Theory of Indian Poker

[cbloom]

I've been thinking about "Indian Poker". Each player takes a card and puts it on their forehead, you don't look at your own card but you see all the other cards. You each ante 1 bet. Betting then proceeds like normal poker, you may bet, raise, check, call, fold. If you get to a showdown, the highest card wins.

This game seems simple enough (heads-up, anyway) to formulate an exact optimal strategy, but I've been getting weird results. Has anyone seen anything about this? Game Theory of "Indian Poker"?

[Dentist]

I enjoy this game - heads up it goes into many levels of thinking, especially when played pot or no-limit.

You know what he has, but you don't know what you have.

essentially, his card doesn't matter because he doesn't know what it is, his reaction to your bet will be solely based on what he sees that YOU have.

Also, a player might reason that you are betting on what you see that HE has.

The psychology in this game is intense as well.

Heads up I think it is nearly correct to bet nearly every hand, of course if you do this, he will figure out that anytime you hold an 8 or below that he should call, and that a 9 or above requires some thought.

I would be interested in the theory behind check-raising and raising in this game for sure.

I've also played it in a group of 4, pot-limit.... nothing is worse than trying to run a bluff when you have a 2-5 on your head.....

Either way, it's a fun game, exact game theory I don't think I'd bother to calculate....

[MMMMMM]

I never read anything about the strategy of Indian Poker. Most people probably think it's just a joke. Many years ago however I did manage a very nice win at it. The game was 7-handed, we played it lowball, and it was a blast.

[cbloom]

Yeah, I think most people think it's just a silly game, but actually a skilled player can easily take a huge amount of money off novices very quickly. There are several very profitable configurations - when someone else has a deuce, when two other players have the same rank card, etc. Also, since you see the other cards, the order they occur is very important. For example three-handed if you're first to act and you see {K,4} it's very different than when you see {4,K} ; I think think you probably check the first one to see what the K does, but bet the second one, because the 4 will fold fearing the K and the K may fold if you have anything decent.

The heads-up game is just an inverted version of "one card poker", but the multi-way game is much more complex.

[Wake up CALL]

"This game seems simple enough (heads-up, anyway) to formulate an exact optimal strategy, but I've been getting weird results. Has anyone seen anything about this?"

The optimal strategy in Indian Poker is to sit facing a mirror.

[MMMMMM]

Yeah it's actually a game where it's pretty important to be able to trust the other players.

I can also imagine getting some pretty 'weird results' if your opponent were the one sitting facing a mirror. LOL.

[cbloom]

For those who are curious, this is what I come up with for a simplified version of pot-size-bet heads-up Indian Poker.

Player I has card X; player II has card Y. So I sees Y, II sees X.

I bets if Y <= J or >= A (and half of the time with K)
II calls if X <= 9

In practice this is very similar to just saying I almost always bets and II calls if X <= 8-10. This isn't accounting for check-raising or anything like that which is pretty important.

[Crazy Clown]

One note, if you ever play w/ spectators like I did 2 years ago, the spectators eyes will be on the player w/ the highest card. I still remember betting into a K heads up and then pulling an A off my forehead. And players who are in the hand will ignore the person with the best hand. They glance at him and look away quickly and look longer at the people w/ small cards.