The Perfect Strategy

[tommo]

I am in a disagreement with a friend of mine right now. He believes that it is possible to play a perfect rule based game and beat no limit.

I think it may be possible to do this at small stakes but that at higher stakes it is necessary to profile your opponents. Basically I believe in 2nd and 3rd level thinking as it is usually referred to on these forums. What do you guys think?

[CallMeIshmael]

[ QUOTE ]
He believes that it is possible to play a perfect rule based game and beat no limit.

[/ QUOTE ]

The correct answer is:

There exists a rule based strategy (that is, you can define this strategy and not take into account any reads) that would do no worse than tie all oppoenents, and would almost certainly be a winning strategy, at all levels of play.

Using reads, however, allows you to improve on this strategy.

[tommo]

[ QUOTE ]
[ QUOTE ]
He believes that it is possible to play a perfect rule based game and beat no limit.

[/ QUOTE ]

The correct answer is:

There exists a rule based strategy (that is, you can define this strategy and not take into account any reads) that would do no worse than tie all oppoenents, and would almost certainly be a winning strategy, at all levels of play.

Using reads, however, allows you to improve on this strategy.

[/ QUOTE ]

how do you know that the rule based strategy exists? It seems to me that it is too often the case that a move will be +ev against one player and -ev against a different player.

[CallMeIshmael]

[ QUOTE ]
how do you know that the rule based strategy exists? It seems to me that it is too often the case that a move will be +ev against one player and -ev against a different player.

[/ QUOTE ]

There exists a strategy that is part of a nash equilibrium. This strategy necessarily exists, but would take probably millions of years to find given current computing limitations.

Let's say all other 8 players knew this exact nash equilibrium strategy, and knew you were the one following it to the exact letter. Could they exploit that? Assume they aren't colluding of course. I guess not--by definition of the formula.

I guess we're actually pretty close to this w/Heads Up theory when the BB/stack ratio gets large. If your opponent goes all in almost every time, basically the best you can do is the same thing which makes it a coin flip. Luckily just increasing to 3 players sends the strategy into exponentially more complication. 9 players? Fuggetaboutit. Instinct and verve.

So does this mean there's a nash equilibrium to Mortal Combat? (assuming you both lay Liu Kang of course) What about Madden 05?

[tommo]

[ QUOTE ]
Let's say all other 8 players knew this exact nash equilibrium strategy, and knew you were the one following it to the exact letter. Could they exploit that? Assume they aren't colluding of course. I guess not--by definition of the formula.

I guess we're actually pretty close to this w/Heads Up theory when the BB/stack ratio gets large. If your opponent goes all in almost every time, basically the best you can do is the same thing which makes it a coin flip. Luckily just increasing to 3 players sends the strategy into exponentially more complication. 9 players? Fuggetaboutit. Instinct and verve.

So does this mean there's a nash equilibrium to Mortal Combat? (assuming you both lay Liu Kang of course) What about Madden 05?

[/ QUOTE ]

very interesting. I'm reading about it (Nash Equilibrium) right now. However, thinking about your heads up example where you're opponent goes all in on every hand, you can do a lot better than heads up. If the stacks are deep enough a much more optimal strategy would be to wait for AA or KK. and a decent strategy would be to wait for any hand with a probability of winning greater than 50%. This of course depends on how deep the stacks are.

[ QUOTE ]
There exists a rule based strategy...

[/ QUOTE ]

I hate to nitpick, and correct me if I'm wrong, but I think OP was talking about a static rule-based strategy. That's what most people are referring to when they talk about rule-based strategy.

I suppose if you "roll out" by brute force every possible playing style and have an if-then clause to every situation, you could have a rule-based strategy... But otherwise, it's a decision-based strategy using mostly heuristics.

[tommo]

[ QUOTE ]
[ QUOTE ]
There exists a rule based strategy...

[/ QUOTE ]

I hate to nitpick, and correct me if I'm wrong, but I think OP was talking about a static rule-based strategy. That's what most people are referring to when they talk about rule-based strategy.

I suppose if you "roll out" by brute force every possible playing style and have an if-then clause to every situation, you could have a rule-based strategy... But otherwise, it's a decision-based strategy using mostly heuristics.

[/ QUOTE ]

Yep you're right. However, I've been reading that Nash Equilibrium business and it seems like there actually should be a static rule based strategy that would be impossible to beat. Although it wouldn't be optimum against most players.

[ QUOTE ]
it seems like there actually should be a static rule based strategy that would be impossible to beat. Although it wouldn't be optimum against most players.

[/ QUOTE ]

Assuming this is true, then to me the interesting part is that as you pursue this strategy, you basically push the game towards a coin flip. I just posted this over on the sleepy poker theory board. I'm still trying to wrap my head around why this doesn't feel right. Like a brain itch I can't scratch.

[b33nz]

No. It's not possible.