Flopping Quads Promotion EV
March 31st, 2012 at 1:23:22 AM
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This is my 2nd time writing this post.. I just had a long typed-out post and accidentally hit backspace.. so here I go again lol:
I want to know the expected value per hand from this new promotion.
Please correct me if any of these assumptions are incorrect.
On this poker site (rpm), you are awarded a certain amount of money each time you flop Quads. This is the list.
2222 = $5
3333 = $5
4444 = $5
5555 = $5
6666 = $5
7777 = $10
8888 = $10
9999 = $10
TTTT = $20
JJJJ = $30
QQQQ = $40
KKKK = $50
AAAA = $100
I believe that to calculate the EV of this, you just take the average of all the dollar amounts divided by 13 (hands you can make Quads with) to get the EV for flopping Quads (I mean your expected value for that exact, single hand when you flop Quads.)
$295 / 13 = +$22.69 (I will be rounding to make it easier)
You flop Quads 1 in 407 times you see the flop with a pocket pair. This is also expressed as 0.25%.
Last month, I played 117,953 hands. I saw the flop with a pocket pair 4,420 times. That means I saw the flop with a pocket pair 3.747% of the time. I am expected to flop Quads 0.25% of those 4,420 times. That means I should have flopped Quads 11.05 times (Rounding 11.05 to 11 from now on.) (I actually flopped Quads 16 times lol) (Note that each person uses a different strategy pre-flop. Some people may see the flop more than others. Some people like to call 3bets with pocket pairs so they see the flop more often. Some like to open limp instead of raise so they see more flops. This is just using MY specific pre-flop strategy based on 117,953 hands.)
That means I am expected to flop Quads (using my specific strategy/game) 0.009325748391% of the time (decimal is 0.00009325748391, so multiply that number by 100 to get the percent)
(0.009325748391% (odds I'll flop Quads in a given hand) * 117,953 (hands played) = 11 (times I am expected to flop Quads)
Cash Value / hand = money made per hand
Cash Value = 11 Quads * EV of Quads = 11*22.69 = $249.59
$249.59 / 117,953 hands = $0.0021160123099879 per hand
I now have a number that I can use to multiply by the number of hands I want to play. (Using my strategy only, can't calculate using other people's EV)
So lets do an example:
$0.0021160123099879 * 60,000 hands in April (2k per day) = Cash Value = $126.96
Now I want to calculate the rakeback. I rake $0.0162433 per hand at 25nl. The rake I will pile up over 60k hands at 25nl will be equal to $974.60.. I now take the amount I get back from this promotion, and divide it by the amount I raked. (That's how you calculate rakeback)
$126.96 / $974.60 = 13.026% rakeback
I think this is incorrect.. That seems like a lot of extra rakeback for flopping Quads.
Clearly I won't flop Quads 11 times every month, but that is how variance works..
I feel like it's incorrect because that's a lot of extra value lol.
The only problem I can see with my math is possibly the EV of the promotion for when you hit Quads. I don't know if your EV is +$22.69.. I mean the odds of you hitting Quad Ducks and Quad Kings are exactly the same.. (You will see the flop more often with AA than you will with 22 though.. to go more in-depth/realistic, I could calculate my EV based on how often I see the flop with 22-AA, but I think that's a bit too much.. I think my sample size is large enough to know the basic % of the time I see a flop with 22 compared to AA.. )
I want to know the expected value per hand from this new promotion.
Please correct me if any of these assumptions are incorrect.
On this poker site (rpm), you are awarded a certain amount of money each time you flop Quads. This is the list.
2222 = $5
3333 = $5
4444 = $5
5555 = $5
6666 = $5
7777 = $10
8888 = $10
9999 = $10
TTTT = $20
JJJJ = $30
QQQQ = $40
KKKK = $50
AAAA = $100
I believe that to calculate the EV of this, you just take the average of all the dollar amounts divided by 13 (hands you can make Quads with) to get the EV for flopping Quads (I mean your expected value for that exact, single hand when you flop Quads.)
