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

MarkGritter · #1 08-31-2005, 02:25 AM

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 · #2 08-31-2005, 02:53 AM

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 · #3 08-31-2005, 03:06 AM

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

[ QUOTE ]

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 · #4 08-31-2005, 03:20 AM

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

[ QUOTE ]

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 · #5 08-31-2005, 03:30 AM

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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 · #6 08-31-2005, 03:35 AM

[ QUOTE ]
[ QUOTE ]

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.

[/ QUOTE ]

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

MarkGritter · #7 08-31-2005, 03:38 AM

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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 · #8 08-31-2005, 03:54 AM

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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 · #9 08-31-2005, 03:56 AM

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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. [img]/images/graemlins/wink.gif[/img]

MarkGritter · #10 08-31-2005, 04:03 AM

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.