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

[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.

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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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[ QUOTE ]
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.

[/ QUOTE ]

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).

[/ QUOTE ]

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.