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If we give villain a river range:
- overcards: AQ+ (28 combos). I purposedly limited the range to AQ+ to reflect the fact that he does not always call the flop with his naked A high hands.
- pairs: A4, 66-88, 22-33 (42 combos)
- busted FD: let's say we add 22 combos of flush draws (KhQh, AhJh, KhJh, QhJh, AhTh, KhTh, QhTh, JhTh, Ah8h, Kh8h, Qh8h, Th8h, Ah7h, 8h7h, Ah6h, 8h6h, 7h6h, Ah5h, 7h5h, 6h5h, Ah3h, Ah2h). Note that a good deal of these beat Hero if Hero checks back the river.
If Hero checks back the river, the above range wins 88.6% of the time.
We assume he always folds his A high hands and busted flush draws and always calls with his pairs. So he calls (and wins) 45.7% of the time.
EV of bluffing = 0.543*$1.45-0.457*0$.60=$0.51
EV of checking = 0.114*$1.45 = $0.17
So it looks to me that in the end, bluffing is much better than checking.
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