What are the pre-flop odds for these hands?

[HoldemOrFoldem]

Hi everyone!

I have been searching everywhere but I can't find a 'pre-flop odds' list. Could you please correct any of the following if you know what the correct odds are? :

1. The flop will improve unsuited connector hole cards (e.g. 8c 7h) into a straight draw - 1 out of 11 times

2. Any two hole cards will improve to a pair on the flop - 1 out of 3 times

3. A pocket pair will improve to trips - 1 out of 11 times

4. Suited connectors (Jd Td) improve on the flop - 1 out of 3 times

5. One gapped suited connectors (e.g. Kh Jh) improve on the flop - 1 out of 5 times

6. One gapped unsuited connectors improve on the flop - 1 out of 11 times (???)

7. Any two suited cards will catch a flopped flush draw - 1 out of 11 times

I am trying to learn WHY I should be playing certain hands early or late in terms of position, (rather than just playing by the rules and not knowing the odds).

many thanks for all replies!

[aloiz]

1. The flop will improve unsuited connector hole cards (e.g. 8c 7h) into a straight draw - 1 out of 11 times

hmm, a open-ended/double belly buster? A gutshot? Any type of straight draw including a runner-runner?

2. Any two hole cards will improve to a pair on the flop - 1 out of 3 times

Well if you don't have a pair in the hole, you flop a pair and no better 14.5% of the time.

3. A pocket pair will improve to trips - 1 out of 11 times

Pocket pair flops a set 11.5% of the time (1 out of 8.7 times), and makes a set by the river roughly 18% of the time.

4. Suited connectors (Jd Td) improve on the flop - 1 out of 3 times

What do you mean by improve?? A flush draw, pair, straight draw, any overcard?

5. One gapped suited connectors (e.g. Kh Jh) improve on the flop - 1 out of 5 times

Again, define improve.

6. One gapped unsuited connectors improve on the flop - 1 out of 11 times (???)

Define improve

7. Any two suited cards will catch a flopped flush draw - 1 out of 11 times

You flop a flush draw about 11% of the time (1 out of 9). This does not include the times you flop a flush.

aloiz

[bomblade]

you have two cards in which to get in order to flop a set, when you hold a pocket pair...you have 6 cards in which to get, if you hold any two cards that are not pairs...yet, you believe the odds of flopping a pair to flopping a set is only a 14.5-11.5. I don't believe this is correct. I believe the odds of flopping a set is more like 1 out of 7.5...and the 3-1 in flopping a pair is accurate.

[BruceZ]

[ QUOTE ]
you have two cards in which to get in order to flop a set, when you hold a pocket pair...you have 6 cards in which to get, if you hold any two cards that are not pairs...yet, you believe the odds of flopping a pair to flopping a set is only a 14.5-11.5. I don't believe this is correct. I believe the odds of flopping a set is more like 1 out of 7.5...and the 3-1 in flopping a pair is accurate.

[/ QUOTE ]

You're correct. The 14.5% is off by about a factor of 2. The probability that hole cards of different ranks flop a pair and no more is 6*44*40*3/(50*49*48) = 26.9% or 1 in 3.7. The probability that they flop a pair or better is 1 - C(44,3)/C(50,3) = 32.4% or 1 in 3.1.

The probability that a pair flops a set and no more is 2*48*44*3/(50*49*48) = 10.8% or 1 in 9.3. The 1 in 8.7 figure aloiz quoted includes full houses. The probability that a pair flops a set or better is 1 - C(48,3)/C(50,3) = 11.8% or 1 in 8.5 or 7.5-to-1 (not 1 in 7.5). This does not include all 3 flop cards the same.

[aloiz]

Odds of flopping a set. I did not include the times that you flop four of a kind. C(2,1) * C(48,2) /C(50,3) = .115

Yea I did make an error for the pair. It should be twice what I said, and also I should have been more specific. I was assuming that he did not want to include the times the board pairs. If this is the case then the odds of pairing one of your hole cards is 2* (3 * C(44,2)/C(50,3)) = .289 If you include the times you flop two pair with both of your hole cards the answer comes out to 1/3.

aloiz

[BruceZ]

[ QUOTE ]
Odds of flopping a set. I did not include the times that you flop four of a kind. C(2,1) * C(48,2) /C(50,3) = .115

Yea I did make an error for the pair. It should be twice what I said, and also I should have been more specific. I was assuming that he did not want to include the times the board pairs. If this is the case then the odds of pairing one of your hole cards is 2* (3 * C(44,2)/C(50,3)) = .289 If you include the times you flop two pair with both of your hole cards the answer comes out to 1/3.

aloiz

[/ QUOTE ]

2* (3 * C(44,2)/C(50,3)) = .289 still includes times the board pairs in the final 2 cards. You have only eliminated pairing your hole cards again. To eliminate pairing the board you replace C(44,2) with 44*40/2. Similarly with a set, if you don't want to count full houses, you replace C(48,2) with 48*44/2.

[aloiz]

Thanks, I was aware of both cases, but I thought I clearly stated what I was calculating. I guess since he originally said a set it might be better to not include the times you hit a boat on a flop that pairs. Now whether any of my calculations is what the original poster was looking for is another question.

aloiz

[BruceZ]

[ QUOTE ]
Thanks, I was aware of both cases, but I thought I clearly stated what I was calculating.

[/ QUOTE ]

But you didn't calculate what you stated you were calculating:

[ QUOTE ]
I was assuming that he did not want to include the times the board pairs. If this is the case then the odds of pairing one of your hole cards is 2* (3 * C(44,2)/C(50,3)) = .289

[/ QUOTE ]

You are stating that this does NOT include the times the board pairs, but it actually does include the times the board pairs. To not include the times the board pairs, it should be 2*3*(44*40/2)/C(50,3) = 26.9%. Or equivalently, 6*44*40*3/(50*49*48) = 26.9%.

[aloiz]

You're right, in the future I need to be clearer. What I was intending to say was I did not include the times that the flop pairs and a hole card doesn't as a way of making the pair.

aloiz