[elindauer]

This is a pretty easy situation to deal with mathematically.

Let's assume the worst case, where the opponent will bet the river when he really has a queen, but check behind when he was bluffing. Let's also assume that when you catch an ace, you win, on average, another 1.5 BBs. Let's call p(bluff) x, which means p(!bluff) = 1-x. Then we can figure the exact probability he must be bluffing for you to consider folding, like this:

when you miss...

44/46

and he's bluffing

x

you win

12.5 BB.

Similarly, when you miss, and he's not bluffing, it'll cost you 3 BB:

44/46*(12.5x - 3(1-x))

and when you catch, you win 14BB...

44/46 * (12.5x - 3(1-x)) + 2/46 (14) = EV

what does x have to be so that calling has 0 EV? Just set this to zero and solve for x. And you thought your middle school algebra class wouldn't be useful in real life. Shame on you.

x ~= .15

So your opponent must be bluffing 15% of the time or less for calling down to be the best play. So this situation is easy to handle, if you know your opponents tendencies. If you don't, it's hard. Folding is the bigger mistake though, so if you're unsure, call down.

Note that if your opponent never bluffs, calling down costs you a lot of money, over two big bets wasted right there. Worse, if he bluffs a lot and you fold, you've given away even more. Finally, note that this situation is very common. What's the point? This decision is worth a lot of money to you if you can get it right consistently, so pay attention to your opponents' tendencies.

Good luck.
Eric