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.