Solving preflop strategies

When attempting to solve a poker game using a Game Theoretically Optimal (GTO) strategy, one must first establish the conditions under which the algorithms will be applied. The key factors to consider are: the number of players and their respective stack sizes, the initial ranges of hands they hold, the bet sizes available at each street, and the starting point for training (preflop, flop, turn, or river).

The computational demands of solving a game increase exponentially with a larger number of players, bigger starting stacks, multiple bet sizes (particularly smaller bets), and additional streets to be considered.

Traditionally, when solving complex GTO solutions for preflop strategies (to create starting hands chart), the strategies size was reduced by making concessions in the only elements that could be optimized: the cards in a player’s hand, achieved through range abstractions (also known as private buckets), grouping similar boards (or public buckets), and restricting players to use a single large bet size. The drawback of this approach is that it trades memory efficiency for accuracy, especially in later streets where the results may become less reliable.

Our solution

To address this memory issue, we train these large strategies with that kind of abstractions but we focus on the most frequent situations to provide them with optimal configurations, ensuring we maintain their accuracy. We enhance the solutions for the following scenarios:

• All single raised pots of 2 and 3 players

• All 3bet and Squeeze pots of 2 and 3 players

• All 4bet and cold 4bet pots of 2 players.

• All Small Blind vs Big Blind spots.

And What about limping?

In Omaha games without antes, GTO solutions typically include a minimal amount of limping as the initial action for all players in every position, except for the Small Blind vs Big Blind scenario where it is quite common.

However, since the percentage of the range used for limping is so small, it is more beneficial to construct the solution without the option to limp at all. In small-stakes games, it is common to find players who limp but their range tends to be unbalanced. Therefore, the solution we can provide for a “Raise over limper” situation may not be practical or useful in such cases.

So what’s the message I’m getting?

It means that you are seeing a branch in the browser that represents an scenario that occurs less than 1% of the time in real poker gameplay. Consequently, the GTO solution we present is based on training with abstractions and limited bet sizes. While the resulting strategy is accurate, there is room for improvement in terms of its precision.