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Old 07-05-2008, 11:00 AM   #1
Hobbes413
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Pocket Pairs: Odds you'll see overcard on flop

Can someone post the percentage of times you'll face an overcard on the flop when holding the different pocket pairs?
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Old 07-05-2008, 04:38 PM   #2
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Re: Pocket Pairs: Odds you'll see overcard on flop

KK 23%
QQ 43%
JJ 59%
TT 71%
99 81%
88 88%
77 93%
66 97%
55 99%
44 99.7%
33 99.9%

This is from page 99 of Mike Petriv's Holdem Odds Book.
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Old 07-05-2008, 07:52 PM   #3
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Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
Originally Posted by Izatnice View Post
KK 23%
QQ 43%
JJ 59%
TT 71%
99 81%
88 88%
77 93%
66 97%
55 99%
44 99.7%
33 99.9%

This is from page 99 of Mike Petriv's Holdem Odds Book.
These aren't quite right. Assuming the dead cards are random, this is the right answer.

Code:
KK	22.6%
QQ	41.4%
JJ	57.0%
TT	69.5%
99	79.3%
88	86.7%
77	92.1%
66	95.8%
55	98.1%
44	99.4%
33	99.9%
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Old 07-06-2008, 02:45 PM   #4
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Re: Pocket Pairs: Odds you'll see overcard on flop

Findingneema is correct given the wording.

Mike Petriv's numbers assume you do not get trips or quads. In that case, the exact probabilities are:

KK 23.43%
QQ 42.88%
JJ 58.72%
TT 71.32%
99 81.06%
88 88.30%
77 93.41%
66 96.76%
55 98.73%
44 99.68%
33 99.98%
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Old 07-07-2008, 08:52 AM   #5
Izatnice
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Re: Pocket Pairs: Odds you'll see overcard on flop

you are correct in that he assumes four higher cards are available but are not those numbers the same as what you typed? i mean rounded up, or am i missing something? there is simply not enough difference in any of them to matter....
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Old 07-07-2008, 12:46 PM   #6
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Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
Originally Posted by Izatnice View Post
you are correct in that he assumes four higher cards are available but are not those numbers the same as what you typed? i mean rounded up, or am i missing something? there is simply not enough difference in any of them to matter....
I'm pretty sure Aaron just added the extra precision in the numbers to show the difference between mine and his.
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Old 07-22-2008, 08:01 PM   #7
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Re: Pocket Pairs: Odds you'll see overcard on flop

I am sure findingneema numbers are correct.

Quote:
Mike Petriv's numbers assume you do not get trips or quads. In that case, the exact probabilities are:

KK 23.43%
QQ 42.88%
JJ 58.72%
TT 71.32%
99 81.06%
88 88.30%
77 93.41%
66 96.76%
55 98.73%
44 99.68%
33 99.98%
I don't get it.
You flop set quite often so 99.98% can't be correct unless you mean :
(flops where overcard flops) / (all flops without a set) but I don't see any use for such number.
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Old 07-22-2008, 09:31 PM   #8
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Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
Originally Posted by punter11235 View Post
I am sure findingneema numbers are correct.



I don't get it.
You flop set quite often so 99.98% can't be correct unless you mean :
(flops where overcard flops) / (all flops without a set) but I don't see any use for such number.
Obv for 33 the number is academic, you're generally only continuing if you flop a set. For the hands like 99-KK, the number is pretty meaningful. And since 99% of the time you flop a set, you don't care if there's an overcard or two, Aaron's numbers are slightly more useful than mine. But it really doesn't matter, given that there's no practical difference between them.
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Old 07-22-2008, 09:50 PM   #9
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Re: Pocket Pairs: Odds you'll see overcard on flop

I mean he is counting the wrong thing. I think what matters is % of flops when w don't have overpair AND we don't have a set. In other words the % of flops on which we doesn't have a very strong hand.
This number is always higher than % of flopping a set.
For KK it's 20.67%
For QQ it's 37.84%
For JJ it's 51.82%
...
for 33 it's 88.22%

Last edited by punter11235; 07-22-2008 at 09:56 PM.
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Old 12-14-2008, 07:02 PM   #10
James Campbell
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Re: Pocket Pairs: Odds you'll see overcard on flop

Awesome Post!
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Old 12-14-2008, 07:49 PM   #11
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Re: Pocket Pairs: Odds you'll see overcard on flop

AA 0%
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Old 12-14-2008, 08:16 PM   #12
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Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
Originally Posted by TheDream7777 View Post
AA 0%
I simulated it and I am quite sure this is correct.
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Old 02-13-2010, 11:32 AM   #13
bAd JQKe 10
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Re: Pocket Pairs: Odds you'll see overcard on flop

Can someone please post the method of calculation for this percentages ?
Let's say odds you'll see an overcard when holding TT, including flops with sets & quads.

