On page 173 of M.O.P., the authors computer the EV of betting an Ace for bet size r as the following:
<A, bet r> = ((r-r^2))/((2)(1+r))
This seems wrong. The EV of betting an Ace is:
P(Y has King)* P (Y calls with King)* (Bet Size)
We know that Y will call with (1 - a) of Y's Kings, and so we have:
<A, bet r> = (1/2)*(1 - r/(1+r))(r)
But:
1 - r/(r+1) = (r + 1 - r)/(r+1) = 1/(r+1)
Thus:
<A, bet r> = ((1/2)*(1/(r+1)*(r) = (r)/(2*(r+1))
....
What the hell? Is this another typo? It doesn't seem to be, because they calculate the indifference between betting and checking as if their formula is correct.
