MDA AI

The number of possible poker boards is enormous. There are 1,755 possible flops, and 85,995 possible boards when turns are included.

It is not realistic to collect a statistically sufficient amount of real hand data for every one of those boards.

Because of this, conventional MDA could only analyze abstract board categories, such as A-high boards. It could not show tendencies for each exact board.

GTO, on the other hand, is normally calculated for each exact board. In other words, GTO works at a fine board-by-board scale.

As a result, MDA, which only works at an abstracted scale, and GTO, which works board by board, could not be compared on the same scale. Comparing them properly would require re-aggregating MDA for each exact board as well, but as described above, that was not possible.

To solve this problem, we developed AI that predicts player-pool tendencies for each board. By estimating MDA tendencies at the board level, the AI makes it possible to handle MDA at the same scale as GTO.

The model input is the sequence of the play line up to the decision point being predicted. Here, play line means the flow of which player chose which action in which situation, from preflop up to that point.

The model output is an action probability distribution showing how likely the overall player pool is to choose each action in that spot. A probability distribution means the set of probabilities assigned to each action.

• When checking is available, the model outputs probabilities for check and each bet-size category.
• When facing a bet or raise, the model outputs probabilities for fold, call, and raise.

The core of this model uses a Transformer. A Transformer is one of the widely used mechanisms in modern AI, and it is also used in large language models such as ChatGPT.

In the same way that a language model predicts the next word from context, this model reads context such as the game flow and board state, then predicts how often the overall player pool chooses each action in that spot.

A Transformer's strength is that it can consider multiple pieces of information at the same time and automatically judge what matters in the current spot. This makes it well suited to decision-making situations like poker, where many factors interact.

MDA does not have one dataset that can be called the single correct answer. For that reason, we use averages from a sufficient amount of real data as the benchmark. When many actions from similar situations are collected, their average becomes a reliable comparison target.

This model has two goals. It should preserve the overall tendencies while making more accurate predictions in detailed situations. Specifically, the goals are as follows.

• For large groups, the model's average predictions should match the real-data averages.
• For individual spots, the model should predict more accurately than a simple average.

The test used about 8.5 million records that were not used for training. This confirms that the model generalizes to unseen data rather than simply memorizing the training data.

We split the test data into groups, or nodes, by conditions such as situation, pot type, player positions, and player type. For each node, we compared the average action probabilities predicted by the model with the actual action frequencies in the real data. The results showed that, in nodes with enough data, the predictions almost matched the real-data action frequencies, and large deviations appeared only in rare situations with few data points. The specific numbers are as follows.

• The average deviation across all nodes, weighted by sample count, was no more than 0.2 percentage points.
• The node with the largest deviation was about 12.3 percentage points, and it was a rare situation with 136 data points.

The node averages used in Test 1 are accurate as overall tendencies, but they are limited when used directly for individual spots. For that reason, we compared predictions made by using node averages directly with predictions made by the AI model.

Log loss is a metric that checks how high a probability the model assigned to the action that was actually chosen. A lower value means the model assigned a high probability to the correct result with more confidence.

Brier score is a metric that checks the size of the gap between the probability distribution predicted by the model and the actual result. Here as well, a lower value means the prediction is more accurate.

On both metrics, the AI model was more accurate than using node averages directly. This confirms that accuracy improved without depending on only one specific measurement. The specific numbers are as follows.

• Log loss was 0.8623 for the AI model, compared with 0.9278 for node averages, a 7.1% improvement.
• Brier score was 0.4959 for the AI model, compared with 0.5306 for node averages, a 6.5% improvement.