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

[MarkGritter]

Having played some razz and PL O/8 recently, the matter of manipulating pot size and number of players naturally comes to mind.

A poster over on the Stud board made a very good point about not making the pot so large that it was automatically correct to call despite catching bad on 4th. The reason is: it makes bad players who chase correct, and eliminates the ability for a good player to make a good decision on 4th by folding.

An analagous situation in triple draw is a 2-card draw that misses the first draw. For what pot size is it correct to keep drawing with a quality 3-card seven draw vs. a player who drew 1 or 2 and bets into you?

If he is pat your implied odds stand at about N+2 : 2.5. Maybe N+3 : 1.5 at best if you are drawing to the nuts and can get a raise in. The odds of completing an 7 with a 3-card draw are about 7:1, and of completing an 8 are about 3.5:1. Thus the call is only automatic against a pat opponent (that needs a 7 to beat) if there are 15.5 BB in the pot already! It might be correct with only 6.75 BB if an 8 will do. But either way this is pretty unlikely.

Suppose your opponent is drawing one. He is about 45% to make this hand. You can probably still win 13% of the time by making your 7. The remaining 55% of the time you will win at least 25% (by making an 8), and let's say another 15% you win with a worse hand. This totals 0.45*0.l3+0.55*0.40 = 28%. This is odds of 2.6:1. Thus the call is 'automatic' if there are are 4.5 BB (9 SB) in the pot already.

(It might be good to look at how often you have to fold to a big bet next round as well. And of course everything gets complicated multiway.)

An exercise for the reader: calculate appropriate pot sizes given the risk that a bettor who drew 1 or 2 the first round is actually pat.

Now let's switch roles.

Suppose you raise preflop, get reraised by the SB, and cap with a 1-card draw. This puts 9 SB in the pot. So if you brick villian is correct to call with any quality 3-card draw. If you merely call, then there are only 7 SB in the pot, and villian should definitely fold (but often won't.)

If you are the small blind you should seriously consider smooth-calling rather than reraising so that you can afford to fold your bricked, OOP draw. If you smooth-call and BB folds you can fold the 5 SB pot to a 1-card draw if you brick. If you reraise and BB comes along anyway, the pot will be at least 9 SB and you will be tied to your hand.

Another example: You are in the BB with a 2-card draw. An EP player raises, and there is one cold-caller. If you smooth call there will be 6 or 6.5 SB in the pot. If you improve to a 1-card draw and your opponents do not, then they are (individually, although perhaps not considered together) incorrect to call your bet on the next round. If there is another caller or you reraise then your opponent's call on the next round is automatically correct.

On the other hand, with a quality 1-card draw it is almost certainly better to reraise after two or more players. You have an equity edge, and if you catch good then their next round calls will be a large mistake (well, bounded by 1 SB, I guess). However, when you brick, your opponents will certainly have odds to chase given the huge pot.

I found it helpful to work through this as I've been sticking with 2-card draws too far, and didn't have a good idea what pot size to look for. It is also helpful as a guide for games in which there is a lot of limping and cold-calling.

(Of course, I just dropped 45BB at the $1/$2 table tonight, so you may want to avoid any advice from me until I get back on a winning streak...)

[timprov]

This is not exceptionally coherent. I'd like to comment on it, but I'm having a hard time figuring it out. Can you give a specific hand example maybe?

[timprov]

I'm just going to pull something out that makes no sense to me:

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The odds of completing an 7 with a 3-card draw are about 7:1, and of completing an 8 are about 3.5:1. Thus the call is only automatic against a pat opponent (that needs a 7 to beat) if there are 15.5 BB in the pot already!


[/ QUOTE ]

Now if you're 7:1 to make a 7 by the end, and presume that will always be good, you're going to be putting 1.5 BB into the pot to get to the end, and so will the villain. So you can't possibly need more than 11 BB in the pot.

