Surprising Equities ... - Gambling and Probability

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10-31-2015 , 12:06 PM

DiceyPlay

old hand

Join Date: Jul 2004 Posts: 1,507

I played a hand and was curious about actual real equity. So, when I got home I found that I was ahead (OTF) but a 1:2 dog.

pokenum -h 5h 7h - ac 9c / 4h 6c 7c
Holdem Hi: 1221759 enumerated boards
cards win %win lose %lose tie %tie EV
7h 5h 423630 34.67 791430 64.78 6699 0.55 0.349
Ac 9c 791430 64.78 423630 34.67 6699 0.55 0.651

At the table when I saw opponents cards I sort of figured it was close to 50/50 as he had 15 outs twice but I had TP, OESD, and a backdoor FD. 35/65 surprised me.

Please share surprising equity scenarios you've come across.

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10-31-2015 , 12:15 PM

nickthegeek

journeyman

Join Date: Sep 2011 Posts: 273

It's 7h5h vs Ac9c on a 4h6c7c flop? I get about 50/50 on PokerStove. I think you selected the 4h6c7c as dead cards in your line.

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10-31-2015 , 12:42 PM

DiceyPlay

old hand

Join Date: Jul 2004 Posts: 1,507

Damn!!

Thanks - you're exactly correct. That's the blunder I made.

Well, I guess it's good that my "at game speed" assessment was correct.

And it's bad that I can make a mistake like that!

Thanks again.

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10-31-2015 , 12:47 PM

Jimulacrum

Pooh-Bah

Join Date: May 2010 Posts: 3,670

There are only 45 × 44 = 1,980 possible ways the turn and river can run out. Order doesn't matter in determining who wins, so for our purposes, it's 990.

I don't know why your simulator ran out over a million hands for this scenario. It's not only unnecessary, but counterproductive, as we can calculate the exact theoretical probabilities rather than simulating to estimate the probability experimentally.

ProPokerTools calculates this one as essentially a coin flip:

ProPokerTools Hold'em Simulation

990 trials (Exhaustive)

board: 4

Hand	Pot equity	Wins	Ties
57	50.40%	496	6
A9	49.60%	488	6

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10-31-2015 , 12:50 PM

Jimulacrum

Pooh-Bah

Join Date: May 2010 Posts: 3,670

Ahh, just saw the other post about entering the cards incorrectly. Yep, that'll do it.

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