Preflop
UTG limps. Other players fold. Button raises. UTG calls.
Flop:
A
UTG checks. Button bets. UTG calls.
Turn:
A
UTG checks. Button bets. UTG calls.
River:
A
UTG checks. Button . . .
Now consider the button's correct play if he has:
- A
K 
- A
T 
- A
A 
For AK, if he bets the pot he's probably a dog to the range of hands that call him. If he bets something small, he can often get paid by a smaller ace or maybe even a smaller pair. So if he bets, a smaller bet seems better.
For the other hands, the button can bet something more and still get paid. A strong ace pays off AT.
A flush or A3 certainly pays off AA. So a larger bet seems better.
In practice, I probably check behind with the AK and maybe the AT. Why? Isn't there a bet amount that insures I'm a favorite to the range of callers? Is it just that I'm afraid of being bluffed? Part of the problem is that I can't just bet proportional to my hand strength without giving away information.
The fact that he might bluff in itself shouldn't dissuade me from betting. I can still pick off the bluff. Maybe I should occasionally just sell the big hands cheap on the river, inviting an occasional bluff. And maybe I should sometimes pay off the raise with one pair. It's clear that I can't bet small with AK and then fold every time I'm raised. That's pretty easy to exploit.
Sklansky and Miller's book has made me challenge some pretty basic crap.
Fire away.
