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Originally Posted by Bill Haywood
^^^Thanks.
We are routinely admonished to play the range, not the individual hand. Do you have a more general explanation for this?
I wasn't clear. The solver maximizes the overall strategy EV, and each individual hand within that strategy, but that does not mean it is playing each hand as if it was the only poker hand you'll ever play (to quote amok).
For instance when a solver says we should check our entire range does it believe that is the best way to play each hand in that range? Yes, but that is conditional on maximizing the strategy EV. If your range consisted of just that one hand and you would never play another hand again it very well may decide that leading is the best strategy. If you change the range composition given to a solver the strategy will change.
I think it's helpful to understand how the algorithm actually works.
It starts by taking random action for a hand in a given scenario, working through the tree, and calculating the strategy EV of that decision. Then it looks at the alternative actions and calculates the strategy EV of those actions. These are the counterfactuals in counterfactual regret minimization (CFR). It then adjusts the weight for each action based on these strategy EV's and will lean towards the action with the highest strategy EV. At each point the opponent is doing the exact same thing.
In simple terms, the computer is trying to maximally exploit the opponent, who is then trying to counter-exploit. Eventually, things converge close to a GTO solution where neither player is being exploited.
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Originally Posted by amok
What happens if you play every individual hand as if it was the only poker hand you'll ever play?
Your opponents are (probably) stupid, but not that stupid.
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Example. We raise PF with a good hand. The flop is low. The solver-derived advice is to check our entire range. Why do we check even if we nailed the board? Isn't villain going to think we are bluffing high cards and may raise, allowing a 3! ? Or are we going for a check-raise?
Now, in the context of what I wrote above, you can begin to see why the solver is saying to check the range. Simply put it tried leading your hand and couldn't balance it properly so the opponent was able to exploit that lead bet by overfolding the flop to leads. The computer tried to add more leads and ended up getting exploited in a different way (raises / calls) and eventually the computer settled on maximum strategy EV of checking the entire range and to balance this by check raising a lot (approximately 10-15% of range depending on boards) and calling a lot. Since it is calling a lot it needs to have pretty strong hands in this calling range as well or else the turn strategy gets imbalanced.
It gets pretty complex, but this is what is meant when we say "bet your range".