Check my math!

[B-squared]

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

[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

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.
?

[Icanhastreebet]

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

.

[B-squared]

.

Oops right you are, thankyou!

[spoonitnow]

Oops right you are, thankyou!

Icanhastreebet is yAAwn from the chat btw.

[spoonitnow]

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.

[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.

[B-squared]

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!

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.

[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!

[B-squared]

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!

[spoonitnow]

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