unexploitable push/fold strategy

If one were to play a super turbo SNG and only push or fold and push or fold on the basis of a *perfect* Nash equilibrium push fold strategy then,

1. one would be playing an unexploitable strategy (which may or may not be optimal)

2. the strategy is only optimal against an opponent who is also playing the same strategy and is suboptimal but nonetheless still profitable against a different strategy.

3. If the opponent deviates from an unexploitable strategy then you profit and if he plays the same unexploitable strategy then you both break even excluding rake -> you both just lose the rake as the number of games tends to infinity.



Are these three points correct?

Does playing an unexploitable HU strategy in Super Turbo HUSNGs mean that as the number of games tends to infinity then you will at worst only lose rake and at best turn a profit? If the average HUSNG player does not play an unexploitable strategy then surely you would stand to profit from playing one yourself.



Thanks,
this is just a random question that popped into my head as I don't play HU games but I thought I would ask some peeps to see if what I was thinking was at all correct.

the biggest problem i have with this is that i don't believe that a push/fold strategy is unexploitable.

Play enough hands vs VillainX and he works out what % of hands you are pushing, then calls only with better hands. Thus you are exploited because you are too consistent with your strategy.

Yes, but. Blinds. You neglect to include these in your calculations. An unexploitable strategy is such that your opponent cannot pick a % of hands that will be profitable against you in the long run.

An unexploitable strategy changes with effective stack sizes, blind increases etc... The point is if you are push folding the correct % of hands then the most profitable way an opponent can play is by playing the exact same strategy and any other strategy will not be as optimal as this.


So, if your opponent is push folding in an unexploitable manner then your optimal strategy is to play his strategy. And, I think this would make you both break even in the long run...



The point you raise seems intuitive -> If we have deep enough stacks then push/fold is indeed ridiculous as the only cards we could ever play would be aces essentially as we would only ever be called by aces (if the stacks were large enough this would make sense as stolen blinds and times you were ahead would not make up for the times you got called and were behind) so a non push/fold strategy makes sense although it would be necessarily exploitable.

Anyway, your % of hands that you push/call would increase as effective stacks decreased and I think this strategy only works well with sub 20BB effective stacks which is pretty much a Super Turbo from the get go. I wrote this fairly quick so it may not make any sense but I will look at it laterz.

Ciao

theory makes sense, but i think its a bit like its been concluded upon in a vacuum. How often do you expect to see appropriate stack sizes for this to make sense? If both stacks are short this will rapidly result in either the end of the tourney or one very small vs one average stack.

The push/fold situation occurs in all tourneys as blinds increase and players are forced to bet or bleed their whole stack in blinds. Which often leads to an ever increasing % of hands that are pushed. If there are big stacks around you start seeing players call with worse hands just because its so cheap to bust the villain. I think for your theory to hold true you need to have a short stacked cash game, like a max 30bb buyin.. there's certainly not going to be alot of those around.

Optimal strategy vs shortstack push folder is likely to be deepstack, fold/call. And if the deepstack makes that particular adjustment then it would be in the shortstacks best interest to not push, but rather just make a standard raise for 3-4bb. No point risking the whole stack if your just going to face a hand that either folds or is willing to go all in. Thus begins the never ending spiral of adjustments in heads up poker that makes it a game where no optimal strategy exists based on cards. Only the idea that you should remain aggressive and correctly adjust to your opponents tendencies, whatever stack sizes are involved.

Quote:

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Originally Posted by scott_owen

Optimal strategy vs shortstack push folder is likely to be deepstack, fold/call. And if the deepstack makes that particular adjustment then it would be in the shortstacks best interest to not push, but rather just make a standard raise for 3-4bb. No point risking the whole stack if your just going to face a hand that either folds or is willing to go all in. .

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This is exactly the type of situation where push/fold makes sense. raising 3-4bb into the big stack when you have 20bb left is going to get you in a lot of trouble when he goes over the top of you (gap concept). You want to push a lot of hands and hopefully pick up blinds and antes. If opponent calls too wide then you are likely to double up and if opponent is too tight then you are going to steal a lot of blinds and antes. Unexploitable push fold strategies can be calculated for short effective stack sizes <20BB so that if your opponent calls a with range of hands that is not unexploitable then you are exploiting him.

In the situation you describe both players are effectively short stacks. The big stack plays the right strategy of call/fold and presumably push fold as well, but the shorty raising 3-4bb would not work out well.

This situation would arise in a super turbo HUSNG I think and yep you're right that for moderate to deep stack sizes it is irrelevant but when you are forced to play as a short stack or finish off a short stack then I think it is essential to know about unexploitable strategies.

Quote:

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Originally Posted by frjd2

This is exactly the type of situation where push/fold makes sense. raising 3-4bb into the big stack when you have 20bb left is going to get you in a lot of trouble when he goes over the top of you (gap concept).

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yes ofcourse..

The idea that 3-4bb is better is entirely dependent on the big stack adusting and playing only a tighter range.

its difficult to balance because HU aggression requires you to raise something like 80-90% of buttons.. and if your shoving that many hands as a shortstack youll go bust pretty quick.

By unexploitable, you mean the same as GTO? this is "optimal" against players who are better than you, as they can't exploit you, just as you can't exploit them...but if you want to profit you need to play in a way which could be "exploitable" in order to "exploit" weaker players.