[MarkGritter]

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I'm just going to pull something out that makes no sense to me:

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The odds of completing an 7 with a 3-card draw are about 7:1, and of completing an 8 are about 3.5:1. Thus the call is only automatic against a pat opponent (that needs a 7 to beat) if there are 15.5 BB in the pot already!


[/ QUOTE ]

Now if you're 7:1 to make a 7 by the end, and presume that will always be good, you're going to be putting 1.5 BB into the pot to get to the end, and so will the villain. So you can't possibly need more than 11 BB in the pot.

[/ QUOTE ]

First I should note that I confused 3-card and 2-card draws several times. I'm actually talking about 2-card draws throughout (i.e., holding 3 small cards to a wheel.) I was always bad at proofreading.

I think the issue you're having is that I got the implied odds wrong because you don't need to put in the final-round bet if you don't make your 7. But it's probably worth accounting in some way for the times when your hand is no good or split.

Now, specifically here, the reasoning I used is: If there is 11BB in the pot, you put in 2.5 BB when you make your hand and villian puts in another 2 BB. This gives a 15.5 BB pot. 7 times you lose 2.5 BB = -17.5BB. 1 time you win 13BB = +13 BB.

But, the correct reasoning is: you put in 1.5 BB when you make your hand, while villian puts in 2 BB. 7 times you lose 1.5 BB = -10.5BB, 1 time you win the pot + 2 BB. So only 9 BB is necessary in this case.

[timprov]

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But, the correct reasoning is: you put in 1.5 BB when you make your hand, while villian puts in 2 BB. 7 times you lose 1.5 BB = -10.5BB, 1 time you win the pot + 2 BB. So only 9 BB is necessary in this case.

[/ QUOTE ]

No, that's not right either. You put in 1.5 BB when you don't make your hand, villain puts in either 2.5 BB or 3.5 BB when you do. Even then that's how big the pot needs to be to go to the river.

It's also important to realize that hero can fold after a bricked second draw here. So the pot doesn't need to be nearly so big, as you're only investing 1 sb nearly half the time you miss. I would estimate it as losing 1.5 BB four times, losing .5 BB three times, and gaining pot + 3 BB once. So the pot really only needs to be 4.5 BB.

And all this is assuming villain has #5, which is definitely MUBS. In practice folding 2w7 for one bet on the second round is way too tight, even in a 2 BB pot.

[MarkGritter]

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But, the correct reasoning is: you put in 1.5 BB when you make your hand, while villian puts in 2 BB. 7 times you lose 1.5 BB = -10.5BB, 1 time you win the pot + 2 BB. So only 9 BB is necessary in this case.

[/ QUOTE ]

No, that's not right either. You put in 1.5 BB when you don't make your hand, villain puts in either 2.5 BB or 3.5 BB when you do. Even then that's how big the pot needs to be to go to the river.


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I was assuming there had already been a bet, so villian's 2nd round bet is included in the pot size.

[MarkGritter]

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And all this is assuming villain has #5, which is definitely MUBS. In practice folding 2w7 for one bet on the second round is way too tight, even in a 2 BB pot.

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Villian could have not just #5 but also an 86, which will beat any of your 8s. Someone with 723 can only tie 87432 by keeping an 8, as well.

[MarkGritter]

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It's also important to realize that hero can fold after a bricked second draw here. So the pot doesn't need to be nearly so big, as you're only investing 1 sb nearly half the time you miss. I would estimate it as losing 1.5 BB four times, losing .5 BB three times, and gaining pot + 3 BB once. So the pot really only needs to be 4.5 BB.


[/ QUOTE ]

You're right, I didn't take into account folding after the 2nd draw, but this simplified things too far.

Your 4/3/1 split is probably pretty close to reality. With a 40-card stub and U=10-12 good cards the chance of catching just one are U*28/40C2 = 36-43%, and of catching two good are U*(U-4)/2/40C2 = 4-6%. So you will brick around 40-50% of the time and save a BB.

