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STEMucator

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## Main Question or Discussion Point

Hi,

I found this screenshot on a website and I thought it was crazy. I want to calculate the conditional probability of this event occurring because it seems so impossible.

Assume NLTH is being played. I want to calculate the conditional probability of this hand being dealt. Here is a screenshot of the hand and my work:

Please note I'm computing this because I'm curious and I like to practice.

I made a few assumptions along the way:

First, I'm assuming the players who didn't turn over a hand are getting dealt cards that are not ranked 9, 10, J, Q, or A. This is a reasonable assumption because most of those cards are in the hands of the players who turned them over, and are on the board.

Also, when I calculate the probability of the cards on the board, I assume there are 4 cards of rank 8 left in the deck. I think this is reasonable because there was originally a 32/50 chance that the next card was not a 9, 10, J, Q, or A after the first two cards are dealt. Only 4/32 of those cards were of rank 8, and only 8/32 of those cards are dealt to players pre-flop. So assuming you do get dealt one of those 32 cards, the chance of an 8 would be unlikely. I could go as far as to compute the conditional probability of an 8 being dealt along the way, but assuming all 8s are still in the deck seems reasonable on average.

I also assume no cards of rank 8 are burnt.

Finally, the person next to the right of the dealer button gets dealt to first.

Assuming these things, I find myself looking at a number on the order of ##10^{-16}## (after multiplying by ##100 \%##). So according to that, this should happen roughly 1/10 quadrillion times? I don't think people have collectively played enough cards in a lifetime to see this one.

I found this screenshot on a website and I thought it was crazy. I want to calculate the conditional probability of this event occurring because it seems so impossible.

Assume NLTH is being played. I want to calculate the conditional probability of this hand being dealt. Here is a screenshot of the hand and my work:

Please note I'm computing this because I'm curious and I like to practice.

I made a few assumptions along the way:

First, I'm assuming the players who didn't turn over a hand are getting dealt cards that are not ranked 9, 10, J, Q, or A. This is a reasonable assumption because most of those cards are in the hands of the players who turned them over, and are on the board.

Also, when I calculate the probability of the cards on the board, I assume there are 4 cards of rank 8 left in the deck. I think this is reasonable because there was originally a 32/50 chance that the next card was not a 9, 10, J, Q, or A after the first two cards are dealt. Only 4/32 of those cards were of rank 8, and only 8/32 of those cards are dealt to players pre-flop. So assuming you do get dealt one of those 32 cards, the chance of an 8 would be unlikely. I could go as far as to compute the conditional probability of an 8 being dealt along the way, but assuming all 8s are still in the deck seems reasonable on average.

I also assume no cards of rank 8 are burnt.

Finally, the person next to the right of the dealer button gets dealt to first.

Assuming these things, I find myself looking at a number on the order of ##10^{-16}## (after multiplying by ##100 \%##). So according to that, this should happen roughly 1/10 quadrillion times? I don't think people have collectively played enough cards in a lifetime to see this one.