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> But we can compute the optimal strategy for an abstract version of poker that, for example, during pre-flop betting treats pairs of aces the same way as pairs
by philh 14y ago
> But we can compute the optimal strategy for an abstract version of poker that, for example, during pre-flop betting treats pairs of aces the same way as pairs of kings.
Not a big deal, but the wording of this seems off. It doesn't sound like you're computing the optimal strategy for poker-prime, where poker-prime has the property that in pre-flop betting (but nowhere else?) pocket aces are no more valuable than pocket kings.
Rather it sounds like you're computing a sub-optimal strategy for poker, by taking an optimal strategy and making it computationally simpler at the expense of some correctness.
- querulous 14y agoIt's still optimal because your preflop play with KK is going to be exactly the same as with AA. Similarly, you are going to play 9s8c exactly the same as 9h8d.
- andyakb 14y agothis is not true. suit simplifications can be made without any loss to the value of the solution, but saying AA=KK is not a lossless simplification
- querulous 14y agoEV is different, but optimal course of action at each branching point is identical
- andyakb 14y agoYou have no way of knowing this. If the EV is different, how can you say with any certainty that the action at each branching point is identical? What if there is an ace or a king on the board? These hands are very similar and likely have similar strategies, but they are absolutely not the same and any strategy that treats them that way is not optimal.