Sets / 100 ?

[ginko]

Im curious how often we flop a set assuming we see the flop with every pocket pair.

We get each pair 1 time out of every 220 hands. So thats 14 pairs every 220 hands.

We are 7.5-1 against flopping a set.

So we should flop a set roughly every 110-120 hands right?

Im a math nooblet so correct me if Im wrong.

.9 Sets / 100 ?

[Thornado]

For starters, there's 13 possible pairs, not 14. Anyhow, the probability that you are dealt any random pair is 3/51 (first card doesn't matter, but for second card you need one of the three remaining matching cards out of 51).

The probability that you will NOT flop a set (given that you have a PP) is (48/50)*(47/49)*(46/48)=2162/2450, and thus the probability that you WILL flop a set is 1-2162/2450=288/2450.

Thus, the total probability that you will flop a set is (3/51)*(288/2450)=864/124950=0.00691477 which is approximately .7 sets/100.

(I think this should be mathematically correct, but in case I made some stupid mistake, please correct me.)

[Red_Diamond]

It's 8.3 to 1 for hitting a set.
A random PP is 16 to 1.

[ginko]

Ok thanks guys, cleared things up.

[Duke]

<font color="gray">It's 8.3 to 1 for hitting a set.</font>

That's just wrong. I'm not sure what you did, but it's actually more like 7.506-1.

I'm getting .692 sets/100 with my gorilla math.

[SamIAm]

[ QUOTE ]
For starters, there's 13 possible pairs, not 14. Anyhow, the probability that you are dealt any random pair is 3/51 (first card doesn't matter, but for second card you need one of the three remaining matching cards out of 51).

The probability that you will NOT flop a set (given that you have a PP) is (48/50)*(47/49)*(46/48)=2162/2450, and thus the probability that you WILL flop a set is 1-2162/2450=288/2450.

Thus, the total probability that you will flop a set is (3/51)*(288/2450)=864/124950=0.00691477 which is approximately .7 sets/100.

(I think this should be mathematically correct, but in case I made some stupid mistake, please correct me.)

[/ QUOTE ]

This is a great first post.

Welcome to the forum.
-Sam

[Cobra]

You two are talking about two different things. The odds of hitting exactly a set are 8.28 to 1, the odds of hitting a set or better, including a boat and four of a kind are 7.51 to 1.

Cobra

[sawseech]

[ QUOTE ]
You two are talking about two different things. The odds of hitting exactly a set are 8.28 to 1, the odds of hitting a set or better, including a boat and four of a kind are 7.51 to 1.

Cobra

[/ QUOTE ]