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Thread: ET Fan: More on poker and n-player games

  1. #1
    ET Fan
    Guest

    ET Fan: More on poker and n-player games

    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

  2. #2
    SOTSOG
    Guest

    SOTSOG: off-topic N player games

    I remember in a poker book the author was trying to demonstrate the standard deviation of Hold 'Em. He had 10 identical perfect computer players play a lifetime of poker (about 30 million hands).

    In theory, all players should have ended up about even. 2 of the players ended at a lifetime loss, and 20K - 30K seperated the rest of the players. Don't remember the exact wagering amounts, but I remember it seemed to demonstrate that Standard Deviation is roughly equal to that found in Blackjack.

    The really interesting thing was, he then added to non-perfect players to the game (one was tweaked to play slightly loose, the other was a bit of a rock).

    After the same 30 million hands, the loose player was behind about 6 million, the tight player was behind about 4 million, and the 8 perfect players were all way ahead in the black.

    What really struck me:
    1) When in doubt, it is better to play tight rather than loose.
    2) Find a game with 2 bad players in it!

    I think weak players are the poker equiv of good pen in blackjack, if not more so.

  3. #3
    strix varia
    Guest

    strix varia: thinking like a bj player

    You are thinking exactly like a bj player. First, on your comment about playing with regulars, when you first sit down I agree that you are probably at a disadvantage. However, you should see people making mistakes and therefore find out whether the game is profitable or not. If you don't see mistakes, you leave. And if you are a professional player, most of the time you are the regular. So you are only referring to recreation poker players.

    In your second point, you only go to the second level of thinking in poker play. The expert players in poker think to multiple levels. You stated that the other two know how player A plays, so thus they can team up on him. You are only thinking to the second level. Player A would realize this immediately and know that his opponents know how he plays, so he would change his strategy. However, B & C will now change their strategies. However, since A is the expert he will change his strategy depending on how B & C play him. Like I said, in the higher limit games, players are thinking to 4 or even higher levels. Your simple assumptions do not apply.

    Example of 4 levels of think

    Player A thinks he knows what B has
    Player B knows that Player A thinks he knows what he has
    Player A knows that Player B knows
    Player B knows that player A knows that player B knows

    Whoever the expert is will win this battle, and put a correct read on his opponent.

  4. #4
    SOTSOG
    Guest

    SOTSOG: Re: thinking like a bj player

    Player A thinks he knows what B has
    Player B knows that Player A thinks he knows what he has
    Player A knows that Player B knows
    Player B knows that player A knows that player B knows

    And a 3 of Clubs comes out on the river, giving Player C a nut flush, and he rakes in all of Player A and B's money.

    LOL


  5. #5
    ET Fan
    Guest

    ET Fan: Incorrect

    > And if you are a
    > professional player, most of the time you
    > are the regular. So you are only referring
    > to recreation poker players.

    Not true. The concept holds for any set of players of equal ability. If implicit collusion wasn't an important consideration, poker players wouldn't be so touchy on the subject.

    > In your second point, you only go to the
    > second level of thinking in poker play. The
    > expert players in poker think to multiple
    > levels. You stated that the other two know
    > how player A plays, so thus they can team up
    > on him. You are only thinking to the second
    > level. Player A would realize this
    > immediately and know that his opponents know
    > how he plays, so he would change his
    > strategy. However, B & C will now change
    > their strategies. However, since A is the
    > expert he will change his strategy depending
    > on how B & C play him. Like I said, in
    > the higher limit games, players are thinking
    > to 4 or even higher levels. Your simple
    > assumptions do not apply.

    > Example of 4 levels of think

    > Player A thinks he knows what B has
    > Player B knows that Player A thinks he knows
    > what he has
    > Player A knows that Player B knows
    > Player B knows that player A knows that
    > player B knows

    > Whoever the expert is will win this battle,
    > and put a correct read on his opponent.

    Completely wrong. Just do the math. It simply doesn't matter how A plays in this situation. If he plays S2, he will lose to B and C who are playing S1 against him. If he plays S1, he loses as stated above, because B and C's results have higher variance, in the pots where A drops out, so if B or C tap out, A is left fighting an opponent with a larger bankroll.

    You would like to create more strategies than just S1 and S2, going against premise. These examples need to be simplified to show the general concept. The complex nature of real poker simply creates more opportunities for the general ideas to express themselves.

    You can't undo game theory with poker theory.

    ETF

  6. #6
    strix varia
    Guest

    strix varia: Re: Incorrect

    I disagree. And will not drag this into a long poker discussion regarding this. PLayers of equal ability? Who said that? You definitely didn't in your original post. You can't quantify poker strategy into S1 like blackjack. It varies all the time and changes all the time. Anyways, my point is the expert player will get the money. Expert players play against weaker opponents who make mistakes. What is your point again? It is kind of clouded for me. If your point is that the expert poker player can't beat mediocre B & C, because they could implicitly collude, then my point is maybe B & C aren't mediocre. If all three are of equal expertise, then sure I agree. What's the point of B & C implicitly colluding, when they go ahead and make silly mistakes that A takes advantage of.

    > Not true. The concept holds for any set of
    > players of equal ability . If implicit
    > collusion wasn't an important consideration,
    > poker players wouldn't be so touchy on the
    > subject.

    > Completely wrong. Just do the math. It
    > simply doesn't matter how A plays in this
    > situation. If he plays S2, he will lose to B
    > and C who are playing S1 against him. If he
    > plays S1, he loses as stated above, because
    > B and C's results have higher variance, in
    > the pots where A drops out, so if B or C tap
    > out, A is left fighting an opponent with a
    > larger bankroll.

    > You would like to create more strategies
    > than just S1 and S2, going against premise.
    > These examples need to be simplified to show
    > the general concept. The complex nature of
    > real poker simply creates more
    > opportunities for the general ideas to
    > express themselves.

    > You can't undo game theory with poker
    > theory.

    > ETF

  7. #7
    ET Fan
    Guest

    ET Fan: The point

    > What is your point again? It
    > is kind of clouded for me. If your point is
    > that the expert poker player can't beat
    > mediocre B & C, because they could
    > implicitly collude, then my point is maybe B
    > & C aren't mediocre. If all three are of
    > equal expertise, then sure I agree. What's
    > the point of B & C implicitly colluding,
    > when they go ahead and make silly mistakes
    > that A takes advantage of.

    The point is they don't. B and C play perfectly against A. B and C only play stupidly when playing against each other. They both ignore a strategy that would give them a 3 to 1 edge on those hands -- and make them a strong favorite to win the tournament -- yet A suffers nost of the brunt of their stupidity! He has very little chance to win. Unless you want to call this implicit collusion, in which case they profit by their implicit collusion (which poker players think is ethical). I don't know how to make it any clearer.

    Without the $1M grand prize, the game would be fair. A would consistently eke out a small win, while B and C would lose or win big, but lose a little on average.

    For the rest of it, you're confusing my two (2) hypos.

    ETF

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