at page 173, there is:
X, then, has the following equity from betting t when he holds an ace and Y holds a king:
<A vs K, bet t >=(t)(2/(1+t)-1)=(t-t^2)/(t+1)
and for Y, the fraction of all calling hands that are king is 1/(1+t)-1/2.
So the probability that Y calls is the with king is that 1/(1+t)-1/2 and
probability that he doesnt call with king is 1/2-[1/(1+t)-1/2]
and when he calls, X win t+1, and when he doesnt, X wins 1.
So, the equity would be:
(1+t)*[1/(1+t)-1/2]+1*[1/2-[1/(1+t)-1/2]]
but this isnt the same as in the book.