Triple Draw Decision-- Wynn 10/20 Mixed

[W. Deranged]

Hi folks,

This a hand from this weekend in Vegas, at the Wynn 10/20 mixed game. We're playing four-handed, and everyone seems reasonably competenent. The BB in this hand is 2+2er Death Donkey, who is drunk but playing reasonably sanely if a bit overly aggressive. The other two are decent.

Deranged is UTG with 432xx

Pre-1st Draw:

Deranged raises, Button calls, SB three-bets, Death Donkey four-bets (this could be just about anything), Deranged calls, Button calls, SB calls.

First Draw (4 players, 16 SB): SB draws 1, Death Donkey draws 2, Deranged draws 2, Button draws 2.

Deranged makes 8432x.

Pre-Second Draw:

SB bets, Death Donkey Calls, Deranged calls, Button calls.

Second Draw (4 players, 10 BB): SB draws 1, Death Donkey draws 2, Deranged draws 1, Button draws 2.

Deranged makes 98432.

Pre-Third Draw:

SB checks, Death Donkey checks, Deranged bets, Button calls, SB calls, Death Donkey calls.

Third Draw (4 players, 14 BB): SB is pat (!!!), Death Donkey draws 1, Deranged...

Basically, I did one thing, everyone at the table said that I should do that thing, and now I've thought about it a lot and am totally confident that I should have done the other thing. I have a bunch of comments on this hand but I'll leave them for after some other responses.

[timprov]

You have to draw here.

[W. Deranged]

[ QUOTE ]
You have to draw here.

[/ QUOTE ]

That's what everyone else said, that's what I did, and now I'm almost positive it was the wrong play.

Here's the thought:

When SB check-calls and stands pat, I feel I can pretty confidently put him on a hand (he was pretty ABC). I think that his range is pretty much every 9-high hand and some of the worst 8s, say all 87 hands.

There are 7 choose 4 = 7*6*5*4/4*3*2 = 35 hands that are 9 high, one of which is a straight. Of those 9 high hands, 6 choose 3 = 20 combinations are 98 hands, one of which is a straight. So we have 19 98-hands out of 34 9-high hands. Since I have 98-perfect, I am beating more than half of the possible 9 high hands.

We then have to consider what is the likelihood that he has an 8 high hand. I figure he would bet any 86 hand or better. So his range includes probably no more than the 87 hands, of which there are 5 choose 3 = 10 possibilities, one of which is a straight. So maybe 9 possibilities.

If we add those in, I am beating 18 of his 43 possible hands, which is over 40% of his possible hands. My thought is that we don't really need to discount his range because I hold an 8 in my hand, because it is pretty likely that the two other players are both drawing very strong, probably both to 7s or maybe to something like my 8432 draw. If both hands remaining include 7s and not 8s, I think it actually may be slightly more likely that SB has a 98.

One of the easy things about the decision is that I do know that if I draw and hit any card 5-7 I will beat SB. My thought is that, particularly with the deck likely crippled at this point with 4 players remaining in the hand, it is unlikely that I have a better-than 40% chance of improving (in fact, I very clearly do not).

Therefore, my thought is that the most likely way for me to beat the SB villain is simply to stand pat.

Now, as for the other two players. Based on the action I think it is quite likely that at least one and probably both are drawing very strong, probably to 7s. In that case, in the majority of cases where either of them hit, they will beat my 98 and will beat any hand that I could draw to and hit . The only situation in which they hit and I would have wished I would have drawn is if the best hand either of them make is an 87; namely, only if one or both hit an 8 do I want to have drawn.

So, if either of the two drawing players hit, I'm probably screwed anyway.

So I think it is really quite clear that the best way for me to win this hand is to stand pat.

[randomstumbl]

The really interesting question is what do you do if the river is checked around to you (when you stay pat).

[W. Deranged]

[ QUOTE ]
The really interesting question is what do you do if the river is checked around to you (when you stay pat).

[/ QUOTE ]

Check behind.

I don't have a 55% edge on SB, and based on the way he's played the hand, the fact the game is four-handed and we've been playing fast and loose (and drunk in one case), I think there is basically no chance I'm getting a better hand to fold from the SB (he has acted obviously skeptical all night). Similarly I'm never folding a better hand from the other non-2+2er. (For perspective, he had regularly called down in the Omaha/8 game with 3rd and 4th nut-low draws/hands on the turn and river behind my promotion raise attempts, and was usually correct. He is not going to be pressured out here with a possible winning hand.)