[MarkGritter]

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This is not exceptionally coherent.

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I'm trying to live up to the high editing standards of our favorite publishing company. /images/graemlins/wink.gif

[MarkGritter]

So, are you of the opinion that it's never worth manipulating the pot size predraw, because any 2-card draw to a 7 will be getting odds to chase after the first draw anyway?

What about looking farther ahead to the 3rd round of betting?

Even with fixing my implied-odds math, I think that I will still be overestimating the odds of drawing in large (i.e., multiway) pots because there are more dead cards.

[timprov]

I'll go so far as to say I think the razz example, which is straight out of Sklansky on Poker, is dumb, and based on a substantial flaw in the Fundamental Theorem.

People calling correctly always make you money. They don't make you as much money as calling incorrectly, or folding incorrectly; but the gap is not so wide as Sklansky suggests, and is generally not worth giving up equity elsewhere.

[randomstumbl]

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So, are you of the opinion that it's never worth manipulating the pot size predraw, because any 2-card draw to a 7 will be getting odds to chase after the first draw anyway?

What about looking farther ahead to the 3rd round of betting?

Even with fixing my implied-odds math, I think that I will still be overestimating the odds of drawing in large (i.e., multiway) pots because there are more dead cards.

[/ QUOTE ]

I have a feeling this happens a lot more in A-5 than it does in 2-7. Though, I'm the first to admit that I've never really sat down and thought about the math of the worst case scenarios.

Remember that in A-5 you usually have one less rank of cards to hit and your outs are stolen more often. Therefore, the odds of drawing out are much, much worse.

[randomstumbl]

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I'll go so far as to say I think the razz example, which is straight out of Sklansky on Poker, is dumb, and based on a substantial flaw in the Fundamental Theorem.

People calling correctly always make you money. They don't make you as much money as calling incorrectly, or folding incorrectly; but the gap is not so wide as Sklansky suggests, and is generally not worth giving up equity elsewhere.

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This has always been my gut feeling, but I'm just too lazy to do the math. If anyone's really bored, here's all you need to do to settle this.

Figure out the equity advantage you have on the next betting round when your opponent calls correctly. Then figure out the equity advantage you have when they call incorrectly on the next betting round. Take the difference of these equities. Compare that to the equity you give up by missing a bet.

On top of all that, you miss fold equity and damage your image as an aggressive player (I guess that last one doesn't matter as much to a lot of people).

[timprov]

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I'll go so far as to say I think the razz example, which is straight out of Sklansky on Poker, is dumb, and based on a substantial flaw in the Fundamental Theorem.

People calling correctly always make you money. They don't make you as much money as calling incorrectly, or folding incorrectly; but the gap is not so wide as Sklansky suggests, and is generally not worth giving up equity elsewhere.

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This has always been my gut feeling, but I'm just too lazy to do the math. If anyone's really bored, here's all you need to do to settle this.

Figure out the equity advantage you have on the next betting round when your opponent calls correctly. Then figure out the equity advantage you have when they call incorrectly on the next betting round. Take the difference of these equities. Compare that to the equity you give up by missing a bet.

On top of all that, you miss fold equity and damage your image as an aggressive player (I guess that last one doesn't matter as much to a lot of people).

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Another thing from a poker theory perspective is that a small chance of a bad fold is worth at least as much as a large chance of a bad call. So if you're going to be manipulating at all, it's often a good idea to make the pot bigger.

[dibbs]

First off, I think you mean 2-card draw throughout, no?

I've been thinking about this idea for a long time but never really knew how to put it together in words, well, put together the question at least.

Basically, I have always felt that I push my opponents to make a decent sized mistake in early rounds (I play with good starters, they play garbage), but quite quickly the pot is so large they they aren't making that much of a mistake (if one at all) by calling when they catch up (which happens pretty often it seems). It feels like the later rounds become kind of crap shooty, and that hand strengths come really close together (certainly not 3 to 1 situations like holdem) on the end which makes their chasing not that incorrect. I feel the edge I push is a smallish one by playing good starters and using position, I always wondered if there was more I could do.


