Two Plus Two Poker Forums Probability of flopping a set?
 Register FAQ Search Today's Posts Mark Forums Read Video Directory TwoPlusTwo.com

 Notices

 Poker Theory General poker theory

 03-25-2009, 03:56 PM #1 Illini10 enthusiast   Join Date: Mar 2009 Posts: 50 Probability of flopping a set? I've read that it is around 12%, but I did a quick check and I came up with a different number. Could someone check my numbers, or explain what I did wrong? Player starts with a pocket pair in texas hold em. The odds of him flopping a set are Y, odds of not flopping a set are X. I calculated X using a binomial: Pr(n, k ) = n!/(k!(n-k)!)*pr(k)^k(1-pr(k))^k I define X as the odds of not hitting either of the 2 cards to improve to a set (or quads, since first you have to have 3 of a kind before improving to 4): X=Pr(50, 48)+Pr(49, 47)+Pr(48, 46) First I found Pr(50, 48)=0.276232807 Then Pr(49, 47)=0.27634952 Then Pr(48, 46)=0.276471236 Then X=0.829053564, and Y=0.170946436 This would mean that a pocket pair improves to a set ~17% of the time on the flop, which goes against most of what I googled.
 03-25-2009, 04:19 PM #2 DarkMagus Pooh-Bah     Join Date: Jul 2007 Location: Vancouver, BC Posts: 5,687 Re: Probability of flopping a set? i dont really have any clue what you've done there. i don't think you understand what the binomial distribution does at all. the proper way to calculate this would simply be: (48 c 3) / (50 c 3) = 0.882, which gives you the probability that of the remaining 50 cards in the deck, the flop will contain three of the 48 cards which don't match your pair. subtract this from 1 to get 0.118, the probability of flopping a set.
 03-25-2009, 04:38 PM #3 Illini10 enthusiast   Join Date: Mar 2009 Posts: 50 Re: Probability of flopping a set? Oh. Yeah I did this wrong, I was finding the odds of something unrelated to the question by thinking that n=number of cards rather than the number of times something is done. Thanks for clearing that up
 03-25-2009, 05:27 PM #4 TheWuzi grinder     Join Date: Feb 2009 Location: i has ps3 Posts: 415 Re: Probability of flopping a set? you start with a pair (2 cards). there is 50 cards left in the deck, only 2 remaining cards that can give you a set so your odds are 50-to-2 or 25-to-1 chance of flopping a set. 1 divided by 25 is 0.04 which comes out to 4%. so you have a 4% chance of flopping a set.
03-25-2009, 06:01 PM   #5
dokonoko
stranger

Join Date: Feb 2009
Posts: 13
Re: Probability of flopping a set?

Quote:
 Originally Posted by TheWuzi you start with a pair (2 cards). there is 50 cards left in the deck, only 2 remaining cards that can give you a set so your odds are 50-to-2 or 25-to-1 chance of flopping a set. 1 divided by 25 is 0.04 which comes out to 4%. so you have a 4% chance of flopping a set.
You forget that there are 3 cards on the flop

 03-25-2009, 07:23 PM #6 TheWuzi grinder     Join Date: Feb 2009 Location: i has ps3 Posts: 415 Re: Probability of flopping a set? well the odds of you flopping a set on the turn is still 47-to-2 or little under 24-to-1. 1 divided by 23.5 is 0.04255... which is still 4% lol.
03-25-2009, 07:28 PM   #7
RustyBrooks
Carpal \'Tunnel

Join Date: Feb 2006
Location: Austin, TX
Posts: 21,792
Re: Probability of flopping a set?

Quote:
 Originally Posted by TheWuzi well the odds of you flopping a set on the turn is still 47-to-2 or little under 24-to-1. 1 divided by 23.5 is 0.04255... which is still 4% lol.
You can't flop a set on the turn. You flop a set on the flop. And you have 3 chances at it - the odds are about 12% as shown above.

 03-25-2009, 11:23 PM #8 statmanhal Pooh-Bah   Join Date: Jan 2009 Posts: 3,582 Re: Probability of flopping a set? The term 'flopping a set" is a little vague. Does it mean a set and only a set. What about a full house or quads? Anyway, DarkMagnus' answer of 11.8% is for at least a set.
03-27-2009, 04:59 AM   #9
Octavian
banned

Join Date: Sep 2005
Location: Las Vegas
Posts: 828
Re: Probability of flopping a set?

