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# making trips n the flop

• Bronze
Joined: 15.04.2010
Hi Guys

Can some one give me the stat for making trips on the flop when holding pocket pairs.

I had a feeling it was 1 in 9 but I could be well wrong on that one!!

My stats are 21/309 closer to 1 in 15 - is that a correct stat or just variance?
• 14 replies
• Bronze
Joined: 09.06.2010
12% of the time more or less

Its a weird one for me, it seems everytime i hit a set its ona wet board so i cant get much value from it unless someone wants to pay with a draw, which is surprising a low amount of times!
• Bronze
Joined: 15.04.2010
Originally posted by joeldowey123
12% of the time more or less

Cheers

Last few I have managed to get value.... apart from JJ fl J v QQ, Q on the turn
• Bronze
Joined: 08.11.2008
Hello!

When you have three of a kind and you hold a pocket pair, it is called a set.

When you have three of a kind and there is a pair on the board (you hold the 3rd card in your hand), it's called trips.

I'm not sure if my calculations are collect, but they should be somewhat close.

P(set on flop) = 2/50 + 2/49 + 2/48 = 0,04 + 0,0408 + 0,0416 = 12,24%

Another interesting fact is: You will have a pocket pair in 0.0588 in cases. so 0,0588 * 0,1224 = 0,0072 means that if you see a flop with every pocket pair you hold, you have a probability of 0,72% to hit a set, which means that you will on average hit 7,2 sets per 1k hands, which is equivalent to 1 set every 139 hands.

Best regards,

Primzi
• Bronze
Joined: 15.04.2010
Thanks Primzi for that awesome answer
• Bronze
Joined: 14.03.2009
Originally posted by Primzi
Hello!

When you have three of a kind and you hold a pocket pair, it is called a set.

When you have three of a kind and there is a pair on the board (you hold the 3rd card in your hand), it's called trips.

I'm not sure if my calculations are collect, but they should be somewhat close.

P(set on flop) = 2/50 + 2/49 + 2/48 = 0,04 + 0,0408 + 0,0416 = 12,24%

Another interesting fact is: You will have a pocket pair in 0.0588 in cases. so 0,0588 * 0,1224 = 0,0072 means that if you see a flop with every pocket pair you hold, you have a probability of 0,72% to hit a set, which means that you will on average hit 7,2 sets per 1k hands, which is equivalent to 1 set every 139 hands.

Best regards,

Primzi
When did you learn how to do that?! Or was it a fluke?
• Bronze
Joined: 08.11.2008
That's highschool math duh . Pretty basic stuffs really, I just hope i actually got it right
• Bronze
Joined: 02.02.2009
Actually that calculation isn't correct since the probabilities don't add. (If you flip 2 coins the probability of getting heads is not 1/2 + 1/2 = 1)

If you assume your opponents will have each card with equal probability (not a very realistic assumption) the probability of NOT hitting a set is

P(not set) = (48/50)*(47/49)*(46/48) = 0.8824

so

P(set) = 1-P(not set) = 0.1176,

meaning you hit a set once every 8.5 flops.

If you drop the assumption the probabilities shouldn't change much but would depend on ranges and the preflop action and would be tough to calculate.
• Bronze
Joined: 14.03.2009
Basic answer is 1 out of 7.5 times though

EDIT**
Posted same time as above....

What you`ve said there is wrong, its widely known you get odds close to 8 to 1 to flop a set, but not over.
• Bronze
Joined: 02.02.2009
8 to 1 is the same thing as one in 9 times, so yes you get close to 8 to 1 (7.5:1) but not over. I think you're remembering the 7.5 from the 7.5:1 ratio.
• Bronze
Joined: 14.03.2009
Okay I am wrong. My bad. Sorry
• Bronze
Joined: 08.11.2008
As I said, I wasn't sure if i was correct, but I was somewhat close. The one excluding all the non sets seems about right. I have no idea why the oponent's cards should affect the probability of you hitting a set on the flop though, if we assume that you will see 100% of the flops, the probability should be like that... I see what you're getting at though, like if someone has a tight range and 3bets you preflop, you are less likely to hit the set with AA because his range "steals" some of the cards from the deck? But then again, that only decreases probability of that one case, and in the other case where most of oponents fold it would mean that they probably don't have an ace, which would increase your chances of hitting a set, but all in all everything should even out in the long run and the average probability should be those 11%, right?

Primzi
• Bronze
Joined: 10.07.2010
Originally posted by Primzi
Hello!

When you have three of a kind and you hold a pocket pair, it is called a set.

When you have three of a kind and there is a pair on the board (you hold the 3rd card in your hand), it's called trips.

I'm not sure if my calculations are collect, but they should be somewhat close.

P(set on flop) = 2/50 + 2/49 + 2/48 = 0,04 + 0,0408 + 0,0416 = 12,24%

Another interesting fact is: You will have a pocket pair in 0.0588 in cases. so 0,0588 * 0,1224 = 0,0072 means that if you see a flop with every pocket pair you hold, you have a probability of 0,72% to hit a set, which means that you will on average hit 7,2 sets per 1k hands, which is equivalent to 1 set every 139 hands.

Best regards,

Primzi
I'm not sure if it's correct or not, as I'm not sure if you can simply add probabilities. I prefer using 100% minus the probability of not hitting a set. Probability of not hitting a set is 48/50 x 47/49 x 46/48 = 88.24 percent. So the probabilty of hitting a set is 11.76 percent. Which is more or less 8/1.
Could just be a coincidence that you got near enough to it using addition...but I could be wrong
• Bronze
Joined: 10.07.2010
just realised that sum has already been done up there, my bad...
• Bronze
Joined: 15.04.2010
Originally posted by jass1960

I had a feeling it was 1 in 9 but I could be well wrong on that one!!

Great debate and it seems that 1 in 9 is the correct answer!!