Check my math!

Hey, I was hoping some more experienced players could give me some feedback on this exercise spoony gave me:

Here is the scenario:

• Hero raises pre-flop from early position with AK to $0.08 (playing 2NL).
• A tight-aggressive player on the button calls and everyone else folds.
• The flop comes Qs9h5c and the flop pot is $0.19.
• I want to figure out if a continuation bet of $0.14 is going to be profitable.

My raise would be 0.14 into a 0.19 pot, so: 0.14/(0.14+0.19) = 33%
I need the villain to fold more than 33% of the time for the bluff to be profitable.

I have come up with an arbitrary range for the villain. I see all sorts in 2NL so I don't think this is too unrealistic...

Villain Preflop range: 99+,ATs+,KJs+,QJs,AJo+,KJo+,QJo
Meaning that (taking into account that I hold AK) he has 118/1176 combos that he calls with = 10.03%

Villain Postflop range (in response to my raise): QQ+,99,AQs,KQs,QJs,AQo,KQo,QJo
54/1176 combos = 4.59%

So villain is folding 54/118 to my raise = 46% of the time. 46 > 33, so the bluff is profitable.

Criticism would be much appreciated! Cheers big ears

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

I bet 18c into a 21c pot: 18/(18+21) = 39%. I need the villain to fold more than 39% of the time to make the bluff profitable.

I put his preflop calling range as being super wide:
33-22,K9s-K2s,Q9s-Q2s,J9s+,J3s-J2s,T3s-T2s,93s-92s,83s-82s,73s-72s,63s-62s,53s-52s,42s+,32s,A5o-A2o,KTo-K2o,QTo-Q2o,J9o+,J3o-J2o,T3o-T2o,93o-92o,83o-82o,73o-72o,63o-62o,53o-52o,42o+,32o
Or about 500/1081 (46%) of hands.

By the river, I put his range around (though I didn't think he was slowplaying me, so I think realistically his range is slightly smaller than this):
33-22,K9s-K2s,Q9s-Q2s,32s,K9o-K2o,Q9o-Q2o,32o
About 201/1081 (19%)

201/500 = 40%

40 > 39, so the bluff is about break even in terms of its profitability.
?

Originally Posted by B-squared

My raise would be 0.14 into a 0.19 pot, so: 0.14/(0.14+0.19) = 42%

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Originally Posted by Icanhastreebet

.

Oops right you are, thankyou!

Originally Posted by B-squared

Oops right you are, thankyou!

Icanhastreebet is yAAwn from the chat btw.

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.

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.

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.

This is somewhat off-topic, but your use of the terminology (raise/re-raise) is very slightly off, and it could throw someone off if they weren't familiar with the hands you were talking about.

The first bet on a street is called a "bet." For example, on the turn in that hand, when he puts in $0.02, that's a bet because it's the first time money is put in on the street.

If someone raises that, then it's called a "raise." For example, on the turn you raised to $0.08. You can think of this as the second bet.

If there's a raise put in after that, then we call it a "re-raise." For example, if instead of calling he was to raise you to $0.20, that would be a re-raise. The third, fourth, fifth, etc bets can be called re-raises.

Pre-flop, the posting of the big blind is considered the first bet, so let's say you raise to $0.08 from early position, that's the second bet and is correctly called a raise. If it folds around to someone who re-raises you to $0.22, that's the third bet (which is why the first re-raise before the flop is called a 3-bet). Then if you were to re-raise that person to $0.60, that's the fourth bet (which is called a 4-bet), and so on.

Hope that helps!

Originally Posted by spoonitnow

This is somewhat off-topic, but your use of the terminology (raise/re-raise) is very slightly off, and it could throw someone off if they weren't familiar with the hands you were talking about.

The first bet on a street is called a "bet." For example, on the turn in that hand, when he puts in $0.02, that's a bet because it's the first time money is put in on the street.

If someone raises that, then it's called a "raise." For example, on the turn you raised to $0.08. You can think of this as the second bet.

If there's a raise put in after that, then we call it a "re-raise." For example, if instead of calling he was to raise you to $0.20, that would be a re-raise. The third, fourth, fifth, etc bets can be called re-raises.

Pre-flop, the posting of the big blind is considered the first bet, so let's say you raise to $0.08 from early position, that's the second bet and is correctly called a raise. If it folds around to someone who re-raises you to $0.22, that's the third bet (which is why the first re-raise before the flop is called a 3-bet). Then if you were to re-raise that person to $0.60, that's the fourth bet (which is called a 4-bet), and so on.

Hope that helps!

Oops that's pretty embarrassing...thanks for the tip!

It's cool. Every single person who has done well with poker was screwing that up at some point, I promise you lol.