I wanted to expand a little on a comment I made in a thread below about the validity of zero sum games, where the number of players is > 2. I decided to start a new thread, because I think this is an important point to consider, for blackjack players thinking about spreading some action into poker and similar games.

I gave a simple example below ( http://www.advantageplayer.com/black....cgi?read=9342 ) showing how it's possible to have a negative EV in a poker game, even if you play perfectly, simply because the others in the game know one another well. The fact that they don't know you does not make up for the fact that you don't know them, simply because you are one, and they are many.

No prior arrangement, or conscious "collusion" is necessary for this situation to exist. In fact, far from eschewing special knowkledge, poker players pride themselves on their ability to "read" opponents. After further reading, I now believe the situation I described is the rule, rather than the exception. It's "the pink elephant in the living room," that good poker players know about, but don't like to discuss.

Poker players strain to find the right term. "Collusion," which implies a prior arrangement between two or more players, and private signals at the table, is definitely regarded as cheating. But "implicit collusion," or "semi-collusion," which crop up in the reading below, are not considered cheating by experienced poker players.

Some relevant web pages:
http://en.wikipedia.org/wiki/Poker_collusion
http://www.lasvegas-online-casino.co...llusion-poker/
http://groups.yahoo.com/group/ba-poker/message/146
http://www.twoplustwo.com/digests/ge...msg.html#22040 [Read especially the posts by Dirk(MildManneredMathMan) and "So then, is THIS "wrong" ?" Posted by: J D about a third of the way down the page]

Here is another simple example of a no-win poker situation. Suppose you're in the tournament situation (like the World Series of Poker), and you're playing a very simple poker variant where there are only two viable strategies. Strategy1 is superior to Strategy2, since in a head to head clash, it wins $200 with probability 0.75, and loses $200 with probability 0.25. Strategy1 vs Strategy1 results in a 50/50 chance to win $100. (S1 is "conservative".) Strategy2 vs Strategy2 results in a 50/50 chance to win $300. (S2 is "aggressive.") Whoever wins $10,000 first wins the grand prize of 1 million dollars.

Now, three players remain in this tournament, A, B, and C. They have equal starting capital (say, $2,000). All three players know each other intimately. A is the best player. He uses Strategy1 all the time. B and C know this, so out of fear (or respect?) they always follow suit and play S1 when A is in the pot. When A drops out, however, and they play each other, they always play S2, because they know the other player isn't that good, and they crave the action.

Player A -- the best player in the group -- has virtually no chance to win in this situation. This is not some strange anamoly. It's the general rule in n-player games where n>2, and you accumulate points toward a prize. The other players have to conspire to give you a fair chance to win, no matter how good you are.

I think this is very different from blackjack, where you have a known expectation if you play a well-defined strategy perfectly, and any additional information can only make it better. There's no need to "hold the opponent's strategy invariant" in order to create a Nash Equilibrium as a first step toward calculating EV. Blackjack players thinking of turning to professional poker, as a source of income, might want to consider these facts.

ETF