"Guts" strategy

[LetYouDown]

At our micro limit poker games, we play everything under the sun. There's a game called Guts, which I'm sure some of you are familiar with, although not necessarily by that moniker.

Anyway, everyone is dealt three cards. There's no draw. Everyone looks at their cards, and then the dealer says "1, 2, 3, Drop" and on the word Drop, you have to either hold your cards or drop them. If you drop them, you're out the ante. If you don't drop them, you have to show down against all other players and match the pot if you don't have the best hand. Best hand takes the pot. If only one person stays, they have to beat a dummy hand. If they beat the dummy hand, they win the pot and the game is over. If they lose to the dummy hand, they match the pot and play continues.

The game I play in is typically 4-5 handed. Occasionally someone will stay with a hand as low as A high, good kicker...but it's on the rarer side. Everyone will stay with a pair of 7's or better. Lower pairs are more gut feeling.

Odd note: Despite my explanations, 3 of a kind is considered the strongest hand, with a straight flush 2nd. Straight beats a flush. All other hand rankings are the same.

Is there an optimum strategy to glean from this? I don't much care for the game, so I'd rather just have an ABC formula in my head based on # players, pot size, etc.

Just curious to hear your thoughts.

[aloiz]

22100 possible hands
52 ways to make 3-of-kind
48 ways to make str flush (should be ranked higher than 3 of a kind)
720 ways to make a str (excluding str flush)
1096 ways to make a flush (excluding str flush)
3744 ways to make a pair

If you're playing against three opponents I would think that it'd be optimal to play the top 25% of hands. Which would include all hands through 33x and some 22x hands. Obviously as the pot builds you might be able to increase the number of hands as you would expect your opponents to tighten up. Against 4 opponents 77x seems to be about the cutoff hand.

aloiz

[KenProspero]

Yeah, I find the best strategy is to fold and forfeit the antes.

I don't like coin flips with big penalties if you lose.

[eviljeff]

the way I played it, if a person stays in alone, (s)he gets a "leg". the game ends after one player obtains n legs (1 for a quick game, 3 for a pretty long one).

[AaronBrown]

For heads up GUTS the strategy is to fold p/2 + 1/(p+2) of the time if your opponent folds p. The game theoretic optimum is for both players to fold 3^0.5 - 1 = 0.7321 of the time. That means playing 5,921 of the 22,100 possible hands. Since there are 5,900 hands of a pair or better, playing them and only them is good for two player GUTS against a skilled opponent. But if your opponent plays all his hands, you should play half of yours; and if he plays none of his hands, you should play 1/6 of yours.

If you fold x of the time and your opponent folds p, your positive expectation is the original per-player ante times:

(1 - p)^2 - (1 - x)^2 + (p - x)*(p - x - p*x)

I know this isn't much help for your practical question, but the algebra gets too complicated with more players.