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 08-11-2012, 11:35 PM #1 enthusiast   Join Date: Jun 2012 Posts: 67 Should I have NOT taken this poker prop bet? Well, a good friend of mine came out with this poker prop bet while we were eating at a group gathering. Being a degenerate and also for pride I agreed to the bet. The rules follow as such two hands will be dealt (three cards face down and four cards face up) exactly like 7 card stud. I would have to guess which is the best hand. After my guess the face down cards would be flipped up best 5 card wins. He is giving me 2:1 odds. The bet is \$10 to me if I guess the best hand correctly and \$20 to him if I guess wrongly. We would do this over 100 hands at his place tomorrow. I have to guess correctly more then 66% of the time to show a profit. Generally, I think its beatable if played perfectly but human error would cost a person to lose. Anyway any tips and will you guys take this bet?
 08-12-2012, 12:15 AM #2 veteran     Join Date: Sep 2011 Location: Staking Posts: 2,565 Re: Should I have NOT taken this poker prop bet? I know almost nothing about stud odds, but it seems like a very bad bet for you. You need hand pairings to have an average of 66% equity and then you need to be able to pick the best starting hand correctly. I think it's not going to be very often that a starting hand has more than 66% equity against another.
08-12-2012, 01:03 AM   #3
journeyman

Join Date: May 2012
Posts: 399
Re: Should I have NOT taken this poker prop bet?

Easier way to look at it is having perfect info through 4th and getting to pick your hand. I think it's close but 2-1 is probably a touch heavy. Imagine the probability guys can simulate this fairly easy.

FWIW I don't think human error has much to do with it. I'd bet I could go 100-100 and lay odds. You shouldn't miss very often at all and when you do it should be a very small mistake. You need the average favorite to be 67% (we'll give you a few tenths for error which is probably more than you need) to be fair. I agree with thinking his side is a little better. I mean like a lone over with some decent back-doors is usually doing better than that...

 ProPokerTools Stud Hi Simulation 600,000 trials (Randomized)
Hand Pot equity Wins Ties
Ac 6c 7c 8h37.97% 227,7984
Qd Qs 2h 3c62.03% 372,1984

 08-12-2012, 03:26 PM #4 adept   Join Date: Dec 2007 Posts: 1,191 Re: Should I have NOT taken this poker prop bet? I just tried it - dealing out hands and picking. I was correct 17 out of 20. I have no idea if it would keep at that pace, but most decisions were pretty easy. There were only a small number where I had a tough decision (I don't mean that I could know which one would win, just that it was obvious which one to pick).
 08-12-2012, 09:13 PM #5 veteran     Join Date: Aug 2011 Location: no gamble, no future Posts: 2,097 Re: Should I have NOT taken this poker prop bet? I wouldn't know where to begin figuring the probabilities. I went the empirical route and went 11/15. I hardly know anything about stud but the right choice seemed obvious. It's probably pretty close. Hopefully someone can enlighten us with some hard numbers
 08-13-2012, 11:41 AM #6 journeyman   Join Date: May 2012 Posts: 399 Re: Should I have NOT taken this poker prop bet? Are you guys posting numbers talking about the times you picked the favorite correctly or the times you picked the winner? If the favorite I'm surprised you're missing that much do you remember hands you missed? If the winner it'd be interesting to see some more hands. You both did well enough to win the bet (obv very, very small sample...I just flipped tails 2/3 you know, ). My guess is that 2-1 is a loser but 3-2 is a a winner. With just random run-outs I think there are a lot more flips early in stud hands than say pre-flop in hold em. There are going to be some times you get a very heavy favorite that early but it's so much less frequent to be dominated early in a random stud flip. Would you guys take this bet in hold em where you got to pick the pre-flop hand?
08-13-2012, 12:54 PM   #7

Join Date: Dec 2007
Posts: 1,191
Re: Should I have NOT taken this poker prop bet?

Quote:
 Originally Posted by WheelDraw1020 Are you guys posting numbers talking about the times you picked the favorite correctly or the times you picked the winner? If the favorite I'm surprised you're missing that much do you remember hands you missed? If the winner it'd be interesting to see some more hands.
I looked at the cards and decided which one I thought was most likely to win the hand. So I was picking what I thought would be the favorite. Then I looked at the cards and saw which hand won.

Hands that missed can be all kinds of situations. You can have one hand with a good pair, and the other with nothing - and it has 2 pair or better hidden. You can have 2 really marginal hands, and you have to go with the one with higher cards and the other one is the one that pairs. Just like in regular stud - you can't always tell from the board what someone has underneath. But the majority of the time the board that looks best will probably be best.