$295 / 13 = +$22.69 (I will be rounding to make it easier)
You flop Quads 1 in 407 times you see the flop with a pocket pair. This is also expressed as 0.25%.
Last month, I played 117,953 hands. I saw the flop with a pocket pair 4,420 times. That means I saw the flop with a pocket pair 3.747% of the time. I am expected to flop Quads 0.25% of those 4,420 times. That means I should have flopped Quads 11.05 times (Rounding 11.05 to 11 from now on.) (I actually flopped Quads 16 times lol) (Note that each person uses a different strategy pre-flop. Some people may see the flop more than others. Some people like to call 3bets with pocket pairs so they see the flop more often. Some like to open limp instead of raise so they see more flops. This is just using MY specific pre-flop strategy based on 117,953 hands.)
That means I am expected to flop Quads (using my specific strategy/game) 0.009325748391% of the time (decimal is 0.00009325748391, so multiply that number by 100 to get the percent)
(0.009325748391% (odds I'll flop Quads in a given hand) * 117,953 (hands played) = 11 (times I am expected to flop Quads)
Cash Value / hand = money made per hand
Cash Value = 11 Quads * EV of Quads = 11*22.69 = $249.59
$249.59 / 117,953 hands = $0.0021160123099879 per hand
I now have a number that I can use to multiply by the number of hands I want to play. (Using my strategy only, can't calculate using other people's EV)
So lets do an example:
$0.0021160123099879 * 60,000 hands in April (2k per day) = Cash Value = $126.96
Now I want to calculate the rakeback. I rake $0.0162433 per hand at 25nl. The rake I will pile up over 60k hands at 25nl will be equal to $974.60.. I now take the amount I get back from this promotion, and divide it by the amount I raked. (That's how you calculate rakeback)
$126.96 / $974.60 = 13.026% rakeback
I think this is incorrect.. That seems like a lot of extra rakeback for flopping Quads.
Clearly I won't flop Quads 11 times every month, but that is how variance works..
I feel like it's incorrect because that's a lot of extra value lol.
The only problem I can see with my math is possibly the EV of the promotion for when you hit Quads. I don't know if your EV is +$22.69.. I mean the odds of you hitting Quad Ducks and Quad Kings are exactly the same.. (You will see the flop more often with AA than you will with 22 though.. to go more in-depth/realistic, I could calculate my EV based on how often I see the flop with 22-AA, but I think that's a bit too much.. I think my sample size is large enough to know the basic % of the time I see a flop with 22 compared to AA.. )
March 31st, 2012 at 2:25:52 AM
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I think the maths is sound, but your expectation is way off.
Your going to fold Pocket2's - Pocket 7's a large percentage of the time, if your in early position are you going to limp to raise first in? I think both plays are -EV in early position (obv depends on the format and players). What about TT in late position facing a raise and re-raise? Or worse an all-in?
I think changing your play based on this promotion would cost you more than you will ever win.
Heres some of my stats, I play agressive post flop, and like to see a flop with pocket pairs, but wont chase with a small pair.
Total hands 114,780
22 = 720 times SF 66%
33 = 520 times SF 57%
44 = 561 times SF 54%
55 = 559 times SF 75%
66 = 543 times SF 77%
77 = 581 times SF 72%
88 = 563 times SF 78%
99 = 541 times SF 74%
TT = 399 times SF 75%
JJ = 479 times SF 83%
QQ = 587 times SF 68%
KK = 339 times SF 76%
AA = 382 times SF 89%
In total I made 102 Quads.
But only 20 of those were flopped.
Whats interesting, is the Saw Flops %. I was expecting a gradual increase from 2's to Aces, and I kind of got it. I do like 2's as I either make a set or fold, and nobody ever suspects a set of twos when they have top pair top kicker ;-)
Also the low % on QQ, is probably due to me being agressive pre and everone folding, what do you think?
