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View Full Version : Probability of Pocket Pairs turning into Quads twice in a row?

PocketPaul
10-28-2003, 09:15 AM
Playing micro limit online last night I limped in MP with pocket 3's and flopped the set /images/graemlins/smile.gif. Then to my surprise the 4th 3 appeared up on the turn. /images/graemlins/grin.gif

A few hands later (but the next time I had a pocket pair) I was dealt pocket 9's and once again I flopped the set /images/graemlins/smile.gif and got the quads on the turn /images/graemlins/grin.gif. Both hands gave me nice juicy pots of around 12 - 15 BB each.

My question is - what is the probability of 2 consecutive pocket pair hands turning into quads. Also what is the probability that in both cases the quads are formed by the turn?

thylacine
10-28-2003, 12:29 PM

Homer
10-28-2003, 03:41 PM
I'm going to give this a shot, even though I'm not 100% sure that I will be correct. If I am wrong hopefully Bruce or one of the other gurus will correct me.

1) Given that you have a pocket pair, probability of making quads by the river twice in a row:

P(quads by river) = [C(2,2)*C(48,3)] / C(50,5) = .008163 (.8163% or 1/122.5)

P(quads by river twice in a row) = .008163^2 = .000067 (.0067% or 1/15000)

2) Given that you have a pocket pair, probability of making quads by the turn twice in a row:

P(quads by turn) = [C(2,2)*C(48,2)] / C(50,4) = .004898 (.4898% or 1/204)

P(quads by turn twice in a row) = .004898^2 = .000024 (.0024% or 1/41684)

-- Homer

well
10-28-2003, 05:36 PM
[ QUOTE ]
[...]2) Given that you have a pocket pair, probability of making quads by the turn [...]:

P(quads by turn) = [C(2,2)*C(48,2)] / C(50,4) = .004898 (.4898% or 1/204)

[/ QUOTE ]

By making quads by the turn I don't think you should include the quads already hit on the flop, yet you did.
And, to answer the posed question correctly, I think you should also include boards like TTTT5, disregarding your pocket pair (unless it's the tens).
Unless you supposed the question wasn't posed well, but do not think that is quite polite.

Next Time.

Homer
10-28-2003, 05:52 PM
By making quads by the turn I don't think you should include the quads already hit on the flop, yet you did.

"Making quads by the turn" means you either flop quads or turn quads. Why should I not include instances in which the poster flops quads?

And, to answer the posed question correctly, I think you should also include boards like TTTT5, disregarding your pocket pair

I don't think that was the intent of the poster's question.

Unless you supposed the question wasn't posed well, but do not think that is quite polite.

Not polite? I tried to answer the poster's question to the best of my ability. What do you want from me?

-- Homer

PocketPaul
10-28-2003, 06:36 PM
Homer

You interpreted my question correctly and gave me an answer I could easily understand. /images/graemlins/smile.gif

Thanks