 08-15-2012, 11:18 PM #8 old hand   Join Date: Jun 2012 Posts: 1,541 Re: Should I have NOT taken this poker prop bet? I think you can get 2 out of three rite long term. +ev imo
 08-16-2012, 04:20 PM #9 newbie   Join Date: Sep 2010 Posts: 32 Re: Should I have NOT taken this poker prop bet? I did a small Monte Carlo test, and got inconclusive results. Got 20 pairs of 4-card hands from random.org (asked for 8 cards from a single deck; first 4 cards were one hand, second 4 were the other). Since I'm on my tablet and not a real computer, I then went to twodimes.org and ran the hands through their 7-card stud analyser for 500,000-hand runs. Assuming that you picked the better hand each time (some of them aren't obvious!), the EV is 64.6% and the SD is 11.9%. 2/3 is very much in the confidence interval; anyone want to run a few thousand of these? My hand pairs: 5d 8s Ts 6d - 9h 6h 7s 2s Th 2h 4h 4s - Kc Ah 9s As Qc 2s 3c 6s - 5s 8h 2d Jh Ks 5d 8d 7d - Kd Qh Th 9s 8c 6h Qd 6d - 6c Qs 5c 2h Qc 6h 9c Ac - 4h 6c 7s Ad Qd Th 6h 3c - Ks Kc 4s 7s 7h 4h 3c Th - 4d 5h 8c 2s 8h Qh Th Ks - 9d Qd 3h 5c 6h 4d Kh 4c - Tc 9d 4c 8s Tc 2c 7h 5c - 3h 6s Ac As 8h 4h 4c 3d - Jc Jh 7h 6s Ks 2h Kh 7c - 9s 9c As Kd 4d Qs 4c Jd - 8c Kc Qh 5c 3s 2h 7h Td - 4s Qs 4d Kd 6h As 7d Jd - 3d 7s 9d 4c 3h 3d Qh 3s - 2c 2d 8c Ks 8d 9c Ac 9d - Ks Kh 8h 2h Ad Qd 6c 6s - 8s 5s Kc 7s 4c As 6c 3d - 7d 6d Qs 5c
08-16-2012, 05:44 PM   #10
old hand

Join Date: Apr 2010
Location: Where they don't respect my raises
Posts: 1,665
Re: Should I have NOT taken this poker prop bet?

Quote:
Originally Posted by WheelDraw1020
Easier way to look at it is having perfect info through 4th and getting to pick your hand. I think it's close but 2-1 is probably a touch heavy. Imagine the probability guys can simulate this fairly easy.

FWIW I don't think human error has much to do with it. I'd bet I could go 100-100 and lay odds. You shouldn't miss very often at all and when you do it should be a very small mistake. You need the average favorite to be 67% (we'll give you a few tenths for error which is probably more than you need) to be fair. I agree with thinking his side is a little better. I mean like a lone over with some decent back-doors is usually doing better than that...

 ProPokerTools Stud Hi Simulation 600,000 trials (Randomized)
Hand Pot equity Wins Ties
Ac 6c 7c 8h37.97% 227,7984
Qd Qs 2h 3c62.03% 372,1984
This.

The question is the average equity for two random 7 card hands with 4 known cards for each. (And to a lesser extent how accurately can you pick the right one)

I can throw something together -- I've been wanting write some simulation code anyway.

 08-20-2012, 02:43 PM #11 old hand     Join Date: Apr 2010 Location: Where they don't respect my raises Posts: 1,665 Re: Should I have NOT taken this poker prop bet? I'm getting similar numbers compared to other posters. I'm pretty sure the friend is getting the best of the bet by a decent amount. I think even is probably about 7:4 63.39 % average equity for the favorite 10.13 % standard deviation Well, that took longer than I expected. I did start from scratch and cobble together a crude simulation for this, and then was out of town for a few days. I spent enough time learning about hand evaluators and such, so I started simple from there. I deal 4 cards each for 2 random hands and then do a brute force equity calculation from the remaining stub. I have to research how to quickly sample combinations since 141 million evaluations per match is a bit excessive and picking the starting hands could be optimized as well. I might as well learn some statistics to find a good sample size and get the confidence level along the way: the number of trials to estimate hand equity and the number of hands to estimate the bet odds. Also, as has been noted, it doesn't matter as much if you can pick the right hand since when it's not obvious since the matchups will be close to 50% anyway. Here are some fun ones: ----------- Ks Tc Td As 50.12 % 7s 5h 8d 6h 49.88 % ----------- 6c Js Qc 2c 49.57 % Qd 2h Ts Kd 50.43 % ----------- Jd 2s 4d 3d 49.51 % 6d Qd 5c 3s 50.49 % ----------- 9h 2d Tc Qc 49.91 % 6c Ah Qd 7d 50.09 % ----------- 6d 9s Qd Ks 49.85 % 9d 4d Kc Td 50.15 % ----------- Jd 6d Td 8s 49.78 % 2d 3h 3s Th 50.22 % ----------- Ts 4d 6h 8s 49.88 % 4h Kh 5s 3c 50.12 % ----------- Kc Js 8s 6s 50.04 % 7h 3s 4c 6c 49.96 % It you're missing these, it's problem: 2s 8s Qd 5d 3.56 % 7h 7s 2d 7d 96.44 % ----------- 5h Ah 5c 5d 92.52 % 2h 8h 9s Kh 7.48 % ----------- 2c Qh Qc 2h 88.28 % Qd 3c 4h Kd 11.72 %
 08-21-2012, 12:54 AM #12 journeyman   Join Date: May 2012 Posts: 399 Re: Should I have NOT taken this poker prop bet? Interesting. Just looking at it I thought I'd like his side at 3-2 but his buddy's at 2-1. I also think I may have been a bit generous in how rare it would be to miss. They should all be very small mistakes and shouldn't be that frequent if you have good card sense but I think the typical participant might need more than a few tenths of a percentage juice to make up for mistakes.
 08-21-2012, 11:36 PM #13 journeyman   Join Date: May 2012 Posts: 399 Re: Should I have NOT taken this poker prop bet? Did this bet happen? Did you lose?

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