Plus, I think I am owed some KK and AA!! F****** Pokerstars!
Your going to fold Pocket2's - Pocket 7's a large percentage of the time, if your in early position are you going to limp to raise first in? I think both plays are -EV in early position (obv depends on the format and players). What about TT in late position facing a raise and re-raise? Or worse an all-in?
I think changing your play based on this promotion would cost you more than you will ever win.
Heres some of my stats, I play agressive post flop, and like to see a flop with pocket pairs, but wont chase with a small pair.
Total hands 114,780
22 = 720 times SF 66%
33 = 520 times SF 57%
44 = 561 times SF 54%
55 = 559 times SF 75%
66 = 543 times SF 77%
77 = 581 times SF 72%
88 = 563 times SF 78%
99 = 541 times SF 74%
TT = 399 times SF 75%
JJ = 479 times SF 83%
QQ = 587 times SF 68%
KK = 339 times SF 76%
AA = 382 times SF 89%
In total I made 102 Quads.
But only 20 of those were flopped.
Whats interesting, is the Saw Flops %. I was expecting a gradual increase from 2's to Aces, and I kind of got it. I do like 2's as I either make a set or fold, and nobody ever suspects a set of twos when they have top pair top kicker ;-)
Also the low % on QQ, is probably due to me being agressive pre and everone folding, what do you think?
Plus, I think I am owed some KK and AA!! F****** Pokerstars!
http://wizardofvegas.com/forum/off-topic/general/10042-woes-black-sheep-game-ii/#post151727
March 31st, 2012 at 10:12:14 AM
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Quote: WizardofEnglandI think the maths is sound, but your expectation is way off.
Your going to fold Pocket2's - Pocket 7's a large percentage of the time, if your in early position are you going to limp to raise first in? I think both plays are -EV in early position (obv depends on the format and players). What about TT in late position facing a raise and re-raise? Or worse an all-in?
I think changing your play based on this promotion would cost you more than you will ever win.
Heres some of my stats, I play agressive post flop, and like to see a flop with pocket pairs, but wont chase with a small pair.
Total hands 114,780
22 = 720 times SF 66%
33 = 520 times SF 57%
44 = 561 times SF 54%
55 = 559 times SF 75%
66 = 543 times SF 77%
77 = 581 times SF 72%
88 = 563 times SF 78%
99 = 541 times SF 74%
TT = 399 times SF 75%
JJ = 479 times SF 83%
QQ = 587 times SF 68%
KK = 339 times SF 76%
AA = 382 times SF 89%
In total I made 102 Quads.
But only 20 of those were flopped.
Whats interesting, is the Saw Flops %. I was expecting a gradual increase from 2's to Aces, and I kind of got it. I do like 2's as I either make a set or fold, and nobody ever suspects a set of twos when they have top pair top kicker ;-)
Also the low % on QQ, is probably due to me being agressive pre and everone folding, what do you think?
Plus, I think I am owed some KK and AA!! F****** Pokerstars!
Hmm that is weird why you've seen less flops with QQ.. Maybe just variance.. or you like to 3bet it a ton? It probably has to do with you being aggressive with it, then you get 4bet and have to fold. This would make sense if you just flat call with JJ a lot. (If you 3bet JJ a lot, then you would expect to see a lower saw flop % with both QQ and JJ, but if you just call people's open raises more often than you do with QQ, this would make sense why you see the flop more often with JJ than the lower pocket pairs. Obviously the strength of AA is why it's SF% is so high)
So how can I get a more accurate #?
Take 22-66 and multiply the amount you win by how often you see the flop with them? That doesn't seem right..
I think I would need to take my "Odds to Flop Quads in a Single hand" and multiply it by the amount of times I see the flop with 22 through AA to get a more accurate number. I would then take the product of those two numbers and multiply it by the amount you win. I would then add them all up like a normal EV equation I think.