Quote:
 Originally Posted by Illini10 I've read that it is around 12%, but I did a quick check and I came up with a different number. Could someone check my numbers, or explain what I did wrong?
You will get a PP 5.88%
Now, that you've got that pair you will flop a set or better 11.7%

In more more practical terms, what to expect in real live game:
You will flop 11.7 sets for each 100 PP that you hold. In order to get 100 PP you will have to "play" 1,700 hands.

As you can see, you will have a set on the flop once per (1,700*11.7)/100=199 hands. Now, how many hours takes you to play 199 hands in live poker? Well, you have 199/33=6 hours. On average you can say that you will have at least a set on the flop once every 6 hours of live play. If you game is much faster than 33 hands/hour then you tune 199/(# of hands per hour)

You can associate the set frequency with the frequency of getting a specific premium PP like AA. As we all know, we will get AA once in 220 hands.

So, I would say this: In 6-7 hours of live play we can expect on average to get pocket AA once and besides that to flop some kind of any set also. In a full day of play you can see that you’ll get on average the supreme PP plus some kind of set. We will have at least two big hands during one day of live play. But don't go crazy with your AA after the flop. You can shove all-in preflop if you have the opportunity but be cautious post flop with unimproved AA.

Last edited by Octavian; 03-27-2009 at 05:15 AM.

 03-27-2009, 05:43 AM #10 SimonG adept     Join Date: May 2005 Location: No risk it ~ no biscuit Posts: 708 Re: Probability of flopping a set? To flop a set (or better): You know what 2 cards are because you have them as a pair in your hand. First card off the deck then you have a 2/50 chance to hit. (A) If that fails you will have a 2/49 chance to hit on the second card (B) If that fails you will have a 2/48 chance to hit the last flop card. (C) As you aren't bothered (from the assumption at the start) whether you hit a set, quads or a boat, the maths then becomes [A OR B OR C] which is [2/50 + 2/49 + 2/48] which comes out at a little worse than 7/1 or the 12% previously quoted. There are lots of situations (particularly live play where you don't have your calculator handy) where a rough and ready calculation will do - so [2/50+2/50+2/50] = 6/50 = 12%. You get a small rounding error, but moderate maths ability could get you there during a hand if you wanted to know if you were getting your price. If you are playing a hand and there is a pot of \$585 and it is \$150 to call, for all but the very gifted the decimal places are immaterial as you can't work it out in your head and it shouldn't make a difference anyway if the pot is laying you 12% OR 12.2% Even if you are capable of working it out, it is so close that the difference shouldn't be the difference for you between one play and another. Knowing that you are 'a bit worse than 4/1' from the pot should be all the maths you need to play the hand and all the other factors can come into play.
 03-27-2009, 09:38 PM #11 Zeds_Dead70 centurion   Join Date: Mar 2009 Posts: 100 Re: Probability of flopping a set? Relevance being, most weak players can see flushes or straights on a flop but a set catches them off guard. How big of a raise will you call with a pocket pair under 9s in hopes of flopping a set? The implied odds in low limits are huge. Last edited by Zeds_Dead70; 03-27-2009 at 09:39 PM. Reason: grammage
03-27-2009, 11:15 PM   #12
Octavian
banned

Join Date: Sep 2005
Location: Las Vegas
Posts: 828
Re: Probability of flopping a set?

Quote:
 Originally Posted by Zeds_Dead70 Relevance being, most weak players can see flushes or straights on a flop but a set catches them off guard. How big of a raise will you call with a pocket pair under 9s in hopes of flopping a set? The implied odds in low limits are huge.
With a big pair like AA, KK, QQ I will raise if I’m the first one in or 3bet if opponent raises upfront. Now if I play deep stack, and have PP under 99, I will call based on stack odds. If the raiser is deep too I will call 5% to 7% of my stack. If for example I have \$1,000 and pocket 77, the guy up front open raise for \$50 to \$75, I will call if I figure I’m not going to be re-raised in the back. I call up to 7% of my stack and see the flop even if I suspect the upfront raiser has AA.

In fact, I want him to have AA and I want him to believe that he should play that pair real fast and hard all the way to the river. That is the ideal scenario for your 77. If the raiser bets about 1/15 of his stack and you cover than I would say CALL. If on the other hand the raiser has \$100 stack and he open-raise for \$25 and you suspect him for having a big pair or AK I will not call. Why? Because you will be a big dog against any overpair and about even money against AK and the reward when you hit your set will not cover the losses you accumulate when you miss. He doesn’t have enough dough for you to attack after the flop.

