In the paper for the Poker AI, Libratus, the following is said:

The last two betting rounds, which are exponentially larger, are more coarsely abstracted. The 55 million different hand possibilities on the third round are grouped into 2.5 million buckets, and the 2.4 billion different possibilities on the fourth round are grouped into 1.25 million buckets.

I don't understand how the 55 million and the 2.4 billion hand possibilities in the third and fourth round are calculated. This seems like it would be obvious, but the calculations I'm doing give me different numbers, and I'm unsure what I'm doing wrong. I also know very little about Poker, so it's very possible I'm missing something.

Any help would be appreciated.

  • One factor is whether "the number of hands" is the number of possible hands a single person can have, or whether it's the number of possible overall board states (that is, taking into account every player's hand). If the latter, we would have to know the number of players. Aug 26, 2020 at 4:45

1 Answer 1


An explanation of how these numbers were derived is available in Johanson, Michael. (2013). Measuring the Size of Large No-Limit Poker Games.

Essentially those are the number of card combinations from one player’s point of view in a heads-up limit Texas hold’em game after merging strategically identical combinations.

How to count different card combinations with isomorphism? over on the Mathematics stack has more information on the combinatorics used to losslessly merge isomorphic card combinations.


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