[DeeJ]

He either has 44 or 55. He has 3 ways of holding 44 and 1 way of holding 55. I think he'd play them both the same with an AF of 2. but see below. He will more likely cap a 3 bet only if he has quads because he'd fear you holding a 5X or 22 hand. So yes, I 3-bet and call a cap because it's more likely he holds 44. The penalty is worse if he holds 55.

If I can put him on 44 or 55
P(44) = 0.75 P(55) = 0.25, how many river bets in excess of the one he's called might I win?

<font color="red"> 3-betting </font>

Let's say he caps here with 44 50% of the time cuz he's aggressive but not stupid.

44: you win 3 BB 50% of the time and 1 BB 50% of the time. So you win average of 2BB when he holds 44 which is 75% of the time. <font color="blue"> +1.5 BB </font>

55: he caps 100%, you lose 3 BB all of the time @ 25%. <font color="blue"> -.75 BB </font>

3 betting has a net expectation of +.75 BB

<font color="red"> just calling </font>
44: you win 1 BB <font color="blue"> +0.75BB </font>
55: you lose 1BB <font color="blue"> -0.25 BB </font>

calling has a net expectation of +.5 BB


Buuuut, if you think his river raise means he's more likely to hold 55 rather than 44, say with 50/50 likelihood the numbers go :

3-bet with him holding 44 : +1BB
3-bet with him holding 55 : -1.5BB
call with him holding 44 : +0.5 BB
call with him holding 55 : -0.5 BB

So I guess, if you can put him on 44 or 55 (I totally rule out A3 when he raises the river) and you think his river raise makes it a bit more likely he holds 55 rather than 44, I think you should call.

uber-caveat : This situation happens so infrequently I don't think it's worth worrying about though (despite this post pretending otherwise) [img]/images/graemlins/grin.gif[/img] but probably the principle applies for lesser hands eg set over set, frush over frush...