Poker-AI.org

Say you have an EQ with a mixed strategy (typical of those created with CFRM). Has anybody tried, during live play, using a purification threshold as a means of adaptation/exploitation? For example, you would take the winnings/losses after a hand is played, then either try to increase the probabilities for the actions taken (or reduce them) by raising/lowering the purity threshold for a given section of the game. How those sections are defined and how the thresholds are updated would, of course, be the subject of experimentation.

Some results. 25bb stack level, global threshold adjustment versus a static player, starting at 5% purification. The min/max purification levels were 1%/100%, adjustments were made like:
threshold += threshold * inc

Average (optimum) is probably around 40%, which is about what I expected. A lower delta (increment percentage) would probably have shown a more stable optimum threshold. I don't have a player that can exploit overly predictable strategies (i.e. very pure strategies), so I'm not sure how to show it decreasing it's threshold. It should, though, in theory, against a player with that capability.

The increment sign (+/-) was decided by Zed * Utility of the deviated threshold levels.



Next: somehow model a dynamic threshold based on game state.

How is this different from just mixing in a pure strategy?

What do you mean by 'mixing in'?

30% pure = play pure strategy 30% of the time and play NE 70% of the time

I don't know if the scenario you describe would be exactly the same, but yes, a mix of the pure strategies could be the same as playing a mixed strategy. A completely pure strategy would exclude all but one action, while a completely un-purified strategy might play all available actions. Something in the middle could/would play fewer than all actions, but in the scenario you describe 70% of the time it would be playing all actions if that were the default EQ. That's not really the point of this post, though.

What I'm showing here is that the "amount" of purity can be adapted in real-time to improve equity versus a given opponent. For example, an opponent that plays a very static strategy (like another EQ), it would likely be better to play a more pure strategy. While an exploitative opponent (like most humans), it would be better to play a more defensive (less pure) strategy. You can decide that level by sampling.