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  #17  
Old 12-30-2005, 01:16 PM
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Eh, seems like these top pair / overpair hands vs. a lot of resistance are the most common difficulty.

My first thought was to immediately call with only $4 or $5 more to go. However, looking at the board and the action, I'm starting to like the fold.

Here are my numbers on it, using Harrington's rule that there's always at least a 10% chance of bluffing.

First, given villain's stats, I think we can safely rule out JJ/QQ/KK/AA/AK. A PFR of 10, with only folds in front of him would certainly raise these hands.

AT is also very unlikely, given your hand. KT? Maybe, but a VPIP of 20 is fairly tight.

The preflop call would certainly make sense with a small pocket pair. I really am having trouble putting him on any other hand. Why?

(1) There's no flush draw out there to semi-bluff
(2) He could semi-bluff with the OESD, but then he would have had to call the PFR with something like 97 or Q9. PLUS, he lead the flop, got reraised, and then pushed.

For the above argument, I'm going to run the numbers assuming he has 88 (numbers for 44,TT are about the same). I'll include a 10% chance of a sheer bluff (say top pair only), and a 10% chance that he's holding a lower overpair (JJ,QQ,KK)

Total Bluff (just top pair,3straight)
Td 9c - 24% to win
As Ac - 76% to win

Vs. Lower Overpair
As Ac - 92%
Kd Kh - 8%

Vs. Set
As Ac - 9%
8c 8h - 92%

If you call and lose, you lose 4.92 more.
If you call and win, you net 28.37

so,
SET: (.92)(-4.92)+(.08)(28.37) = -2.25
KK: (.92)(28.37)+(.08)(-4.92) = +25.7
Bluff: (.76)(28.37) + (.24)(-4.92) = +20.38

overall,
.80(-2.25)+.10(25.7)+.10(20.38) = +2.8

So, this looks like a positive EV call, if you think there's at least a 10% chance he's on a total bluff, and a 10% chance he has just an overpair.

If you assume only the 10% chance of the overpair:
(.9)(-2.25)+(.1)(25.7) = .54

Still slightly +EV here.

Given that, I think a call is alright.
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