I made Quads 5 times in 940 hands yesterday. Odds on that? - Gambling and Probability

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I made Quads 5 times in 940 hands yesterday. Odds on that?

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10-13-2017 , 01:08 PM

TRUSTtheDRAWCESS

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Seems pretty unlikely. First 5nl shot on stars. None were just on the board.

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10-13-2017 , 03:10 PM

Didace

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If you play enough hands it's 100% that it will happen at some point.

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10-13-2017 , 03:52 PM

heehaww

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Chance of it happening in a given hand without it being on the board = 13 * C(48,3) * [C(7,3)-5] / C(52,7) / C(7,3)
= about 1 in 694

Chance of it happening at least 5 times in 940 hands = about 1 in 80 (binomial distribution)

Last edited by heehaww; 10-13-2017 at 03:58 PM. Reason: Subtract 5 on-board arrangements, not C(5,2)

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10-13-2017 , 04:17 PM

Didace

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^^ Assumes all hands are played and get to the river, correct?

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10-13-2017 , 04:49 PM

whosnext

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Also, presumably, the 940 boards in question were "rich" in pairs and trips.

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10-13-2017 , 10:08 PM

NewOldGuy

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Bottom line is this sequence of events is mildly interesting and not all that remarkable.

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10-14-2017 , 09:12 AM

heehaww

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Quote:

Originally Posted by whosnext

Also, presumably, the 940 boards in question were "rich" in pairs and trips.

Guess it depends if he means 940 hands dealt in, or 940 hands where he saw a flop (which might be weighted toward pocket pairs).

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Originally Posted by Didace

^^ Assumes all hands are played and get to the river, correct?

Yup. Hero sounds like someone who sees lots flops though

And then to make quads by the river, you need at least a pair by the flop, and Hero probably saw lots of turns/rivers when having a pair on the flop. This might be what Whosnext was alluding to.

Regardless, it's what NewOldGuy said.

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10-14-2017 , 12:13 PM

whosnext

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That might have been what I was alluding to. Maybe yes, maybe no.

It seemed to me that OP was giving himself all the credit when in fact the boards deserved a great deal of the credit too!

Looking back on it now, I realize that it was a silly and largely vacuous comment that probably should not have been made.

Last edited by whosnext; 10-14-2017 at 12:49 PM.

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