blitzing on third and long and the problem with poker forum advice

[pete fabrizio]

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TSo this bluffing into a dry side pot thing isn't really a very good example, because it's not an example of an "optimal" or "equilibrium" solution - it's an example of perturbing the (three-player Nash) equilibrium solution by threatening to transfer equity from one guy to the other in order to make the threatened guy pay you.

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So basically this "isn't really a very good example" because it doesn't fit into the narrowly contrived parameters that make the math work out all pretty.

[Troll_Inc]

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Zero-sum two-player games are a lot different than multiplayer games. Many of the terms and concepts that we define/explain in our book apply ONLY to ZSTPG, and not to other situations, such as multiplayer, in a technical sense, although they are still useful for understanding various situations.


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It's a shame that there isn't more practical game theory discussion for poker situations. There really isn't much useful for me in this thread. It's kind of like a big game theory circle jerk.

TOP really focuses mostly on draw poker with a short holdem example.

I really haven't thought this through, but it seems that overall Pot Limit Omaha has many more difficult situations than even NLHE when it comes to the play of hands. This idea is expressed well by Ciaffone's Either-Or scenario, where a player either has the stone cold nuts or the 35th best hand.

Working backwards, there seem to be many many areas of PLO that would benefit from a mixed strategy.

Starting hands When to raise/when to call from what position.

Draws vs made hands When to raise/when to play passively.

Vs. different opponents Every mixed strategy would have to be changed based on a specific target or different tables as a whole.

[pete fabrizio]

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I would like to see a better example (doesn't have to be a poker example, a contrived game might be even better). I'm not 100% sure if this is possible, a year ago I could have worked it out.

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So I thought about this a little bit, and it seems pretty easy to come up with contrived games where this is possible. Imagine the classic two player game where player 1 chooses a or b, and player 2 chooses x or y. Now just use payout structures:

a, x: 5, -100
b, x: 10, 0
a, y: 10, -10
b, y: 20, -10

For player 1, choice b strictly dominates choice a (in fact, there's an equilibrium at b,x). However, player 1 has an interest in having player 2 choose strategy y instead of strategy x. Therefore, the correct strategy for player 1 is to choose "a" just often enough to force player 2 to always choose "y", which should be just over 10% of the time. This despite the fact that the e.v. for "a" will always be lower.

[RoundTower]

OK I've thought quite a bit about this (the bluffing into a dry side pot question) and done a little maths.

I'm pretty sure I have a proof that no mixed strategy is better than a pure strategy of betting when you have the straight and checking when you have no pair. However this is based on certain "standard" game theory assumptions: that he calls you a predetermined amount of the time, that he is rational and that he assumes you are rational. Also in this context I consider a mixed strategy is a strategy where you decide to bet P of the time, check 1-P, and decide randomly.

However if you could change some of those assumptions the proof breaks down and you may be able to make a case for betting. Specifically, if you can make your opponent think you are irrational, you may be able to make him call you more often without ever having to bluff. A naive opponent might consider you were irrational after seeing you bluff into the dry side pot just once.

In poker this is usually referred to as "advertising". It is important to realise that this is not the same as adopting a true mixed strategy.

Finally a similar example from the world of SNGs. You are on the bubble (of course) in the big blind in a typical SNG paying 50-30-20. You and the SB have very big stacks, the others are more than likely going bust in the next hand or two. Folded to him. He should push any 2 and you should fold any 2 (or close) assuming you are both rational. However if you can somehow convince him that you play irrationally and call too much in this spot, he should fold more often and the spot becomes more profitable for you. But there is no profitable way to expand your calling range in this spot, the most you can do is convince him that it has been expanded.

[RoundTower]

[ QUOTE ]
[ QUOTE ]
I would like to see a better example (doesn't have to be a poker example, a contrived game might be even better). I'm not 100% sure if this is possible, a year ago I could have worked it out.

