> But I'm saying that a mistake-free strategy cannot be found without some kind of mathematical breakthrough.
Is this even possible in a game of imperfect information?
Is this even possible in a game of imperfect information?
Starting out you have 2 cards and you know your opponent has one of 2450 possible combinations of cards.
You know exactly how your 2 cards stack up in chances of winning against those 2450 combinations, and you know how much money is on the table initially. Each time an opponent has an action he can take one of two or three actions (call, raise or fold) - your job is to calculate a strategy that makes either of those decisions have the same expected value for your opponent. That is doable, but quite complex, because it requires you to consider not only what your opponent has, but also what possible hands you could have based on your previous actions.
The complexity is obviously enormous (hence why it hasnt been computed yet) but it is not impossible to compute by any definition.
http://www.econ.ohio-state.edu/jpeck/gametheory/gameL8.pdf
http://robotics.stanford.edu/~koller/Papers/Koller+Pfeffer:I...
It's a problem that is incredibly challenging.