The definition of unexploitable play in a HU game? - Heads Up SNG and Spin and Gos -- Two Plus Two Poker Forums

Two Plus Two Forums Poker Strategy No Limit Tournaments Heads Up SNG and Spin and Gos

The definition of unexploitable play in a HU game?

Post Reply Subscribe

...

06-17-2015 , 09:48 PM

nateofclubs

journeyman

Join Date: Mar 2013 Posts: 244

I'm finding a lot of conflicting information on this in the threads and on Google. Disregarding the effects of rake, does the hero playing unexploitably (when playing Nash) imply:

1) The villain's best way to minimize the hero's EV, assuming the hero will continue to play Nash, is by responding with his own equilibrium strategy.

Or does it mean:

2) The villain cannot choose a counter-strategy that is -EV for the hero.

The difference is that 1) still allows for the hero's EV to be negative (but gives a limit to how negative it can be).

Quote

06-17-2015 , 10:25 PM

yaqh

Pooh-Bah

Join Date: Aug 2007 Posts: 5,745

1 is close, 2 is wrong, check out the sticky in the poker theory subforum

Quote

06-17-2015 , 10:54 PM

nateofclubs

journeyman

Join Date: Mar 2013 Posts: 244

I read your sticky. I'm still confused though. You say "However, it turns out that in poker, if all players are playing their equilibrium strategies, they will break even in the long-term average sense when we average over all positions in the game."

So wouldn't this imply my condition 2) above?

I don't understand how an unexploitable strategy can still be -EV. If I'm choosing a strategy that is -EV against my opponent when I could instead be break-even at worst by choosing equilibrium, then it seems I'm being exploited.

Last edited by nateofclubs; 06-17-2015 at 11:08 PM.

Quote

06-18-2015 , 12:41 AM

chinz

Carpal \'Tunnel

Join Date: Jan 2009 Posts: 9,061

2 is true in rake free game that isn't rigged. I'm not sure what yaqh is implying, probably just read your post wrong.

Or maybe he is just referring to nash push/fold charts and how they're only unexploitable strategy for simple toy game with push/fold being only options, rather than real unexpoitable strategy (although at low bb, you can pretty much view it as such)

Anyway you asked what does "hero playing unexpoitably imply" rather than about those push/fold charts and yes, in that scenario both statements are true. Although there could also be non-equilibrium strategies with same EV for opponent.

Last edited by chinz; 06-18-2015 at 12:48 AM.

Quote

06-18-2015 , 12:57 AM

genher

veteran

Join Date: May 2007 Posts: 2,931

In an unexploitable strategy there is nothing villain can do to decrease your expectation. This doesn't mean that the strategy is +EV.

I think what you might be missing is that folding is -0.5bb.

an example: 10bb deep Nash push/fold strategy will have an EV of about -0.05(I seem to remember that number!? could be wrong). it is better than -0.5 (folding) but still -EV. Also there is nothing villain can do to make you lose more than -0.05. if he deviates from the Nash push/fold strategy (call less or more) you will always do better than -0.05.

Quote

06-18-2015 , 01:01 AM

chinz

Carpal \'Tunnel

Join Date: Jan 2009 Posts: 9,061

^
Playing nash equilibrium strategy for a push/fold game in a 10bb deep game is not unexploitable play (unless rules only allow push/fold) and OP asked what unexploitable play means.

Quote

06-18-2015 , 01:23 AM

genher

veteran

Join Date: May 2007 Posts: 2,931

Quote:

Originally Posted by chinz

^
Playing nash equilibrium strategy for a push/fold game in a 10bb deep game is not unexploitable play (unless rules only allow push/fold) and OP asked what unexploitable play means.

No I am answering to OP saying that he doesn't understand how it can be unexploitable and -EV at the same time. For that I use an example from the push/fold game. Sorry I thought I made it clear

Quote

06-18-2015 , 03:08 AM

yaqh

Pooh-Bah

Join Date: Aug 2007 Posts: 5,745

Quote:

Originally Posted by nateofclubs

mm, concretely, at equilibrium, the BB probably figures to lose money and the SB to win. In that case, if you're in the BB, and you play vs a GTO SB, any strategy you adopt is going to be -EV. It's best to understand that first before noting that, in heads up at least, your winnings in the SB will cancel your losses in the BB.

Quote:

Originally Posted by nateofclubs

I don't understand how an unexploitable strategy can still be -EV. If I'm choosing a strategy that is -EV against my opponent when I could instead be break-even at worst by choosing equilibrium, then it seems I'm being exploited.

The second sentence here is true, but it's not the case that such a breakeven strategy necessarily exists.

Quote

06-18-2015 , 03:07 PM

nateofclubs

journeyman

Join Date: Mar 2013 Posts: 244

Quote:

Originally Posted by genher

The part about me missing that folding is -0.5bb makes sense, but I'm not clear on "In an unexploitable strategy there is nothing villain can do to decrease your expectation.", since no matter what strategy I employ (equilibrium or not) there will always be a best-response strategy he could employ, and there is nothing villain can do to decrease my expectation beyond that.

Quote

06-18-2015 , 05:36 PM

#10

genher

veteran

Join Date: May 2007 Posts: 2,931

Quote:

Originally Posted by nateofclubs

The part about me missing that folding is -0.5bb makes sense.

That's what I thought. Glad that's sorted.

Quote:

Originally Posted by nateofclubs

no matter what strategy I employ (equilibrium or not) there will always be a best-response strategy he could employ.

That's wrong. At Equilibrium there isn't any strategy villain can use to decrease your expectation. both players are maximally exploiting each other. if, in the push/fold game, you play the Nash strategy villain does not have a better response than playing Nash himself.

(Bare in mind, as everyone else has pointed out, that in real game you are not restricted to push/fold.)

I recommend you read Tipton's book where it's all very clearly explained

Quote

06-18-2015 , 07:14 PM

#11

uczniak

grinder

Join Date: Sep 2008 Posts: 582

In real game, if you employ Nash push/folding from SB, villain does not have a better response than calling Nash either. So he cannot decrease our expectation from this strategy, it's just that our strategy itself can be bettered.

Quote

Post Reply Subscribe

...