When you hit your set on the flop and there is a flush or a straight draw possible, don’t rush to raise and re-raise to knock your opponent out of his draw. Just bet enough for him to call as a mistake but do not raise him too much so he’s making the correct play of folding. Bet about halve of the pot. You want him to call you! You have more outs to make a FH or Quads against him. When you have a set on the flop and his drawing to flush he’s got only 7 clean outs while you’ve got the rest of the deck working for you. Actually, from 47 cards left he’s got 7 clean outs to flush while you don’t have to hit anything to beat him unless he hits his flush, after that point you still have 10 outs to kill his hand.

Never slow play a flopped set! Nobody knows you have a monster anyway, therefore, it is stupid to conceal the strength of your hand. Backing off to a raise and then check-raising on the turn is a valid strategy (although not necessarily best). I do not back off when there is a third suited card on board. I feel that I have enough outs to disregard the possibility of a made flush against me.

Note:
1. If you lose with a set, you'll lose a lot of money. If you don't, you are not playing your sets correctly

2. The reverse it’s also true: If you win with a set, you'll win a lot of money. If you don't, you are not playing your sets correctly

Last edited by Octavian; 03-27-2009 at 11:30 PM.

03-28-2009, 10:27 AM   #13
jay_shark
Pooh-Bah

Join Date: Sep 2006
Posts: 3,655
Re: Probability of flopping a set?

Quote:
 Originally Posted by SimonG To flop a set (or better): You know what 2 cards are because you have them as a pair in your hand. First card off the deck then you have a 2/50 chance to hit. (A) If that fails you will have a 2/49 chance to hit on the second card (B) If that fails you will have a 2/48 chance to hit the last flop card. (C) As you aren't bothered (from the assumption at the start) whether you hit a set, quads or a boat, the maths then becomes [A OR B OR C] which is [2/50 + 2/49 + 2/48] which comes out at a little worse than 7/1 or the 12% previously quoted. There are lots of situations (particularly live play where you don't have your calculator handy) where a rough and ready calculation will do - so [2/50+2/50+2/50] = 6/50 = 12%. You get a small rounding error, but moderate maths ability could get you there during a hand if you wanted to know if you were getting your price.

To compute the probability that you will hit a set or better, then using a Venn diagram, you can set the problem up like this:

Deal the cards one at a time and label the first card A, the second card B, and the third card C.

P(A or B or C)

= P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C)

P(A or B or C)

= 2/50 + 2/50 + 2/50 - 2/50*1/49 -2/50*1/49 - 2/50*1/49

~ 11.755%

 03-28-2009, 03:01 PM #14 PantsOnFire Pooh-Bah     Join Date: Sep 2006 Location: Bumpy car ride... Posts: 5,720 Re: Probability of flopping a set? The easy way of doing this is by starting with the approximation that the chances of a particular card coming up is about 2%. So if there are two cards that can help you and there are three cards flipped up, the chance is 2(good cards)x2(%)x3(flop)=12%. Let's delve into this even deeper. Say you have AKoff. You now have 6(good cards)x2(%)x3(flop)=36%. Thank you, thank you, I'll be here all week.
03-29-2009, 10:28 AM   #15
SimonG

Join Date: May 2005
Location: No risk it ~ no biscuit
Posts: 708
Re: Probability of flopping a set?

Quote:
 Originally Posted by jay_shark Your approach has some errors. To compute the probability that you will hit a set or better, then using a Venn diagram, you can set the problem up like this: Deal the cards one at a time and label the first card A, the second card B, and the third card C. P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) P(A or B or C) = 2/50 + 2/50 + 2/50 - 2/50*1/49 -2/50*1/49 - 2/50*1/49 ~ 11.755%

To me all it looks like you have done here is worked out a set or better, and then subtracted the probabilities of hitting a better hand. So your answer looks correct for Probability of hitting a set and only a set. In poker, whilst you are working out your price of flopping a set, you presumably won't mind hitting quads either, so the assumption of "set or better" seems fair.

No matter either way, most of my point is that whether you use a quick and relatively accurate method such as the 2% rule - it is something you can do real time and is therefore helpful to live poker players. Real time, Venn diagrams aren't any use, the maths is interesting from a 'settling a prop bet' angle to 4 decimal places, but for poker, quick and approximate ftw.

03-29-2009, 10:38 AM   #16
jay_shark
Pooh-Bah

Join Date: Sep 2006
Posts: 3,655
Re: Probability of flopping a set?

Quote:
 Originally Posted by SimonG To me all it looks like you have done here is worked out a set or better, and then subtracted the probabilities of hitting a better hand. So your answer looks correct for Probability of hitting a set and only a set. In poker, whilst you are working out your price of flopping a set, you presumably won't mind hitting quads either, so the assumption of "set or better" seems fair.
If you took the time to read it, you'll realize that I actually computed the probability of flopping a set or better. I specifically mention this.

