Two Plus Two Poker Forums Pocket Pairs: Odds you'll see overcard on flop
 Register FAQ Search Today's Posts Mark Forums Read TwoPlusTwo.com

 Notices

 Probability Discussions of probability theory

 07-05-2008, 11:00 AM #1 Hobbes413 grinder   Join Date: Oct 2005 Posts: 443 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?
 07-05-2008, 04:38 PM #2 Izatnice centurion   Join Date: Jun 2008 Location: South of the Mason Dixon Line Posts: 119 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.
07-05-2008, 07:52 PM   #3
findingneema
Pooh-Bah

Join Date: Feb 2007
Location: LOL Math...
Posts: 5,759
Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
 Originally Posted by Izatnice 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%

 07-06-2008, 02:45 PM #4 AaronBrown Pooh-Bah     Join Date: May 2005 Location: New York Posts: 4,240 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%
 07-07-2008, 08:52 AM #5 Izatnice centurion   Join Date: Jun 2008 Location: South of the Mason Dixon Line Posts: 119 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....
07-07-2008, 12:46 PM   #6
findingneema
Pooh-Bah

Join Date: Feb 2007
Location: LOL Math...
Posts: 5,759
Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
 Originally Posted by Izatnice 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.

07-22-2008, 08:01 PM   #7
punter11235
Carpal \'Tunnel

Join Date: Mar 2005
Location: solving poker
Posts: 7,114
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.

07-22-2008, 09:31 PM   #8
findingneema
Pooh-Bah

Join Date: Feb 2007
Location: LOL Math...
Posts: 5,759
Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
 Originally Posted by punter11235 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.

 07-22-2008, 09:50 PM #9 punter11235 Carpal \'Tunnel   Join Date: Mar 2005 Location: solving poker Posts: 7,114 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.
 12-14-2008, 07:02 PM #10 James Campbell newbie     Join Date: May 2005 Location: Los Angeles CA Posts: 22 Re: Pocket Pairs: Odds you'll see overcard on flop Awesome Post!
 12-14-2008, 07:49 PM #11 TheDream7777 banned   Join Date: Dec 2007 Posts: 169 Re: Pocket Pairs: Odds you'll see overcard on flop AA 0%
12-14-2008, 08:16 PM   #12
Victor Kros
veteran

Join Date: Nov 2008
Posts: 3,258
Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
 Originally Posted by TheDream7777 AA 0%
I simulated it and I am quite sure this is correct.

 02-13-2010, 11:32 AM #13 bAd JQKe 10 enthusiast   Join Date: Dec 2009 Posts: 97 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.
 02-13-2010, 10:13 PM #14 spadebidder Actually Shows Proof     Join Date: Aug 2008 Location: This looks interesting. Posts: 7,904 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.
 02-14-2010, 12:43 AM #15 derrickkwa journeyman     Join Date: Dec 2009 Location: Singapore Posts: 361 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.
02-14-2010, 09:04 PM   #16
enthusiast

Join Date: Dec 2009
Posts: 97
Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
 Originally Posted by derrickkwa 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.

08-30-2017, 03:52 PM   #17
Samboyle
stranger

Join Date: Aug 2017
Posts: 2
Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
 Originally Posted by Izatnice 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.

08-30-2017, 07:03 PM   #18
David Sklansky

Join Date: Aug 2002
Posts: 14,261
Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
 Originally Posted by bAd JQKe 10 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.

08-31-2017, 10:11 PM   #19
statmanhal
Pooh-Bah

Join Date: Jan 2009
Posts: 4,076
Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
 Originally Posted by bAd JQKe 10 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

09-02-2017, 09:39 AM   #20
heehaww
Pooh-Bah

Join Date: Aug 2011
Location: Tacooos!!!!
Posts: 4,307
Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
 Originally Posted by statmanhal 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.

 11-12-2017, 09:57 PM #21 ODDSRODD stranger   Join Date: Nov 2017 Posts: 3 Re: Pocket Pairs: Odds you'll see overcard on flop ...AHH, AM I MISSING SOMETHING (JUST FINISHED 24HR GRIND) BUT WHERE IS THE FACTOR FOR NUMBER OF PLAYERS, CARDS ALREADY OUT OF DECK?
 11-13-2017, 11:08 AM #22 heehaww Pooh-Bah     Join Date: Aug 2011 Location: Tacooos!!!! Posts: 4,307 Re: Pocket Pairs: Odds you'll see overcard on flop Number of players makes no difference because you don't know their cards. Whether the unknown cards are lumped into one big pile or piles of two doesn't change any probabilities. See the sticky
 12-31-2017, 08:36 PM #23 DalTXColtsFan veteran   Join Date: Dec 2011 Location: contributing to the poker economy Posts: 3,032 Re: Pocket Pairs: Odds you'll see overcard on flop I would appreciate some feedback on my "calculations" here - I'm trying to calculate the probability of getting "a flop I like" with 99. For this exercise I will define "a flop I like" as flopping either a set or an overpair. I know that we could flop an OESD or a monotone flop or a BDFD as well but I'm going to ignore those for now. There are 50*49*48=117600 total possible flops. There are 30*29*28=24360 total flops where all 3 cards are 9 or less (4 each of 2 through 8, but only 2 remaining 9s because we have 2 of them). We just need to add on the number of flops where at least one card is a 9 and at least one of the other 2 is an overcard. If the first card is a 9 and the second card is an overcard, the 3rd can be anything, so 2*20*48 possibilities. There are 6 total combinations of 9, overcard and anything, so we get 2*20*48*6 = 11,520 So there are 11,520 + 24,360 = 35,880 out of 117600 or 30.5% Repeating the process for JJ, it's (38*37*36+2*12*48*6)/117600 = (50616+6912) /117600 = 57528/117600 = 48.9% Repeating for KK, it's (46*45*44+2*4*48*6)/117600 = (91080+2304)/117600 = 79.4%. Comments?
01-01-2018, 07:55 AM   #24
nickthegeek
journeyman

Join Date: Sep 2011
Posts: 220
Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
 Originally Posted by DalTXColtsFan If the first card is a 9 and the second card is an overcard, the 3rd can be anything, so 2*20*48 possibilities. There are 6 total combinations of 9, overcard and anything, so we get 2*20*48*6 = 11,520
As a general comment, you should use combinations instead of permutations. You say that there are 50*49*48 flops, but order doesn't matter and, for instance, AcKcQc and KcQcAc are the same flop.

