    Noam Brown and Tuomas Sandholm

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Supplementary Text
    • Figs. S1 and S2
    • Table S1
    • References

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