Runout clustering

By simplifying your strategy, you can reduce errors and increase your win rate. Runout clustering is a way to simplify the strategy by reducing the number of different strategies in the game plan. In a single spot, there would be 2,352 different turn and river strategies needed for each strategy node, which would result in more than 16 million different strategies. However, it's important to keep the game plan as simple as possible without compromising the win rate.

The simplification process compares each runout to every other runout and defines a strategy based on possible frequencies weighted by a parameter representing the relative value between different lines. The value of this parameter depends on the available lines and the significance of differences between them. The result is a quantity called delta, which measures the strategy difference between two different runouts.

Delta includes all runouts for all possible lines for all involved players and is used through a two-dimensional clustering method. The goal is to find the minimum number of different clusters without losing range-EV for any player. Delta is interpreted as the "strategy failure parameter," and if delta equals zero for eight different runouts, only one strategy is needed for these runouts.

The outcome of runout clustering is that the forty-nine turn runouts (forty-eight for the river) become "grouped" or "clustered." Each cluster has a representation card with the smallest strategy difference between all cards in the cluster, resulting in each player having their own Runout-Clustering, which may differ significantly from other players in the same situation.

Here are three examples with different levels of simplification:

High-Level Simplification:

Game type:      Cash
Stack size:     100bb
Positions:      MP vs. BU
Preflop:        3Bet
Flop:           As 5s 4s
Flop actions:   MP (Check) | BU (Bet 40%) | MP (Call)

Strategy for BU simplifies from 49 to 2 different strategies on the turn without any EV loss! (~96% simplified)

Medium-Level Simplification:

Game type:      MTT
Stack size:     25bb
Positions:      BU vs. BB
Preflop:        SRP
Flop:           Ks 9d 8d
Flop actions:   BB (Check) | BU (Bet 25%) | BB (Call)
Turn card:      5h
Turn actions:   BB (Check) | BU (Check)

Strategy for BU simplifies from 49 to 12 different strategies on the river (~70% simplified)

Low-Level Simplification:

Game type:      Cash
Stack size:     100bb
Positions:      BU vs. BB
Preflop:        2Bet
Flop:           As Td 8d
Flop actions:   BB (Check) | BU (Check)

Strategy for BB simplifies from 49 to 21 strategies on the turn (57% simplified)

When analyzing the Runout-Clustering feature, it was discovered that two different cards within a cluster could have the same strategy, even if they have a significant difference in their Runout-EVs. This suggests that there are multiple reasons for having a particular strategy.

It's worth noting that the Runout-Clustering calculation only needs to be performed once for each user as the results are saved on our backend. By understanding the different cluster structures and analyzing them, you can gain a new perspective on poker.