Thank you.
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Old 02-13-2010, 10:13 PM   #14
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Re: Pocket Pairs: Odds you'll see overcard on flop

A much more useful calculation is the chance for overcards AND you don't flop a set. You don't care about overcards when you hit the set, in fact you welcome them because you might get paid. The chance for at least 1 overcard AND you don't have a set are approximately:

KK .21
QQ .38
JJ .52
TT .63
99 .72
88 .78
77 .82
66 .85
55 .87
44-22 .88

Edit: I see punter beat me to it.
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Old 02-14-2010, 12:43 AM   #15
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Re: Pocket Pairs: Odds you'll see overcard on flop

FTR has a great chart detailing the odds of an overcard coming, on each street. You can find it here. It also has a rough explanation of how they got the values.
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Old 02-14-2010, 09:04 PM   #16
bAd JQKe 10
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Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
Originally Posted by derrickkwa View Post
FTR has a great chart detailing the odds of an overcard coming, on each street. You can find it here. It also has a rough explanation of how they got the values.
That was what I was looking for. Thanks.
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Old 08-30-2017, 03:52 PM   #17
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Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
Originally Posted by Izatnice View Post
KK 23%
QQ 43%
JJ 59%
TT 71%
99 81%
88 88%
77 93%
66 97%
55 99%
44 99.7%
33 99.9%

This is from page 99 of Mike Petriv's Holdem Odds Book.

Thanks findingneema at first I thought I was going crazy as I could not get the numbers, and I didn't want to say they were wrong.

We can also get the answer by building it up

There are 50 choose 3 combos to choose 3 cards from 50 or (50*49*48)/(3*2*1). IE the flop has 19,600 possible flop combinations. This is the denominator or total outcomes. Now we want to find success divided by total outcomes

Then we have 4 aces in the deck so 46 not ace cards (it's 46 as you hold 2 cards in your hand presumably not aces). The odds that one ace shows up on the flop is

A _ _ This is the flop we want. So we have one ace on the flop and 2 not aces [(46*45)/(2*1)]. So there is 46 not aces * 45 not aces. So you get a number 1035 and this would be the number if there was only one ace in the deck but there are 4. So multipled by 4 aces in the deck is 4,140 combinations or 21% chance.

Now there is also the possibility of A A _ coming out So there are 46 combos for that third card. There are also 6 different ways to have AA come up on flop. As there is 4 aces choose 2 ways to pick it.

So 46 *6 which is 276

Then there is 4 choose 3 ways to pick 3 aces or 4 total ways to get an AAA flop.

All together it's (4140+276+4) /19600 or 22.55%

Having said that, the odds are lower if you think your oppnent has an Ace.

That would lower the combinations to 3105+138+1 or 16.5%. So the true odds are 16.5%. Since the odds you're losing when you have KK to an ace is only 16.5%.

Last edited by Samboyle; 08-30-2017 at 04:02 PM.
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Old 08-30-2017, 07:03 PM   #18
David Sklansky
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Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
Originally Posted by bAd JQKe 10 View Post
Can someone please post the method of calculation for this percentages ?
Let's say odds you'll see an overcard when holding TT, including flops with sets & quads.

Thank you.
Sort of sad that you are the only one who wrote this.
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Old 08-31-2017, 10:11 PM   #19
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Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
Originally Posted by bAd JQKe 10 View Post
Can someone please post the method of calculation for this percentages ?
Let's say odds you'll see an overcard when holding TT, including flops with sets & quads.

Thank you.
Quote:
DS - Sort of sad that you are the only one who wrote this.
I’m not sure how to interpret DS’s comment.

Anyway, here is the equation to calculate the percentage of having an overcard to your pair on the flop.

Assume the pair is of rank R. Then there are 4*(R-2) cards less than R in the deck and 2 cards equal to R.

The probability of at least one flop card greater than R is then 1 – the probabability that all flop cards are less than or equal to R. This is

Pr= 1-C(4*(R-2)+2, 3)/C(50,3)

Example: You have a pair of tens. There are 4*(10-2) + 2 = 34 cards less than or equal to 10.

Pr = 1 – C(34,3)/C(50,3) = 1 – 0.305 = 0.695
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Old 09-02-2017, 09:39 AM   #20
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Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
Originally Posted by statmanhal View Post
I’m not sure how to interpret DS’s comment.
The thread prior to that post was a bit silly, just people listing stats without calculations to back them up. One person lists stats, then another person says, "Those are wrong, here are the correct ones," without providing a reason the others were wrong or why theirs are right.
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