Extensive Game and Basics for CFR Minimization

Important Definitions

​ function mapping each action profile to a vector of utilities for each player

​ a strategy profile which mapping information set and actions' probabilities for player

​ reach probability of game history with strategy profile

​ probability of reaching information set through all possible game histories in

After all things above, we can get these:

We can define the at nonterminal history as:

The of not taking action at history is defined as:

The of not taking action at information set is then:

Let refer to the regret whe players use of not taking action at information set belonging to player . The is defined as:

Then we can use regret matching to get new strategy:

Derivatives