Check my math!

Originally Posted by B-squared

A second bluffing scenario. I am looking at whether my bluff on the river was profitable:

Full Tilt No-Limit Hold'em, $0.02 BB (5 handed) - Full Tilt Converter Tool from http://www.flopturnriver.com

SB is very loose and passive. A 0.02c raise was his go-to bet when he was bluffing (badly).

UTG ($2.78)
MP ($1.03)
Button ($1.33)
SB ($0.91)
Hero (BB) ($1.91)

Preflop: Hero is BB with 4, A
3 folds, SB calls $0.01, Hero checks

Flop: ($0.04) Q, K, 3 (2 players)
SB bets $0.02, Hero calls $0.02

Turn: ($0.08) 2 (2 players)
SB bets $0.02, Hero raises to $0.08, SB calls $0.06

River: ($0.24) 7 (2 players)
SB checks, Hero bets $0.18, 1 fold

Total pot: $0.24 | Rake: $0.01

Results below:

Spoiler: Show

Hero didn't show 4, A (high card, Ace).
Outcome: Hero won $0.23

Which better hands are you getting to fold here? I want you to think about the merits of checking instead of bluffing on the river.

Originally Posted by spoonitnow

Alright so I gave you this problem, and now I'm going to work it out for you based on your assumptions and check what you've got here as far as the combinations go. I might make a mistake but let's hope I don't.

Pre-flop Range: 99+,ATs+,KJs+,QJs,AJo+,KJo+,QJo

I'll make a suggestion here that you combine the hands that include both suited and offsuit versions when listing ranges to make things more concise and easier to work with. For example:

New Pre-flop Range: 99+, AJ+, ATs, KJ+, QJ

We hold AK. I didn't say whether it was suited or offsuit, but it won't matter a lot for this example. If you want to organize the counting of these combinations, then a quick way to do it is just list out how many combinations there are of each hand in each grouping. For example:

99+ = 99(6), TT(6), JJ(6), QQ(6), KK(3), AA(3) = 30 combos
AJ+ = AJ(12), AQ(12), AK(9) = 33 combos
ATs = 3 combos
KJ+ = KJ(12), KQ(12) = 24 combos
QJ = 16 combos

This gives us a total of 106 before the flop. The flop comes Qs9h5c, so here's the new range breakdown:

99+ = 99(3), TT(6), JJ(6), QQ(3), KK(3), AA(3) = 24 combos
AJ+ = AJ(12), AQ(9), AK(9) = 30 combos
ATs = 3 combos
KJ+ = KJ(12), KQ(9) = 21 combos
QJ = 12 combos

For a total of 90 combos after the flop. You think he's folding everything but QQ+, 99, AQ, KQ, QJ. The combinations for his continuing range are:

AA(3), KK(3), QQ(3), 99(3), AQ(9), KQ(9), QJ(12) = 42 combinations

Based on this assumption, he's continuing with 42/90 so he's folding 48/90 = 53.33 percent.

Ah yep, you're right, I didn't adjust his preflop range in light of the flop and for some reason I just pretended my AK wasn't relevant when I figured out his postflop range. Thanks!

Originally Posted by spoonitnow

Which better hands are you getting to fold here? I want you to think about the merits of checking instead of bluffing on the river.

That's a good point...My decision to bet so hard into this hand was based purely off his really transparent betting patterns. I was fairly confident that he had hit nothing- maybe a pair of 3s. Thinking about it more, perhaps he was on a straight draw... But if my range of him on the river is realistic then I think he would have called me with pretty much any of the hands remaining in that range, meaning it probably was better to check. However, I think a large part of the issue is I don't think I have put him on particularly realistic ranges. In retrospect, I think his preflop range was way wider than I specified... and I don't think I have fully taken into account the implications of him calling my reraise on the turn.