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Suppose you raise preflop, get reraised by the SB, and cap with a 1-card draw. This puts 9 SB in the pot. So if you brick villian is correct to call with any quality 3-card draw. If you merely call, then there are only 7 SB in the pot, and villian should definitely fold (but often won't.)

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How many cards did he draw, 2? And we're assuming he missed and trying to make it incorrect for him to call unimproved? And this is just headsup correct?

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If you are the small blind you should seriously consider smooth-calling rather than reraising so that you can afford to fold your bricked, OOP draw. If you smooth-call and BB folds you can fold the 5 SB pot to a 1-card draw if you brick. If you reraise and BB comes along anyway, the pot will be at least 9 SB and you will be tied to your hand.

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Would a smoothcall still be correct with a dynamite draw like 2347? What about 2348 and the likes? Does starting hand strength have any impact here on the decision?





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Another example: You are in the BB with a 2-card draw. An EP player raises, and there is one cold-caller. If you smooth call there will be 6 or 6.5 SB in the pot. If you improve to a 1-card draw and your opponents do not, then they are (individually, although perhaps not considered together) incorrect to call your bet on the next round. If there is another caller or you reraise then your opponent's call on the next round is automatically correct.

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Once again, 237 or other nice 2 card draws that are perhaps better than theirs doesn't make it a raise because you can miss and you're OOP, but even if you hit they get the odds to call anyways?


As for dropping 45 BBs at 1/2, I dont think thats that big of a deal, I don't know how many players on here have experienced it, but I've had multiple sessions where my 1 card draws dont stand a chance against 3 card draws for hours on end, this is one game where I'm pretty good about not steaming either IMO.

[MarkGritter]

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First off, I think you mean 2-card draw throughout, no?


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Yup, I am primarily interested in 2-card draw vs. pat or 1-card draw situations here.

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I've been thinking about this idea for a long time but never really knew how to put it together in words, well, put together the question at least.

Basically, I have always felt that I push my opponents to make a decent sized mistake in early rounds (I play with good starters, they play garbage), but quite quickly the pot is so large they they aren't making that much of a mistake (if one at all) by calling when they catch up (which happens pretty often it seems). It feels like the later rounds become kind of crap shooty, and that hand strengths come really close together (certainly not 3 to 1 situations like holdem) on the end which makes their chasing not that incorrect. I feel the edge I push is a smallish one by playing good starters and using position, I always wondered if there was more I could do.


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That is what I'm wondering about as well. Unfortunately since my implied-odds math was screwed up the play examples are full of crap as well.

Right now I am playing TD very much as a 1st round and 4th round game (starting hands + value bets). But there are decisions to be made on 2nd and 3rd rounds that are more subtle, and might help extract more value from good hands or save value on bad hands.

[MarkGritter]

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People calling correctly always make you money. They don't make you as much money as calling incorrectly, or folding incorrectly; but the gap is not so wide as Sklansky suggests, and is generally not worth giving up equity elsewhere.

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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.

It may well be the case that a correct call is +EV both for you and for another player, at the expense of a third. Or that a correct call on one street leads to an incorrect call or fold on a later street.

If you are trying to make the argument that mistakes in the first round of TD are of more value to you than mistakes in later rounds... that would be interesting to prove.

[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.

Here's the real issue. Come up with an example where you don't bet, have the best hand and then are able to make up the missed value later on in the hand. I've thought about it and I don't think it ever happens at a full table (unless your opponent gives you a lot of extra action on later rounds).

[MarkGritter]

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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.

[MarkGritter]

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Another thing from a poker theory perspective is that a small chance of a bad fold is worth at least as much as a large chance of a bad call. So if you're going to be manipulating at all, it's often a good idea to make the pot bigger.

