I'm a long-time lurker and I'd just like to thank all the posters here for helping me improve my game tremendously. Something I don't think happens enough on this forum, however, is looking at situations mathematitcally, especially ones like this one where the ranges are defined and there is only one card to come.

Even in a situation like this one, where if we are sure villain won't lay down the best hand calling down is quite clearly wrong, I think its useful to see how the numbers play out. I also think it would be useful to show how big his range would have to be in order for calling down to be +EV = 0.

15/12 is prett tight. If we take his 3betting range to be AT+, 77+, KQ, and KJs:

_______________#of Combos___# of Outs
A. AK,AQ,AJ____36___________3
B. 77,99, AA___9____________0
c. 66,88_______12___________6
D. TT,JJ,QQ,KK_24___________3
E. AT__________6____________Tied
F. KhQh/KhJh___2____________14 outs against (flush draw)
G. KQ/Kjs______18___________6 outs against

Total Combos: 107
Cost of Calling Down: 2BB
Payoff if when we win: 5BB in pot now + another BB on river = 6BB*
*Good approximation, since if we hit our Ace he will check call the river, and if we hit our ten and it is actually an out is doubtful he will payoff more than that.

EV of Calling Down =
A. (36/107)[(43/46)(-2BB) + (3/46)(6BB)]
B. (9/107)[(-2BB)]
C. (12/107)[(40/46)(-2BB) + (6/46)(6BB)]
D. (24/107)[(43/46)(-2BB) + (3/46)(6BB)]
E. (6/107)[2BB]
F. (2/107)[(14/46)(-2BB)+(32/46)(6BB)]
G. (18/107)[(6/46)(-2BB)+(40/46)(6BB)]

= -0.09BB
no flush draw = -0.066BB
no KJs = -0.274BB

Adding only KJo to his range makes our calldown enormously profitable: +0.417BB.
The calldown is EV neutral if he 3bets KJo as little as 1/6 of the time.

So in summary, the +EV of this calldown depends very heavily on the combos that you are ahead of. If the TAG is 3betting A8o and A7s type hands and following through with them on the turn then calling down is a must. If you suspect he's 3betting QJs, you really should be calling down.

Let me know if you guys think this type of analysis is useful, or if you think that i'm just wasting everybody's time.