2-card draws and manipulating the pot size in TD 2-7

[randomstumbl]

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This cannot be true as stated. If the decision to call (rather than fold) is correct and is +EV for the caller, then it cannot also be +EV for you. The money has to come from somewhere.


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I think this is were reading the Theory of Poker gives you the wrong idea. If I'm 80% to win, but you have 10:1 pot odds, I win money on your call. I'd win more money if you folded, but I still win 6/10 of a bet on this round.


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Your bet makes you money (compared with checking or folding) but my call does _not_ make you money. As you say, you'd prefer that I didn't call and gain the additional equity.

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+EV is a really clunky term. In this example, one player is in a dominant position. Anything except folding has a positive expectiation for that player.

If you define +EV how you seem to then nothing except having your opponent put in 3 bets and fold is really ever +EV.

[MarkGritter]

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+EV is a really clunky term. In this example, one player is in a dominant position. Anything except folding has a positive expectiation for that player.

If you define +EV how you seem to then nothing except having your opponent put in 3 bets and fold is really ever +EV.

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I define +EV as net positive expectation, not just absolute positive expectation. Both sides have positive expectation (because of money already in the pot) but it's change in expectation that's relevant. (Or, more precisely, maximizing expectation.)

Your opponent could certainly make a mistake. Mistakes are -EV. It's just in this case, the round has two parts--- your bet, which makes you money, and his call, which costs you money. The net for the round is positive for you, certainly (as it would be whether his call is correct or not) but you are not making as much money as you could be.

The point I'm trying to make is that his calls are not the part making you money. If they were, he should fold instead, since folding has an expectation of zero. He's trying to minimize--- he can't minimize without costing you something relative to just giving up the pot.

[timprov]

It's worth looking at this from a second perspective as well, since we're headsup: how big does the pot need to be to make betting into a two-card draw with a random hand profitable if he will always fold if he misses? It's much easier to come up with the answer to that: with a 12-out 2-card draw, you're going to brick out 35/47 * 34/46 or about 55% of the time. So the pot in fact only needs to be 1 SB to make a bet profitable. Ergo you can't fold 2w7 headsup on the second round.

[timprov]

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The point I'm trying to make is that his calls are not the part making you money. If they were, he should fold instead, since folding has an expectation of zero. He's trying to minimize--- he can't minimize without costing you something relative to just giving up the pot.

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You need to make a justification for using just giving up the pot as your comparator. I don't think its legitimate.

[MarkGritter]

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The point I'm trying to make is that his calls are not the part making you money. If they were, he should fold instead, since folding has an expectation of zero. He's trying to minimize--- he can't minimize without costing you something relative to just giving up the pot.

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You need to make a justification for using just giving up the pot as your comparator. I don't think its legitimate.

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But sophism is what Marks do best! [img]/images/graemlins/tongue.gif[/img]

Are you arguing that expected value is ill-defined after just Hero's bet? Or merely that somehow both Villian and Hero benefit from Villian's choice? Or that Villian's move does not change your EV at all because it's just what you expected to happen? (I can get behind the last one as it doesn't change my contention that the call is not making you money, only the bet. I might even be convinced that the first view is appropriate.)

Take your pick, I can always come up with bogus rationales post hoc since we've descended into the depths of philosophy:

1) Practical: Doing nothing is equivalent to folding. In fact, if he delays long enough, his hand will be folded automatically. So fold makes sense as a default.

2) Metaphorical: All poker is a struggle for the pot [sic]. Your EV against a rational opponent cannot be higher than what's already in the pot.

3) From analysis of algorithms: Villian decreases your EV by performing better than a random or fixed strategy.

4) Teleological: If Villian is not decreasing your EV by making a correct choice or increasing it by making the wrong one, what the heck is he doing?

5) Simplicity: Because folding always has a known expectation in any situation.

6) Utility: Which choice is Hero happiest with? How can you be less happy unless your expectation has decreased? (OK, this is an argument for comparison to raising.)

[timprov]

You're just saying you don't believe in the no-win situation.

If my bet makes me money regardless of what you do, then obviously you calling me is profitable for me. I think you might be treating the pot as hero's money here.

A simple holdem example: I have K[img]/images/graemlins/club.gif[/img]9[img]/images/graemlins/club.gif[/img] on a flop of K[img]/images/graemlins/heart.gif[/img]9[img]/images/graemlins/heart.gif[/img]2[img]/images/graemlins/diamond.gif[/img]. You have A[img]/images/graemlins/heart.gif[/img]7[img]/images/graemlins/heart.gif[/img]. Approximating for simplicity, I have 65% equity, you have 35%, and we're both going to the river. So if there are ten SB in the pot, 6.5 of them are "mine", and 3.5 of them are "yours". But of course you can't take your 3.5 out and take them home, the only choice where ev is truly zero. I bet, and you call correctly. Now there are twelve bets in the pot; 7.8 of them are "mine" and 4.2 of them are "yours". So by betting 1 SB, I get back 1.3 SB when you call. By calling 1 SB, you lose .3 SB immediately, but by doing so you save your 3.5 SB of previous pot equity.

Calling here is the least bad option, but it still makes me .3 SB when you do it. In fact, whatever you do against my bet, I make money.

I'm not convinced that the bet without the response to the bet is a valid state, which is what you seem to be claiming. Can you quantify the equity during it?

[MarkGritter]

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If my bet makes me money regardless of what you do, then obviously you calling me is profitable for me. I think you might be treating the pot as hero's money here.


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(Hero always owns the pot until it's wrested from his clutching hands! Villian is Villian, after all.)

Checking will still earn Hero money no matter what Villian does, just not as much as betting will. If Hero's decision to bet rather than check is a +EV choice for Hero, how is Villian's decision to call rather than fold not a -EV choice for Hero?

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I'm not convinced that the bet without the response to the bet is a valid state, which is what you seem to be claiming. Can you quantify the equity during it?

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With a default choice for Villian, yes. [img]/images/graemlins/smile.gif[/img] If it is undefined before Villian acts, why not before Hero acts? The first person to act does not have a monopoly on changes to expected value.

I think that using whatever definition saying Hero's move increases his EV, Villian's correct call can't be viewed as also increasing it. Either Hero has correctly anticipated Villian's action (and thus his Villian's move does not change EV) or Villian is acting in a way that decreases Hero's EV. Hero simply shouldn't get credit when Villian makes a move that is not in Hero's best interest.

[timprov]

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I think that using whatever definition saying Hero's move increases his EV, Villian's correct call can't be viewed as also increasing it. Either Hero has correctly anticipated Villian's action (and thus his Villian's move does not change EV) or Villian is acting in a way that decreases Hero's EV. Hero simply shouldn't get credit when Villian makes a move that is not in Hero's best interest.

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But here's the thing -- every move is in Hero's good interest. Sure, Hero would prefer he raised a couple times and then folded. Barring that, Hero would prefer he just folded right away and sacrificed the 3.5 SB he has in the pot, rather than paying .3 SB to maintain it. But paying .3 SB to maintain it is still pretty good.

[lgas]

I could be wrong here, but what % chance do you give to the guy thats just had too much to drink or is otherwise impaired and makes a horrible play? I think, based on my condition, that you could face this situation >30% of the time.

Peter Forsberg. Avalanche. Say ho.