Game theory question re "The Mathematics of Poker"

[de Moivre]

I'm having a little trouble understanding "The Mathematics of Poker" by Chen and Ankenman.

Take for example the AKQ game #1 on page 140. They give the "ex-showdown" payoff matrix. The term is explained on page 85---it means equity outside of the current pot. Why do they do that? Why are the antes in the pot not included in the payoff matrix, since they're still up for grabs? It never would have occurred to me to omit them like that, and I don't like to accept something just because the experts say so. There must be a good reason.

[ShaneP]

At a quick glance, that game is a half street game; the second player can either call or fold if there is a bet by the first player, and just check if there is no bet. So looking at the Y has a K, X has an A, normally X would win the pot. That is the base payoff that they are using.

Then, if Y bets and X folds, Y gets the pot that he wouldn't have gotten earlier, so his payoff is 2 bigger than the base (or +2). If X calls, then Y loses one more than the base case (the -1). So the initial pot of 2 is in fact in the matrix, it's just that the payoffs are the deviations from the amounts the players would get in the check-check situation.

Shane

[de Moivre]

Thanks, Shane, that helps.

[jogsxyz]

[ QUOTE ]
I'm having a little trouble understanding "The Mathematics of Poker" by Chen and Ankenman.

Take for example the AKQ game #1 on page 140. They give the "ex-showdown" payoff matrix. The term is explained on page 85---it means equity outside of the current pot. Why do they do that? Why are the antes in the pot not included in the payoff matrix, since they're still up for grabs? It never would have occurred to me to omit them like that, and I don't like to accept something just because the experts say so. There must be a good reason.

[/ QUOTE ]

The antes are included in the pot size.