Is this poker proposition bet beatable?

[McBandit]

A friend whom I gamble with on all sorts of crazy proposition bets has offered me an interesting game.

He will play me a heads-up NL Holdem freezeout with equal starting stacks. He will play every hand blind, but I have to give him 2:1 on the money.

I mentally went over it in my head to figure out what the deal is. I figure he will raise all-in every single hand preflop to steal the blinds and skew the stacks sizes. Even if I call my AK to his 72 I am only about a 75:25 favorite to win the hand. He will be happy to go heads up with anything 66:34 or better, but with all the blinds he will steal is this a game I can beat in the long run?

Now I suspect this game is beatable if the blinds are small compared to the stack sizes. Like 500 chips each with 1/2 blinds so I'll have time to wait for 99-AA, AJ-AK, KQ.

My friend, while a smart gambler, is not a big poker mind, so I doubt he cooked up this game on his own. I bet it's a prop that has been out in the poker community before and he heard about it somewhere.

Anyways, I wanted to try it for $20, but he won't take anything less than my $1000 to his $500 per game, so I know he is really confident about his end of the bet.

What do all you stats/math/probablility people think?

[mosquito]

Sklansky discusses this very problem in his
book on tournament poker. It related to strategy
by a weak player against a skilled player, and
various related issues such as how much to
settle a tournament prize fund between these
two based on optimum strategy.

I don't recall everything, but you should
look at the book. I'm sure your pal did.

[Iceman]

If the stacks are 10000, and the blinds are 50-100, if he just raises all-in every hand he has a 39% chance against perfect play. That's because almost all hands in holdem run close in value preflop - except for the rare occasion of the time you have a high pair you're unlikely to be much of a favorite over a random hand.

[JRegs]

That's interesting. Let us know how it goes, if you go through with it.

Personally, I think that $1000 is a little steep though, especially if you don't know exactly what you're getting into.

[bigredlemon]

And that's presuming he's going all in everyhand.

Can he just call the blinds and then fold after?

[thirddan]

there would be no purpose for him to just call preflop, he won't know if the flop helps him or not because he doesn't get to look at his cards...

[McBandit]

Ya, the numbers you give don't surprise me. I need to find blinds that push him below 33% against perfect play. Do you think 1/2 blinds with 1000 chips would beat him? That should give me enough time to wait for a dominating hand.

I also toyed with the idea of folding half of my horrible small blinds and calling with half. He would still have to raise all-in everytime I called the SB, and those calls would of course include my premium hands. This would slow the rate at which I bleed my chips to him.

Cheers,
McBandit

[snowbank]

Will your friend do proposition bets with anyone?

[bigredlemon]

[ QUOTE ]
there would be no purpose for him to just call preflop, he won't know if the flop helps him or not because he doesn't get to look at his cards...

[/ QUOTE ]Looks like I misread the question.

I thought he was pulling a Neganeau... calling every hand for a flop and seeing if he could still win based upon betting strategy and psychology.

[aLOWdAkING]

According to Sklansky, it's a major advantage for your friend as discussed in TPFAP. Also, based on a very small sampling I have done, I would agree.

[McBandit]

He'll gamble with anyone if he thinks he's got the best of it.

Do you want this bet from him or do you have prop bets of your own?

I got him once for a few hundred bucks by offering him 20 tries to roll a 12 with two dice for even money. To people with only a subtle understanding of probabilities it seems like 18 rolls is the break even point, but its actually 24.5.

[bigredlemon]

[ QUOTE ]
He'll gamble with anyone if he thinks he's got the best of it.

Do you want this bet from him or do you have prop bets of your own?

I got him once for a few hundred bucks by offering him 20 tries to roll a 12 with two dice for even money. To people with only a subtle understanding of probabilities it seems like 18 rolls is the break even point, but its actually 24.5.

[/ QUOTE ]Wouldn't it be 1 in 36?
1/6 * 1/6 = 1/36 ?

[bigredlemon]

two high cards vs two lower cards, he has a 10% edge over you. If you wait for a high pair to call his all in with, then you're in good shape.

But, that's presuming he'll go all in each hand. If he raises just a small amount and then fold to a reraise, then it'll depend on how well you two bluff. He'll have a huge edge if bluffing is used because he gets +EV to go all in with any hand except a hand you have an overpair.

[flatline]

[ QUOTE ]
Wouldn't it be 1 in 36?
1/6 * 1/6 = 1/36 ?

[/ QUOTE ]

I think the math goes like:
The chance to hit a single twelve in one throw is 1/36=0.02777777 or 1 to 0.02777777
The chance to hit a single twelve in two throws is ((1.0277777)^2)-1=0.0563 or 1 to 0.0563
And so on... it gets to 1 to 1 between 24 and 25 attempts.

I really need something better to do with my time.

[Iceman]

[ QUOTE ]
Ya, the numbers you give don't surprise me. I need to find blinds that push him below 33% against perfect play. Do you think 1/2 blinds with 1000 chips would beat him? That should give me enough time to wait for a dominating hand.

[/ QUOTE ]

You would have better than a 2/3 chance if the blinds were that small, since you'd probably have time to wait for a premium hand before the blinds would make any serious dent in your stack. Lets say you just call with AA-TT, all of which have at least a 3/4 chance of beating a random hand, and which average a 4/5 chance. You have more than a 2/3 chance of getting one of those in your first 50 hands, and there's only a 10% chance you won't get one of them in your first 100 hands.

[Subfallen]

The math behind the 24.5 break-even point goes like this:
- The probability of not rolling 12 once is 35/36.
- The probability of not rolling a 12 over n rolls is (35/36)^n.
So the EV for the person rolling is:
- EV = (1 - (35/36)^n) - (35/36)^n

EV = 0 (even money bet) when:
- (35/36)^n = 0.5 =>
- n log (35/36) = log 0.5 =>
- n = 24.5

[bigredlemon]

[ QUOTE ]
The math behind the 24.5 break-even point goes like this:

[/ QUOTE ]that makes so much sense I wonder why I didn't think of it earlier. Maybe I'll go edit my post and take credit for it ahead of you guys /images/graemlins/laugh.gif

[McBandit]

Thanks for the stats for two overcards vs. two undercards. I figured that if I could essentially guarantee having two overcards (ie. AK, AQ) then I would be in good shape...I'll guess I'll have to wait for the big pairs.

Later,
McBandit

[snowbank]

I want to give him prop bets.

[pokerswami]

You say that you gamble with your friend on all sorts of proposition bets. I guess that you have played a lot of poker either with him or at least where he could watch you. Maybe he expects to add significantly to his EV because he believes he can read you - at least enough to give him an advantage over you.

Since this is a proposition, why not make an additional condition. Figure out a way where you can watch him but he cannot see you. It would be best if he couldn't even watch your hands enter chips. You could place them in a tray and have a third party push them into view of your friend. You could have some index cards already marked with all poker actions - "call" "fold" "raise" "bet" etc. - so he wouldn't hear you speak.

Just a thought.