[/ QUOTE ]

So I thought about this a little bit, and it seems pretty easy to come up with contrived games where this is possible. Imagine the classic two player game where player 1 chooses a or b, and player 2 chooses x or y. Now just use payout structures:

a, x: 5, -100
b, x: 10, 0
a, y: 10, -10
b, y: 20, -10

For player 1, choice b strictly dominates choice a (in fact, there's an equilibrium at b,x). However, player 1 has an interest in having player 2 choose strategy y instead of strategy x. Therefore, the correct strategy for player 1 is to choose "a" just often enough to force player 2 to always choose "y", which should be just over 10% of the time. This despite the fact that the e.v. for "a" will always be lower.

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Correct (so long as player 2 realises that player 1 is choosing A 10%+ of the time and will not change).

However I still think this doesn't apply in the poker situation, because the amount you lose when you bluff and get called is the same as the amount you win when you value bet and get called. I'm less sure now though.

[grizy]

[ QUOTE ]

I'm pretty sure I have a proof that no mixed strategy is better than a pure strategy of betting when you have the straight and checking when you have no pair. However this is based on certain "standard" game theory assumptions: that he calls you a predetermined amount of the time, that he is rational and that he assumes you are rational.

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The assumption that's broken in Pete's case and my simple game is that your opponent does not have a predetermined mixed strategy; his strategy (his probabilities) are some function of yours (aka he is observant and will adjust). Once your opponent's actions are some function of yours (aka you're the superior player that dictatesthe flow of the game) it becomes possible for you to play a "maximally" exploitative game as long as you know how your opponent will change his strategy. Pete's example is especially poignant because your opponent is giving up a major main pot so if he believes there is any chance at all you're betting without the goods, he would call. However, if you never bet without the straight, after some time, he will never call you, despite overwhelming pot odds. (this is actually a very very relevant concept in limit omaha I imagine)

[grizy]

[ QUOTE ]
[ QUOTE ]
TSo this bluffing into a dry side pot thing isn't really a very good example, because it's not an example of an "optimal" or "equilibrium" solution - it's an example of perturbing the (three-player Nash) equilibrium solution by threatening to transfer equity from one guy to the other in order to make the threatened guy pay you.

[/ QUOTE ]

So basically this "isn't really a very good example" because it doesn't fit into the narrowly contrived parameters that make the math work out all pretty.

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Right, even though poker is usually a zero-sum game, Pete has managed to create a non-zero sum situation for the only two players with choices to make, shouldn't we explore it?

[pete fabrizio]

[ QUOTE ]
[ QUOTE ]

Zero-sum two-player games are a lot different than multiplayer games. Many of the terms and concepts that we define/explain in our book apply ONLY to ZSTPG, and not to other situations, such as multiplayer, in a technical sense, although they are still useful for understanding various situations.


[/ QUOTE ]

It's a shame that there isn't more practical game theory discussion for poker situations. There really isn't much useful for me in this thread. It's kind of like a big game theory circle jerk.


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What I want to know is, where do they spread pot-limit ZSTPG against optimal opponents? I want in!

[grizy]

You can find them on play money tables when there is no rake.

[Jerrod Ankenman]

[ QUOTE ]
[ QUOTE ]
TSo this bluffing into a dry side pot thing isn't really a very good example, because it's not an example of an "optimal" or "equilibrium" solution - it's an example of perturbing the (three-player Nash) equilibrium solution by threatening to transfer equity from one guy to the other in order to make the threatened guy pay you.

[/ QUOTE ]

So basically this "isn't really a very good example" because it doesn't fit into the narrowly contrived parameters that make the math work out all pretty.

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Well, yes, if you define "narrowly contrived parameters that make the math work out all pretty" as "parameters that describe a game that is at all similar to the one being discussed." Concepts that apply to zero-sum two-player games don't necessarily apply to two-player NON-zero-sum games, and so using the latter as an example to argue about the former is pretty much the definition of "a bad example."

Luckily for me, the "narrowly contrived parameters" are neither narrow nor particularly contrived, so they apply to a wide variety of situations that occur in practice.