In this part 2 of 3 PowerPoint presentation video on poker math. Philip discusses at the table math including outs, ratios, percentages and combinatorics.
Your series will soon become a must see for all beginners as well as any experienced players (Aejones?) who are looking to brush up on the foundation of poker math.
I am sure many players would agree that you have condensed in two videos what took most of us hours of toil (and then some) to come up with.
Thank you for your time and efforts. Truly appreciated.
You have 5 outs, calculate your equity on the flop and on the turn.
On the turn there are 52 - 6 = 46 cards unknown.
5/46 = 0.1087 = 10.87%
On the flop there are 52 - 5 = 47 cards unknown. On the flop we will miss 47 - 5 = 42 times and on the turn we will miss 46 - 5 = 41 times. The probability that we miss both streets is (42/47)(41/46) so we must hit:
1 - (42/47)(41/46) = 1 - 0.7965 = 0.2035 = 20.35%
Approximate your equity using the 2 & 4 method.
On the flop:
(5x2)+1 = 11%
On the turn:
(4x2) - 0 = 20%
How much of the effective stacks must go into the pot on the flop before youre committed?
EV = (equity x amount you win) [(1 equity) x amount you lose)]
0 = (0.2035 x ($100+Y)) - (0.7965 x ($100-Y))
0 = $20.35 + 0.2035Y - $79.65 + 0.7965Y
Y(0.2035 + 0.7965) = $59.30
Y = $59.30
59.3% of the effective stacks must go in before you're committed.
What about the turn?
EV = (equity x amount you win) [(1 equity) x amount you lose)]
0 = (0.1087 x ($100+Y)) - (0.8913 x ($100-Y))
0 = $10.87 + 0.1087Y - $89.13 + 0.8913Y
Y(0.1087 + 0.8913) = $78.26
Y = $78.26
78.26% of the effective stacks must go in before you're committed.
Convert 6.5:1 into a percentage.
1/(6.5 + 1) = 13.33%
Convert 45% equity into a ratio.
55%:45% = 11:9 = 1.22:1 against
Theres $11 in the pot on the flop, your opponent bets $8, how large would a pot sized raise be?
($8 x 3) + $11 = $35
If this raise puts you all-in, what was the SPR in this hand?
$35:$11 = 3.18:1
How many combinations are in the range 66+, A9s+, AJo+, T9s-KQs?
66+ - 9 x 6 = 54 combos
A9s+ - 5 x 4 = 20 combos
AJo+ - 3 x 12 = 36 combos
T9s-KQs - 4 x 4 = 16 combos
54 + 20 + 36 + 16 = 124 combos in total.
If you hold KJo, how many combinations are left in that range?
66+ - (7 x 6) + (2 x 3) = 48 combos
A9s+ - (3 x 4) + (2 x 3) = 18 combos
AJo+ - (1 x 12) + (2 x 9) = 30 combos
T9s-KQs - (1 x 4) + (3 x 3) = 13 combos
Your series will soon become a must see for all beginners as well as any experienced players (Aejones?) who are looking to brush up on the foundation of poker math.
I am sure many players would agree that you have condensed in two videos what took most of us hours of toil (and then some) to come up with.
Thank you for your time and efforts. Truly appreciated.
RedJoker mentioned it, but it needs to be said again. JUST BECAUSE YOU WERE VALUE BETTING THE TURN AND HAVE 33% OF YOUR STACK COMMITED DOESN'T MEAN YOU CALL A SHOVE. If you have JJ and value bet the turn on 9732r and the nittiest of nit shoves, YOU FOLD. You still have to do the math based on the pot odds and your likely equity. In this case, you probably have 2 outs and can't call.
A better example is with preflop play. You're in a 1000NL 6 max game with A5s playing at 100bb effective. For some reason you 4B to $330, you are commited to calling his shove. You will have roughly 35.5% equity even against only his value range (this doesn't include his bluffs)
I thought it was a good idea that Leggo have a series, but I never could have imagined that we'd get Philip to do something that was so comprehensive and easily applicable for math people and also 'feel' players.
This is definitely going to be my first recommendation to many people looking to play online poker, or even players who think they're weak at the math aspect of the game. I hope word of mouth travels on how great this series is, it deserves as many views as possible.
I thought it was a good idea that Leggo have a series, but I never could have imagined that we'd get Philip to do something that was so comprehensive and easily applicable for math people and also 'feel' players.
This is definitely going to be my first recommendation to many people looking to play online poker, or even players who think they're weak at the math aspect of the game. I hope word of mouth travels on how great this series is, it deserves as many views as possible.
In the combinatorics section with regard to the 99 vs QQ+, AK, AKs:
Is it this a legal way of doing it too ---> 18:16 -----> .5294:.4705
Then multiply each by the repective equities 99 has vs them:
(.5294*.2)+(.4705*.5) = 34.19%
seems right, just want to make sure.
Yeah, that's the more accurate version, you could also stove your equities against the two ranges and make it even more accurate. I used 50:50 as it was an example of how you could apply combinatorics while playing. 53:47 is a good bit harder to work out.
The other quick question is, is the combo for A9s+ 5, or 6? I see five but results say six A9, AT, AJ, AQ, AK.
Prob top 5 series I've seen in last two years, great work.
Very good spot, there was bound to be a mistake somewhere. Fixed now.
On the exercises, you have one question "If you hold KJo, how many combinations are left in that range?".
I can't find the same solution as you on AJo+.
Shouldn't it be that AJo has 4 aces left and 3 jacks since we have one jack, 4*3 = 12
And AQo, 4 aces and 4 queens = 4*4 = 16
And AKo, 4 aces and 3 kings = 4*3 = 12
Which makes 40 cominations but on your solution you have come up with different answer, why is that?
On the exercises, you have one question "If you hold KJo, how many combinations are left in that range?".
I can't find the same solution as you on AJo+.
Shouldn't it be that AJo has 4 aces left and 3 jacks since we have one jack, 4*3 = 12
And AQo, 4 aces and 4 queens = 4*4 = 16
And AKo, 4 aces and 3 kings = 4*3 = 12
Which makes 40 cominations but on your solution you have come up with different answer, why is that?
Thanks!
Hey Pickaface,
Your calculations include the suited combinations, I did those seperately.
If you wanted to you could do AJ+ like you have and then do A9s/ATs on their own:
A9s/ATs - (2 x 4) = 8 combos
AJ+ - (2 x 12) + (1 x 16) = 40 combos
which is the same as I got with
A9s+ - (3 x 4) + (2 x 3) = 18 combos
AJo+ - (1 x 12) + (2 x 9) = 30 combos
Both methods are equally valid, whatever way you feel minimizes the risk of double counting or missing any hands is fine.
I see where I did the mistake. Yea, I shouldn't be including the suited ones if we're trying to calculate the unsuited ones. Thanks for the quick reply, now I can go immediately to episode 3. :)
