Determining an optimal strategy in a guts-like game

[donkeyradish]

Say N players are dealt 5 cards face down and each has the choice of winning or losing a pot by "declaring" they have the best poker hand. (They all seed the pot with a $1 ante)

If such a player indeed has the best hand (of those who declare) they win the pot, but if another declarer has a better hand, a pot-sized forfeit must be paid instead. (Which goes into the pot for the next hand).

Not declaring at all just loses you the ante for that hand. "Declarations" are all simultaneous.

2 Questions

1) What is the optimal strategy to play, assuming you don't know any other players strategy.

2) Suppose you happened to know EXACTLY what strategy each of the other players were using. And suppose these were all far from optimal (but also, all different). How would you use this information to your maximum advantage?


(PS. I don't know the answers, this isn't a Quiz! [img]/images/graemlins/crazy.gif[/img])

[Victor]

What if you are the only one who drops? Do you win the pot then?

This depends on the amount of opponents. With 3 opps drop with any 2 pair. With 10 opps drop with aces up or better.
This would be my guess, and I have played many of these crazy drop games. It is far better to drop with only great hands than to push marginal hands. Remember your odds are only 1:1

[donkeyradish]

So without getting specific about actual hands, do we simply say that with 4 players you just want to play any hand ranked in the best 25% of possible hands?

How does it change when you know what your opponents will do? For example P1 will only call with Quads or better, P2 will only call with a Straight Flush! P3 will call with any hand containing at least one Club! What now? P3 sounds crazy, but - is he?

PS. I know this isn't realistic, its the theory behind making these decisions that interests me.

[Louie Landale]

Opting out has the unique BENEFIT that if there is a show-down then it costs nothing for you to fold since the pot remains in place (actually reestablished by the loser of the showdown). In a loose game this is a lot like playing with no ante.

Anyway, opting to show-down is basically an even money proposition: you either win or lose the size of the pot. If you win there is little difference to you between a contested pot and an uncontested pot. You should therefore declare in when you have a 50:50 or better chance of winning. You can theoretically calculate the show-down minimum value to declare in or out; and it depends on N. For some reason I've gone brain dead and have the actual calculation; but its pretty close to 1/n (play your best 1/nth hands).

This doesn't change whether the game is loose: if you declare "In" with say JsUp or better it doesn't matter to you if players declare in with KK or better. Well, it DOES matter since that makes the next pot juicier, but it doesn't affect your EV for this hand.

If the game it tight you CAN realistically bluff; and bluff often. If they are consistently tight (and nobody is IN over half the time) you can bluff ALL the time.

- Louie

[jedi]

While I'm enjoying this discussion, let's change the game a little bit.

If NO ONE plays, all hands are revealed and the best hand has to match the pot. How does this change your strategy?

[Aisthesis]

That pretty much sums it up. Seems very logical to me.

Two comments:

1) If there is a showdown involving more than just 2 players, the pot actually INCREASES in size, hence yet another benefit.

2) 1/n isn't a bad approximation on this. More precisely, if p is the percentile ranking of your hand (weighted among 5 card hands with hand-frequency and such) and n is the number of players, you should want .50 = 1 - (p)~(n-1), hence (p)~(n-1) = .50 or p to be the (n-1)th root of .50
I don't think 1/n will be all that far off from that for n<=10.

[Aisthesis]

That's an interesting one. A precise answer is tough, so I'll state the obvious: You should call more often... [img]/images/graemlins/smile.gif[/img]

Also, you want those guys who only play extremely strong hands at your table...

[donkeyradish]

Come to think of it, if you have a relatively giant stack of chips and your opponents are all glued to their chairs, couldn't you simply call every time no matter what?

[well]

Two aspects of the game are not clear to me:

1) If someone loses the showdown, he must pay the potsize and this goes into the next pot,
do in this case the players still ante for the next game?
2) If there are more than two players in the showdown, do all losing players pay, or just the player
with the worst hand?

Thanks.

[donkeyradish]

1) We play it that all players ante each hand, yes. But that's just our rule, there is no 'general' rule I know of.

2) In our game, all losing players pay. But your alternative suggestion would work too. Depends how fast you want the pot to grow.

good luck