In the quoted passage, you double count some combo. The right number of flops containing at least a 9 and at least an overcard is 1520 (=9120 permutations) and so your total is wrong.

However, you should proceed differently to make sure to not double count combos. Let U be an undercard and X any not-9 card. The correct way to proceed is to count the combos for each of these kinds of flops:

UUU
9XX
99X

As you can see, in this way there isn't any flop that belongs to more than a group and you avoid double counting. I think you can proceed from there (also the above formulation is easily generalizable for any rank).

01-01-2018, 06:16 PM   #25
DalTXColtsFan
veteran

Join Date: Dec 2011
Location: contributing to the poker economy
Posts: 3,032
Re: Pocket Pairs: Odds you'll see overcard on flop

Quote:
 Originally Posted by nickthegeek As a general comment, you should use combinations instead of permutations.
With this understood and agreed, shouldn't I still get the correct answer if I count permutations because I'm looking for a percentage?

I mean, in the case I'm calculating there, isn't the number of permutations exactly the number of combinations times 6?

Also, in my quoted calculation, can you figure out where I'm going wrong? I mean there are 2 different 9s that could be the first card, there are 20 different overcards that could appear second, and then the third card could be any of the 48 cards that didn't appear in the first or second (including the case 9). I can't figure out what was inaccurate there.

Lastly, while I agree that your UUU/9xx/99x approach is significantly cleaner than my 9s and lower plus at least one 9 and at least one overcard, was my approach incorrect? It seems to me that if I count 9s and lower first, then there are no duplicated permutations when I count at least one 9 plus at least one overcard. Am I missing something?

DTXCF

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Links to Popular Forums     News, Views, and Gossip     Beginners Questions     Marketplace & Staking     Casino & Cardroom Poker     Internet Poker     NL Strategy Forums     Poker Goals & Challenges     Las Vegas Lifestyle     Sporting Events     Politics     Other Other Topics Two Plus Two     About the Forums     Two Plus Two Magazine Forum     The Two Plus Two Bonus Program     Two Plus Two Pokercast     The Best of Two Plus Two Marketplace & Staking     Commercial Marketplace     General Marketplace     Staking - Offering Stakes     Staking         Staking - Offering Stakes         Staking - Seeking Stakes         Staking - Selling Shares - Online         Staking - Selling Shares - Live         Staking Rails         Transaction Feedback & Disputes     Transaction Feedback & Disputes Coaching & Training     Coaching Advice     Cash Game Poker Coach Listings     Tournament/SNG Poker Coach Listings Poker News & Discussion     News, Views, and Gossip     Poker Goals & Challenges     Poker Beats, Brags, and Variance     That's What She Said!     Poker Legislation & PPA Discussion hosted by Rich Muny     Twitch - Watch and Discuss Live Online Poker     Televised Poker General Poker Strategy     Beginners Questions     Books and Publications     Poker Tells/Behavior, hosted by: Zachary Elwood     Poker Theory     Psychology No Limit Hold'em Strategy     Medium-High Stakes PL/NL     Micro-Small Stakes PL/NL     Medium-High Stakes Full Ring     Micro-Small Stakes Full Ring     Heads Up NL     Live Low-stakes NL Limit Texas Hold'em Strategy     Mid-High Stakes Limit     Micro-Small Stakes Limit Tournament Poker Strategy     STT Strategy     Heads Up SNG and Spin and Gos     Mid-High Stakes MTT     Small Stakes MTT     MTT Community     Tournament Events Other Poker Strategy     High Stakes PL Omaha     Small Stakes PL Omaha     Omaha/8     Stud     Draw and Other Poker Live Poker     Casino & Cardroom Poker         Venues & Communities         Regional Communities     Venues & Communities     Tournament Events         WPT.com     Home Poker     Cash Strategy     Tournament Strategy Internet Poker     Internet Poker         nj.partypoker.com         Global Poker     Commercial Software     Software         Commercial Software         Free Software General Gambling     Backgammon Forum hosted by Bill Robertie.     Probability     Sports Betting     Other Gambling Games 2+2 Communities     Other Other Topics         OOTV         Game of Thrones     The Lounge: Discussion+Review     EDF     Las Vegas Lifestyle     BBV4Life         omg omg omg     House of Blogs Sports and Games     Sporting Events         Single-Team Season Threads         Fantasy Sports     Fantasy Sports         Sporting Events     Wrestling     Golf     Chess and Other Board Games     Video Games         League of Legends         Hearthstone     Puzzles and Other Games Other Topics     Politics     History     Business, Finance, and Investing     Science, Math, and Philosophy     Religion, God, and Theology     Travel     Health and Fitness     Laughs or Links!     Computer Technical Help     Programming International Forums     Deutsch         BBV [German]     Français     Two Plus Two en Espańol

All times are GMT -4. The time now is 01:24 PM.

 Contact Us - Two Plus Two Publishing LLC - Privacy Statement - Top