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This, at least, I agree on. A bad call cannot cost more than the bet, and frequently much less. A bad fold costs some fraction of the pot. Against players who are making bad folds you want a bigger pot.

Against player who are making bad calls...?

Suppose we have a simple model where an opponent is a 20% dog and 10% dog on the middle two rounds of betting.

His second round call is correct if he is getting 4:1. His third round call is correct getting 9:1. Let's give Hero psychic instinct (and an unbreakable hand) so he folds as soon as Villian makes his hand, denying Villian any implied odds.

20% of the time Villian wins on the second draw and Hero loses 0.5 BB. 8% of the time Villian wins the third draw and Hero loses 1.5 BB. The remaining 72% of the time Villian wins the third round. How much does Hero gain or lose by having Villian chase?

1.0BB pot: 1.58 (+0.58)
1.5BB pot: 1.94 (+0.44) (second round call becomes correct)
2.0BB pot: 2.3 (+0.3)
2.5BB pot: 2.66 (+0.15)
3.0BB pot: 3.02 (+0.02)
3.5BB pot: 3.38 (-0.12)
4.0BB pot: 3.74 (-0.26)
4.5BB pot: 4.1 (-0.4)
5.0BB pot: 4.46 (-0.54)
5.5BB pot: 4.82 (-0.68)
6.0BB pot: 5.18 (-0.82)
6.5BB pot: 5.54 (-0.96)
7.0BB pot: 5.9 (-1.1)
8.0BB pot: 6.26 (-1.38) (both calls become correct)

The most Hero wins from incorrect calls is about 1 small bet. But, Hero can lose a small bet on later streets despite the incorrect third round call in a 5BB pot or larger.

Now, suppose before the first draw Villian and Hero are 50/50. How many bets does Hero want in the pot if it is equally likely that Hero and Villian will be the dog afterward, if Hero plays correctly but Villian draws to the end?

Hero's EV on 2nd and 3rd rounds when behind for various pot sizes:

1.5BB pot: 0.0
2.0BB pot: 0.1
3.0BB pot: 0.2
3.5BB pot: 0.3
...
6.5BB pot: 0.9
7.0BB pot: 1.14
7.5BB pot: 1.28

etc.

But something interesting happens when you compare the two. It is always +EV for Hero to play against this Villian. But the EV is maximized at a 1BB pot, if Hero and Villian are equally likely to be the dog after the first draw (and there is no money in the pot.)

1.0: 0.29
1.5: 0.22
2.0: 0.2
2.5: 0.18
3.0: 0.16
3.5: 0.14
4.0: 0.12

Similarly, a 55/45 edge for Hero makes 1 BB the optimal pot size (EV=0.369) and in fact EV decreases until the pot reaches 6.5 BB!

Now if we give hero a 60% edge on the first round (instead of 50/50) in the same model, Hero's EV is higher at 1 BB or 4 BB than at the range in between.

1.0: 0.448
1.5: 0.414
2.0: 0.42
2.5: 0.426
3.0: 0.432
3.5: 0.438
4.0: 0.444
4.5: 0.45
5.0: 0.456

A 66/33 edge for Hero narrows this gap to just one bad pot value so a preflop raise is always going to be correct.

1.0: 0.5428
1.5: 0.5304
2.0: 0.551

So, I think there is some validity to the idea of keeping pots small with narrow preflop edges, against opponents who will call too far. Whether this model is really applicable to the game of Triple Draw is a more challenging problem.

[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! /images/graemlins/tongue.gif

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/images/graemlins/club.gif9/images/graemlins/club.gif on a flop of K/images/graemlins/heart.gif9/images/graemlins/heart.gif2/images/graemlins/diamond.gif. You have A/images/graemlins/heart.gif7/images/graemlins/heart.gif. 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. /images/graemlins/smile.gif 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]

[ QUOTE ]

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.

[/ QUOTE ]

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.