guts analysis

[chocaholic]

I play in a seven-handed dealer's choice home game in which guts is frequently called. I have been trying to work out an optimal strategy for calling or folding when one away from the button. I figure if you go in and your opponent folds, you win 7 units (the size of the pot). If you go in and are called by a worse hand, you win 8 units. If you go in and are called by a better hand, you lose 10 units (your initial bet plus matching the pot). I am trying to figure out what percentage of the time you need to win when called, given the expected chance of your opponent folding. Your EV is 7x + (1-x)(8y - 10(1-y)) where x is the chance of your opponent folding and y is your chances of winning if called. To figure out your break-even percentage, I solved for y and came up with y=(1-x)((-7x+10)/18). Does this look right?

I've also been trying to figure out the frequency with which various hands are dealt. The problem is that we play a weird version of guts; everybody is dealt 3 cards face down and 1 card face up and the lowest card face down is wild. Starting with the left of the dealer, everybody decides whether to go in or fold. With this structure, I don't know how to calculate the odds of particular hands being dealt without manually dealing out hundreds of hands. Any help would be appreciated.

Thanks,

Dan

[chocaholic]

Should I have posted this in the Other Poker Forum?

[Lottery Larry]

[ QUOTE ]
I play in a seven-handed dealer's choice home game in which guts is frequently called. I have been trying to work out an optimal strategy for calling or folding when one away from the button. I figure if you go in and your opponent folds, you win 7 units (the size of the pot). If you go in and are called by a worse hand, you win 8 units. If you go in and are called by a better hand, you lose 10 units (your initial bet plus matching the pot). I am trying to figure out what percentage of the time you need to win when called, given the expected chance of your opponent folding. Your EV is 7x + (1-x)(8y - 10(1-y)) where x is the chance of your opponent folding and y is your chances of winning if called. To figure out your break-even percentage, I solved for y and came up with y=(1-x)((-7x+10)/18). Does this look right?

I've also been trying to figure out the frequency with which various hands are dealt. The problem is that we play a weird version of guts; everybody is dealt 3 cards face down and 1 card face up and the lowest card face down is wild. Starting with the left of the dealer, everybody decides whether to go in or fold. With this structure, I don't know how to calculate the odds of particular hands being dealt without manually dealing out hundreds of hands.

[/ QUOTE ]

I got to here
[-7x/(1-x]+10=18y, leading to y=[-7x/(1-x)+10]/18 which doesn't match yours, but I'm not sure if I screwed up.

As to calculating the hand frequency in your guts game, I definately can't do that.

[NIX]

I'm bored, so I'll take a stab at this.

First, for the break even value of y, I got y = [(-7x)/(18(1-x))] + (5/9) which matches Larry after rearranging.

As for the hand frequency, I think I have a simulation for it, but have a question. The only possible hands are one pair, three of a kind, four card straighs, four card flushes, four of kind, and four card straight flushes. Am I interpretting this correctly?

[chocaholic]

I'm sure you guys are right about the formula, I can't do algebra [img]/images/graemlins/smile.gif[/img]

As to the hand frequency, you are correct NIX except that we don't count straights, flushes, or straight flushes. High hand is four of a kind, followed by trips, followed by a pair.

Dan

[warewulf]

I think you're losing sight of the true purpose of guts -- there's not much of a strategy, just drink and try to win a huge pot! [img]/images/graemlins/smile.gif[/img]

I do have a strategy for 7/27 though -- If i'm dealt 7 or 27 I will play. If i'm dealt under a 7, I will probably try to hit 7 and fold if I go over. Never try to hit 27 if you're dealt an 8 or 9. It will cost too much to keep taking cards and then you will end up going over.

[chocaholic]

Larry and Nix: I just plugged your formula into excel, and it gave me a negative number for x=.6 and above. I think the problem is that the original formula is set equal to EV, and the subsequent formula eliminates EV from the equation. I think that what I did was to say that -7x=(1-x) 8y -10(1-y), because, in order to break even, you can't lose more money when your opponent calls than you win when he folds. I'm still not sure if the resulting formula is correct [img]/images/graemlins/smile.gif[/img]

Warewolf: Yeah, I'd probably be happier not worrying about all of the math and just enjoying the game. I'm sort of obsessive about these things [img]/images/graemlins/smile.gif[/img]
Dan

[NIX]

Ok, here we go. [img]/images/graemlins/tongue.gif[/img]

First, chocoholic, if when you write your EV formula as -7x=(1-x) 8y -10(1-y), you mean -7x=(1-x) [8y -10(1-y)], then your formula matches mine and Larry's. However, when you solve for the breakeven values of x and y, you don't eliminate the EV value. You just set it equal to 0. All three of us did that. If there is an error, it is in the EV formula.

However, if I understand guts correctly (I've never actually played it), it goes like this right? Everyone folds to you, you bet one unit and your opponent calls one unit. If you win, you collect the pot of 9 units (7 from antes plus your and your opponent's bets). As a penalty for losing, your opponent now has to match the pot of 9 units by adding that to his ante in the next hand. In this case, the size of the pot should be a variable in our EV formula, such that EV = 7x + (1-x)((p+1)*y) - (1-x)((p+3)(1-y)), where x = the percentage your opponent will fold, y = the percentage you'll win when called, and p = the size of the pot before your action. Again, I never actually played, so I'm guessing at this.

And secondly, for the frequency of being dealt a given hand. I made two assumptions for this. One, if the lowest down card you have is paired, either in the hole or split, both counted as wilds. And two, my two semesters of probability haven't failed me. If my math is right, I have the hand frequency as:

Four of a kind: 1.96%
Three of a kind: 30.42%
Pair: 67.61%

I can show you my calculations if you want, but I feel pretty confident in those.

[NIX]

Correction: EV = p*x + (1-x)((p+1)*y) - (1-x)((p+3)(1-y))

[danderso8]

you might try searchin the poker theory archives...I believe someone "solved" guts a couple years ago, though it may have been a slightly different variation. I think my friend rocketmanjames posted in the thread, though i don't remember who solved it.

--dan