4 ms·

Just a note, you don't have to mathematically solve a game in order to win it.

by pepve 13y ago

ianstallings 13y ago
I agree that it can win, but so can pros and they make mistakes everyday. But I'm saying that a mistake-free strategy cannot be found without some kind of mathematical breakthrough. Unlike say chess, where clear pathways to a checkmate can be calculated using mathematics, no matter how the opponent plays. It's impossible to do that, right now, using computers, when the opponents are human and unpredictable and don't always follow the optimum strategy. Also poker is an information-sparse environment where you can't always win with a certain strategy because you simply don't have enough information, such as the other player's hole cards.
- omni 13y ago
  > 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?
  - jib 13y ago
    Yes, because you know all possible states of the game. 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.
  - ianstallings 13y ago
    Not to my knowledge. Not with current computing power and software. That's why I think it would require a breakthrough in mathematics. It boggles my mind even thinking about how it could be tackled. I did find a few papers that dig into the topic: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.1824 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.1... http://www.econ.ohio-state.edu/jpeck/gametheory/gameL8.pdf http://www.econ.ohio-state.edu/jpeck/gametheory/gameL8.pdf http://robotics.stanford.edu/~koller/Papers/Koller+Pfeffer:IJCAI95.pdf http://robotics.stanford.edu/~koller/Papers/Koller+Pfeffer:I... It's a problem that is incredibly challenging.

Just a note, you don't have to mathematically solve a game in order to win it.

by pepve 13y ago

Just a note, you don't have to mathematically solve a game in order to win it.

I agree that it can win, but so can pros and they make mistakes everyday. But I'm saying that a mistake-free strategy cannot be found without some kind of mathematical breakthrough. Unlike say chess, where clear pathways to a checkmate can be calculated using mathematics, no matter how the opponent plays. It's impossible to do that, right now, using computers, when the opponents are human and unpredictable and don't always follow the optimum strategy. Also poker is an information-sparse environment where you can't always win with a certain strategy because you simply don't have enough information, such as the other player's hole cards.

omni 13y ago
> 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?
- jib 13y ago
  Yes, because you know all possible states of the game. 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.
- ianstallings 13y ago
  Not to my knowledge. Not with current computing power and software. That's why I think it would require a breakthrough in mathematics. It boggles my mind even thinking about how it could be tackled. I did find a few papers that dig into the topic: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.1824 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.1... http://www.econ.ohio-state.edu/jpeck/gametheory/gameL8.pdf http://www.econ.ohio-state.edu/jpeck/gametheory/gameL8.pdf http://robotics.stanford.edu/~koller/Papers/Koller+Pfeffer:IJCAI95.pdf http://robotics.stanford.edu/~koller/Papers/Koller+Pfeffer:I... It's a problem that is incredibly challenging.