I also don't think I'm getting many calls from inferior hands from either Death Donkey or the button. So I don't think the river qualifies as a betting situation where I might not win >50% but would win greater than 33% in a three-way pot or something like that. So I see no value in a bet either.

The tough question for me is what to do if I check, button bets, SB calls, Death Donkey folds, and it's to me. I think it's a pretty easy fold to a bet and an overcall, as I'm now parlaying and I think the button was not going to bet many weak hands there. It's obviously a very easy fold if any raising starts or in the very, very unlikely event button bets, SB calls, and the Death Donkey overcalls.

[randomstumbl]

With your read, you're probably right to check the river.

Also, I think you can fold to just about any bet on the river (though I'd probably call if it was one bet to me without any overcalls). It would be the bluff of the century to try to go through two pat hands and a draw.

[MarkGritter]

I plugged the numbers into a spreadsheet which directly takes into account the cards you hold in calculating the distribution of pat hands. 87632 and worse are 75% of all possible opponent pat hands, while the hands that you beat form about 31%. So your estimate of beating 40% of his holdings is pretty good. It's about 38% if we extend his range down to 87432.

If we kill two 7s then the numbers change to 75% and 33%, so you beat about 45% of his holdings.

But, this pat hand was made from a 1-card draw that was worth three-betting. This should eliminate any the hands 96543, 97543, 97643, 97653, 97654, 98654, 98754, and 98764.
On balance this helps you about as much as killing the 7's, beating 45% of his hands. With both adjustments made you are about even odds to be ahead.

So, yes, I agree you can profitably stand pat in a large pot if that was the only consideration. (In a small pot paying off the value bet or making one becomes more important.)

Those two players drawing worry me somewhat more, though.

They could each have quite a few outs. If you are ahead of SB then he holds a 5 or a 6, so 7432 is drawing to no more than 2+2+3+4 = 10 outs and probably no less than 6. But it is slightly more likely that the others hold a 5 or a 6 because you don't.

Let's say you are a 50% favorite (I did some twodimes numbers and this seems reasonable) if you are ahead and pat. You have about 20% equity if you are behind to SB's 9 and drawing, possibly as high as 30% if ahead and drawing.

To keep the math simple:
Ahead: P=0.5, equity of drawing = 0.3, equity of standing = 0.5
Behind: P=0.5, equity of drawing = 0.2, equity of standing = 0.

With these estimates it is a dead heat between drawing and standing pat. If you are a 60% favorite when pat instead, then it's still only 55/45 in favor of standing pat. But if you only beat 40% of SB's pat hands instead, draw is the 55/45 favorite. If it is this close then last-round considerations should influence you to draw even in a decent-sized pot. (10% loss of equity = 1.4BB here, so if you stand pat correctly but pay off or draw incorrectly but get paid off that almost covers the 10% range.)

What I would really like to see is to work out the probabilities on all three of your opponent's hand ranges like I did for the pat hand. There are a fair number of decent 7 draws and I'm not sure how 'dead' the deck really is on average.

[DeathDonkey]

I have absolutely no recollection of this hand, but I don't remember much from that night. I do know I was killing at triple draw, and I probably sucked out on this hand. I think you should have raised 4th btw.

-DeathDonkey

[bugstud]

[ QUOTE ]
I have absolutely no recollection of this hand, but I don't remember much from that night. I do know I was killing at triple draw, and I probably sucked out on this hand. I think you should have raised 4th btw.

-DeathDonkey

[/ QUOTE ]

can we name someone here this weekend that remembers much of anything?

[goofball]

I wonder who the SB is in this hand. I play in that game regularly and if he's the moron who usually checks calls while standing pat then you should definietly not draw. He could easily have a worse 9 or a T. You can't bet the river but your hand is good too often to break. This guy is a typical local nit, he's decent if weak bad at the other games and probably a small winner for some of the games. He must be a big loser in teh 2-7 part though because his play is just atrocious.

My favorite from him is, after a dealer either a) doesn't give him the card he needs, b) gives his opponent a card they need, or c) generally wrongs him somehow, he'll sit out and say "she's only gonna get me once"