If you had solely mentioned that the approximate probability of flopping a set or better is 12%, then I would have let it go. You did actually make an attempt at a more rigorous approach which is theoretically wrong and I had to correct you.

It's only fair.

 03-29-2009, 12:56 PM #17 maximumprobability grinder   Join Date: Jan 2008 Location: Stanford CA USA Posts: 596 Re: Probability of flopping a set? And why not do it the simplest possible way ie you have 50 cards left and 2 of which 1 at least you want to come at flop . That of course = 1 - chance the flop doesnt have any of the 2 . Since there are (50,3) possible flops and only (48,3) that dont have the card you want the chance of no (set or better) is (48,3)/(50,3) so p(set+)=1-48*47*46/50/49/48=11.7551...% Also people will recognize this as 1-(48/50)*(47/49)*(46/48) which is 1 - products of probabilities to miss the critical cards on each one of the three flop cards, since you want all 3 to miss it its a product! (already used above by DarkMagus but in the form above people can relate to it with probabilities instead of combinatorics. However combinatorics brutal force method is the best way to handle such problems as they become more complex in other special questions and conditional probabilities can lead to confusions sometimes.) Obviously this is close to 1-96%^3 (96% ~48/50 approx 47/49 approx 46/48 of cards dont get get you to set or better per trial) since 1-96%^3~12% you get a rough answer fully understanding the spirit of all above but using a fast approximation like (1-x)^n~1-nx for small x , here n=3 and x=4% ps: (n,k)=n!/k!/(n-k)!
 04-27-2009, 07:19 PM #19 Rushton14 journeyman   Join Date: Nov 2008 Location: nova scotia Posts: 286 Re: Probability of flopping a set? chances of floping a set are like 1 in 7.5 or close to it.
04-27-2009, 07:39 PM   #20
moki
Carpal \'Tunnel

Join Date: Oct 2005
Location: Rochester, NY
Posts: 8,037
Re: Probability of flopping a set?

Quote:
 Originally Posted by Rushton14 chances of floping a set are like 1 in 7.5 or close to it.
Yes, I know this -- that wasn't my question.

04-27-2009, 08:05 PM   #21
SuitedEights
journeyman

Join Date: Mar 2009
Posts: 203
Re: Probability of flopping a set?

Quote:
I can't answer your question exactly, but I will give it a shot. Math guru's butcher my post after this. If you are calculating the odds of your flopping a set, you are roughly 1:7.5. However, when you look for your opponent also flopping a set, now there are only 2 cards on the flop that he could have hit a set with compared to the general "1:7.5" odds, so just for the odds that your opponent also has a set, it might be lower. Then for you to flop a set and him to flop a set, I'd say you'd have to multiply these two numbers and that would give your final statistic of both of you flopping a set.

Ok, here is what I think…

Odds of your not flopping a set = (48/50)*(47/49)*(46/48)=88.2%
Odds of your opponent not flopping a set = (1)*(47/49)*(46/48)=91.9%
(the (1) here being a sure thing because you have to have a set card)
Odds of your flopping a set= 100%-88.2%=11.8%
Odds of your opponent flopping a set= 100%-91.9%=8.1%

Odds of both events happening= 11.8%*8.1% = 0.96%

Last edited by SuitedEights; 04-27-2009 at 08:24 PM.

 04-27-2009, 08:26 PM #22 Senator Wright journeyman     Join Date: Jan 2008 Location: Grinding my Live Roll Online Posts: 352 Re: Probability of flopping a set? you'd also have to take into account the odds of another player having a pocket pair.
04-27-2009, 11:59 PM   #23
moki
Carpal \'Tunnel

Join Date: Oct 2005
Location: Rochester, NY
Posts: 8,037
Re: Probability of flopping a set?

Quote:
 Originally Posted by SuitedEights I can't answer your question exactly, but I will give it a shot. Math guru's butcher my post after this. If you are calculating the odds of your flopping a set, you are roughly 1:7.5. However, when you look for your opponent also flopping a set, now there are only 2 cards on the flop that he could have hit a set with compared to the general "1:7.5" odds, so just for the odds that your opponent also has a set, it might be lower. Then for you to flop a set and him to flop a set, I'd say you'd have to multiply these two numbers and that would give your final statistic of both of you flopping a set. Ok, here is what I think… Odds of your not flopping a set = (48/50)*(47/49)*(46/48)=88.2% Odds of your opponent not flopping a set = (1)*(47/49)*(46/48)=91.9% (the (1) here being a sure thing because you have to have a set card) Odds of your flopping a set= 100%-88.2%=11.8% Odds of your opponent flopping a set= 100%-91.9%=8.1% Odds of both events happening= 11.8%*8.1% = 0.96%
Thanks for your reply -- I guess that last line is the crux of the argument, though.

