Quote:
Originally Posted by punter11235
Yes although once you do that your solution is already quite worthless as the hands which played into that branch now are assigned somewhere else randomly (I think they go to the last action now but it's really not defined).
In general it's a better idea to build a new tree without that branch. I am not sure what you are trying to achieve, if you want to see how much worse choosing a different action is you can do that by looking at EV. Maybe try elaborating on a use case so I can try to help you.
What I would like to do is to see how a simplified strategy (removing some options) performs against a player who is unaware that I am not using them.
Let's say we 3B OOP and we hit a flop where we have a very high CB% using a small sizing (say, CB 85%). For such cases we can achieve almost the same EV (and CB unexploitably something like 95%) by check-folding our very worst hands and betting the rest. This is an attractive option because it's simplifies our flop strategy to two options (bet or c/f) and the simplification comes at very little theoretical cost.
If we put such a tree into Pio (removing our flop Check-Bet-Call and Check-Bet-Raise branches), Pio will of course bluff every time we check. I was curious how such a simplified strategy would perform against an unaware player who will play against our checking range as if we still are using the c/c and c/r options.
If he doesn't bluff every time we check, our weak checking range will get to realise some equity on future streets (stabbing options, spiking something) and make some money against an opponent who is unaware what we are doing and believing our flop checking range is proper.
On the flop it's easy, we can compute the equilibrium, save Pio's ranges, remove our c/c and c/r options, recalculate, and insert/lock Pio's flop equilibrium ranges vs our bets and checks for the full solution into the simplified solution. But I have no clue how to continue that experiment on the turn. Let's say we do these things, and look at the branch where Pio checks back it's full-game-equilibrium checking range on the flop and we arrive at the turn with a handful of junk hands vs that range.
Am I right to assume that we should now be able to stab profitably at some turns with our junky range, if Pio was operating under the assumption that we had our optimal flop checking range? (which is much stronger than our actual range).
My idea (which might be a bad one) is that if we have Pio landing on the turn with it's full-game-equilibrium strategy for all turn cards, we could figure out the turn cards where Pio would fold often enough (believing our turn range was our full-game-equilibrium range) to allow profitable junk stabs. Then we could cherry-pick those turns for exploitative +EV bluffing opportunities.
Does this make sense? Not claiming this is particularly useful study project (might be useful in an anonymous pool where the opposition would not be able to catch on), but I got curious about exploring it. :-)