face up game, collusion proof ?

Imagine a hypothetical poker game, where all cards where dealt face up, especially all player cards. The game would feature several no-limit betting rounds about not-yet dealt cards which might improve everyones hands. (Say, the game plays like NL Texas Holdem, expect all cards are face up).

As I would understand this game, in a heads up scenario the perfect playing strategy would be to exactly play the odds of the upcoming cards, i.e. always offering your opponent zero-EV (so you don't care about the opponents reaction). You would then hope your opponent could not implement this perfect strategy, and grind out all his improper bets. At least you would not give up EV playing this game, right ? (of course the rake would kill you)

But what if this game would be played by 3 people, all following a similar kind of "perfect strategy" (i.e. all offered play devisions would yield the same EV for any player). My question is: Would one player be in a losing position if (for him unknowningly) two players would play from the same bankroll, or those two players would collude their play ?

I believe the answer is yes.

The player in question ONLY has all the info he needs to make perfect EV decisions if he can predict the opponents strategy. Presumably, everyone is trying to maximize their EV, so you can create a strategy based on that in a regular game.

But if the strategy of the other 2 players is to beat YOU, they may make 'unusual' decisions that you would not have predicted otherwise, which could cost you some EV. However, it wouldn't last long, once you realized what they were up to. You could adjust your strategy to facing the two of them.

Quote: dwheatley

I believe the answer is yes.

The player in question ONLY has all the info he needs to make perfect EV decisions if he can predict the opponents strategy. Presumably, everyone is trying to maximize their EV, so you can create a strategy based on that in a regular game.

But if the strategy of the other 2 players is to beat YOU, they may make 'unusual' decisions that you would not have predicted otherwise, which could cost you some EV. However, it wouldn't last long, once you realized what they were up to. You could adjust your strategy to facing the two of them.

What strategy would allow a single hand to be +EV vs. two hands?

In this scenario, I imagine the perfect strategy is for the best hand pre-flop to always raise, and the worst of the three hands to always fold. However, two colluding hands can "squeeze" the single player with a middle hand by having the worst hand re-raise instead of folding. Even when the single player has the best pre-flop hand, he will either have the middle hand fold to his raise, or he will have to face two callers, either of whom may catch a hand on the flop. I can't see a scenario where the single player has a chance to turn the tables.

That's also what I thought (the players inherent disadvantage) - although I couldn't think about a specific scenario (although the team re-raise should have been quite obvious). Thanks for your thoughts !

Ever played Blind Man's Bluff?