[Jerrod Ankenman]

[ QUOTE ]
jerrod,

Are we assuming Y knows X's calling frequency and X knows
Y's bluffing frequency on every street? They just don't
know what the other is doing on this hand.
Under those conditions Y must bluff 39.6% of his other
hands. If he bluffs less often, X can hold Y to less
than -$0.5 by folding every time on street one. That's
more than two bluffs for every value bet on street one.
Haven't done any follow up analyses on later streets
after this overbluffing on street one yet. But think
it's possible X should call more than 1/7.

jogs

[/ QUOTE ]

Well, when finding the optimal strategy, you assume that both players are maximally exploiting each other's strategy.

It turns out that the non-clairvoyant guy just calls (1-alpha) of the time on each street. For him it is kind of like three separate streets chained together.

You're right about the overbluffing on street 1. Y bluffs a whole bunch of hands on the first street, way more than he could if it were a one-street game. X can't exploit this because when he calls, he now faces more streets of betting.