In the 3rd and final part of Philip's PowerPoint presentation video series on poker math, Philip discusses implied odds, effective odds and fold equity.
Pre-Flop: 5 5 dealt to Hero (CO)
UTG folds, [color=red]Hero raises to $8[/color], [color=red]BTN raises to $24[/color] , 2 folds, Hero?
If we call, how much do we need to win on the flop on average if we can only win by hitting a set?
Solution:
Part 1
The probability of hitting a set on the flop is 1 - (48/50)(47/49)(46/48) = 1 - 0.88245 = 0.11755.
In the video I calculated the probability of hitting a set as 0.12234, in that case I knew that my opponent didn't hold one of my outs. Either number is fine.
1 – (46/48)(45/47)(44/46) = 1 – 0.87766 = 0.12234
Part 2
EV = [equity x amount you win] – [(1 – equity) x amount you lose] + Probability of improving x how much you expect to win on later streets when you do improve.
0 = [0.11755 x $35] – [(0.88245) x $16] + [0.11755 x Y]
Part 3
0 = $4.11425 – $14.1192 + 0.11755Y
0.11755Y = $10.00495
Y = $10.00495/0.11755
Y = $85.11
We need to win an average of $85 postflop every time we hit a set to breakeven on the call.
Pre-Flop: A 7 dealt to Hero (BTN)
2 folds, [color=red]CO raises to $7[/color], [color=red]Hero raises to $22[/color] , 2 folds, [color=red]CO raises to $54[/color], Hero?
We know villains range for calling a 5bet is JJ+ and AK. How often do we need villain to fold to make a shove profitable?
Solution:
Part 1
A7s has 29.592% equity against JJ+/AK:
Board:
Dead:
equity win tie pots won pots tied
Hand 0: 29.592% 28.62% 00.97% 16170918 550218.00 { Ah7h }
Hand 1: 70.408% 69.43% 00.97% 39234678 550218.00 { JJ+, AKs, AKo }
Part 2
We're risking $200 - $22 = $178 to win $54 + $22 + $2 + $1 = $79 if he folds and $200 + $22 + $2 + $1 = $225 if he calls.
Part 3
EV = (P. Fold)(amount in current pot) + (1 – P.Fold){[equity when called x amount you win] – [(1 – equity when called) x amount you lose]}
EV = (P. Fold)($79) + (1 – P.Fold){[0.29592 x $225] – [(0.70408) x $178]}
Part 4
EV = (P. Fold)($79) + (1 – P.Fold){[$66.582] – [$125.32624]}
EV = (P. Fold)($79) + (1 – P.Fold){-$58.74424}
EV = (P. Fold)($79) - $58.74424 + (P.Fold)($58.74424)
(P. Fold)($79 + $58.74424) = $58.74424
P.Fold = $58.74424/$137.74424
P.Fold = 0.4265
We need villain to fold 42.65% of the time.
Exercise 3
In the value betting example I said that if villain were to bluff with 11% worse hands, we’d always call and villain would lose expectation. What is villain’s expectation in this case?
20% of the time villain has the best hand and wins $200 ($100 in pot + our $100 call). 11% of the time villain has the worst hand and loses his $100 bet. The remaining 69% of the time villain checks and loses nothing.
EV = (20% x $200) - (11% x $100) - (69% x $0)
EV = $40 - $11 - $0
EV = $29
If villain were to bluff with 9% worse hands, we’d always fold and villain would also lose expectation. What is villain’s expectation in this case?
29% of the time villain bets and wins the $100 in the pot. The remaining 71% of the time villain checks and loses nothing.
EV = (29% x $100) - (71% x $0)
EV = $29 - $0
EV = $29
If villain were to bluff with 10% worse hands, calculate villain’s expectation if we always call. Calculate villain’s expectation if we always fold.
If we always call then 20% of the time villain has the best hand and wins $200 ($100 in pot + our $100 call). 10% of the time villain has the worst hand and loses his $100 bet. The remaining 70% of the time villain checks and loses nothing.
EV = (20% x $200) - (10% x $100) - (70% x $0)
EV = $40 - $10 - $0
EV = $30
If we always fold, 30% of the time villain bets and wins the $100 in the pot. The remaining 70% of the time villain checks and loses nothing.
I've got a question. I can't find a way to calculate to see how our opponent needs to fold to our 3-bet if we only can win the hand if he folds.
Lets say, it's folded to villain on BTN and villain opens it to 3bb and it's folded to us on BB and we decide to 3-bet to 11bb. If we assume we can only win the pot if villain is folding and we'll lose everytime if villain calls/shoves.
How does the math look to find out how often villain has to fold to us for us making profit immediately?
I've got a question. I can't find a way to calculate to see how our opponent needs to fold to our 3-bet if we only can win the hand if he folds.
Lets say, it's folded to villain on BTN and villain opens it to 3bb and it's folded to us on BB and we decide to 3-bet to 11bb. If we assume we can only win the pot if villain is folding and we'll lose everytime if villain calls/shoves.
How does the math look to find out how often villain has to fold to us for us making profit immediately?
Hey Pickaface, thanks very much.
We're risking 10bb (11bb - 1bb) to win 4.5bb (3bb + 1bb + 0.5bb). We'll say that villain folds Y% of the time and find out how big Y has to be to break even:
(Y% x 4.5bb) + ((1-Y%) x -10bb) = 0
So, in words, Y% of the time villain folds and we win 4.5bb and 1-Y% of the time villain shoves and we lose 10bb. By adding these together we find our EV and by setting this equal to 0 we can solve for Y.
Pre-Flop: 5 5 dealt to Hero (CO)
UTG folds, [color=red]Hero raises to $8[/color], [color=red]BTN raises to $24[/color] , 2 folds, Hero?
If we call, how much do we need to win on the flop on average if we can only win by hitting a set?
Solution:
Part 1
The probability of hitting a set on the flop is 1 - (48/50)(47/49)(46/48) = 1 - 0.88245 = 0.11755.
In the video I calculated the probability of hitting a set as 0.12234, in that case I knew that my opponent didn't hold one of my outs. Either number is fine.
1 – (46/48)(45/47)(44/46) = 1 – 0.87766 = 0.12234
Part 2
EV = [equity x amount you win] – [(1 – equity) x amount you lose] + Probability of improving x how much you expect to win on later streets when you do improve.
0 = [0.11755 x $35] – [(0.88245) x $16] + [0.11755 x Y]
Part 3
0 = $4.11425 – $14.1192 + 0.11755Y
0.11755Y = $5.89245
Y = $5.89245/0.11755
Y = $50.13
We need to win an average of $53 postflop every time we hit a set to breakeven on the call.
hey how are you getting this # 0.11755Y = $5.89245 i don't seem to be able to get to it in the video i got the example but here it's not working by Subtracting this ]0 = $4.11425 – $14.1192
hey how are you getting this # 0.11755Y = $5.89245 i don't seem to be able to get to it in the video i got the example but here it's not working by Subtracting this ]0 = $4.11425 – $14.1192
Hey grips,
Yeah, I have no idea where those values came from. Sorry about that, fixed now.
Can you please check my maths for me in this post? I'm the 5th reply... it's finding out how much money we have to make on average on the flop to call a 3bet if we only win when we flop a set.
I think it's right, but I don't have many correct examples to be ccompletely confident with my answer.
5
dealt to Hero (CO)
7