One of the guys at our game is saying that if we assume you have *already* flopped a set, and with that given, what are the odds that someone else also has a set in the hand.

My contention is that the odds would be as you describe them... because you need to know when two events happen at the same time. His contention is that the fact that you've already flopped a set means the calculation is different.

04-28-2009, 01:26 AM   #24
PantsOnFire
Pooh-Bah

Join Date: Sep 2006
Location: Bumpy car ride...
Posts: 5,720
Re: Probability of flopping a set?

Quote:
 Originally Posted by moki His contention is that the fact that you've already flopped a set means the calculation is different.
Well tell him that if you don't flop a set, the calculations are very easy. Then walk away.

04-28-2009, 03:17 AM   #25
SuitedEights
journeyman

Join Date: Mar 2009
Posts: 203
Re: Probability of flopping a set?

Quote:
 Originally Posted by PantsOnFire Well tell him that if you don't flop a set, the calculations are very easy. Then walk away.
But your posts always contain a flopping set, how am I supposed to just walk away?

 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 Two Plus Two     Two Plus Two Magazine Forum     The Best of Two Plus Two     The Two Plus Two Bonus Program     Two Plus Two Pokercast     Two Plus Two Videos     Marketplace         Classified Listings         General Marketplace         Staking - Offering Stakes         Staking - Seeking Stakes         Staking - Selling Shares - Online         Staking - Selling Shares - Live         Staking Rails         Transaction Feedback & Disputes     Commercial Marketplace     Classified Listings     Staking - Offering Stakes     About the Forums Fantasy Sports     Fantasy Sports         Sporting Events General Poker Discussion     Beginners Questions     Live Casino Poker         Poker Venues         Regional Communities     Poker Goals & Challenges     Books and Publications     Poker Theory     Poker Tells/Behavior, hosted by: Zachary Elwood     News, Views, and Gossip, Sponsored by Online Poker Report     Twitch - Watch and Discuss Live Online Poker     Televised Poker     Home Poker     Poker Legislation & PPA Discussion hosted by Rich Muny     That's What She Said!     Poker Beats, Brags, and Variance Coaching/Training     Coaching Advice         SpinSng.com - Smart Spin Team     Cash Game Poker Coach Listings     Tournament/SNG Poker Coach Listings     SpinSng.com - Smart Spin Team International Forums     Deutsch         BBV [German]     Français     Two Plus Two en Español Limit Texas Hold'em     High Stakes Limit     Medium Stakes Limit     Small Stakes Limit     Micro Stakes Limit     Mid-High Stakes Shorthanded     Small Stakes Shorthanded     Limit-->NL     Heads Up Limit No Limit Hold'em     High Stakes PL/NL     Medium Stakes PL/NL     Small Stakes PL/NL     Micro Stakes PL/NL     Medium-High Stakes Full Ring     Small Stakes Full Ring     Micro Stakes Full Ring     Heads Up NL     Live Low-stakes NL Tournament Poker     STT Strategy     Heads Up SNG and Spin and Gos     High Stakes MTT     Midstakes MTT     Small Stakes MTT         MTTSNG     MTTSNG     MTT Community     MTTc - Live         WPT.com Other Poker     High Stakes PL Omaha     Small Stakes PL Omaha     Omaha/8     Stud     Draw and Other Poker General Gambling     Backgammon Forum hosted by Bill Robertie.     Probability     Psychology     Sports Betting     Other Gambling Games Internet Poker     Internet Poker         Winning Poker Network         nj.partypoker.com         Poker Bonuses, Rakeback, and Affiliates     Internet Bonuses     Affiliates, RakeBack, and Bonuses     Commercial Software     Software         Commercial Software         Free Software     nj.partypoker.com         WPT.com 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     Wrestling     Golf     Pool, Snooker, and Billiards     Chess and Other Board Games     Video Games         League of Legends         Hearthstone         Starcraft 2         World of Warcraft     Puzzles and Other Games Other Topics     Politics         Economics     Politics Unchained     Business, Finance, and Investing     Travel     Science, Math, and Philosophy     History     Religion, God, and Theology     Health and Fitness     Student Life     The Studio     Laughs or Links!     Computer Technical Help     Programming

All times are GMT -4. The time now is 06:17 AM.

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