Runouts clustering
As you may have read in the article about line-elimination, a simplified strategy implies less errors, which translates into an increase in your win rate. The runout clustering simplifies the strategy by reducing the number of different strategies you have in your gameplan.
Without any simplification, you would need to have 49 turn and 48 river strategies (49*48 = 2352) for each strategy node (an action taken by a player) in a single spot. The amount of strategy nodes depends on the boundary conditions which we determined in Stage 1.
On average, there are about 6900 strategy nodes for a 2-Bet spot. Implementing the 2352 different runouts shows that there are more than 16 million different strategies for a single 2-Bet spot.
In every single scenario, there is a possibility to make a mistake which reduces your win rate. This is why it is so essential to make the gameplan as simple as possible, but no simpler.
The simplification we performed was done by comparing every single runout to every other runout. For each runout, there exists a specific strategy called x.
The strategy is defined by the possible frequencies weighted by a parameter representing the relative value between different lines. The value of this parameter depends on which lines are available and how significant the differences between these lines are.
For example, an All-In frequency gap between two different runouts should be weighted higher than a frequency gap for a Check. This gives a new quantity, which we call δ. The quantity δ (Ac, Ks) measures the strategy difference for these two different runouts.
δ includes all runouts for all possible lines for all involved players. This quantity was used through a 2-dimensional clustering method, which has the goal of finding the minimum amount of different clusters with the condition of not losing Range-EV for any player.
Because δ is measuring the relative strategy difference, we interpret it as the "strategy failure parameter."
If, for example, δ goes to 0 for eight different runouts, than there is only one strategy which is needed for these eight runouts.
The result is that the 49 turn runouts (48 for the river) become "grouped" or "clustered." Each cluster has a representation card which has the smallest strategy difference between all cards of the cluster.
An interesting finding of this is that you can have the same strategy for two different cards of a cluster - even though they have a big difference in their Runout-EVs. This shows that there exists multiple, different reasons for having a particular strategy.
Learning what kind of clusters this happens on, and the analysis of these different cluster structures opens a new door to understanding poker.