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Old 11-07-2005, 11:29 PM
MarkGritter MarkGritter is offline
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Join Date: Jan 2005
Location: Eagan, MN
Posts: 244
Default Re: Triple Draw Decision-- Wynn 10/20 Mixed

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.
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