15 million to 1?

Please could someone check my math.

I was playing blackjack on a table with 3 other players when the dealer amazingly dealt a perfect pair to each of the 4 boxes.

What are the odds of this occuring? We play using 6 decks here in the UK and I have calculated this to be aprrox 1 in 15 million.

This is even more unlikely than winning our national lottery so I would appreciate it if anyone could confirm or correct these sums.

Thanks,

Jon from Portsmouth England

What's a "perfect" pair?

Quote: jonfourtwenty

Please could someone check my math.

I was playing blackjack on a table with 3 other players when the dealer amazingly dealt a perfect pair to each of the 4 boxes.

What are the odds of this occuring? We play using 6 decks here in the UK and I have calculated this to be aprrox 1 in 15 million.

This is even more unlikely than winning our national lottery so I would appreciate it if anyone could confirm or correct these sums.

Thanks,

Jon from Portsmouth England

If you simply mean a pair of identical-value cards, the odds would be much lower, so I assume by "perfect pair" you mean exactly identical cards, like two Kings of Spades.

Assuming six decks:.

If you deal one card out of the shoe, there are five remaining identical cards. There are 311 cards left in the shoe, so the chances of getting that card are 5/311. This simplifies to 1/62 (rounded).

This event has to happen four times, so we multiply (1/62)(1/62)(1/62)(1/62). Because I'm lazy, I am ignoring minor adjustments, such as the fact that after the first identical pair has been dealt, subsequent identical pairs are slightly more likely (specifically, 5/309, 5/307, and 5/305).

Using the simplified calculation, I get 14,776,336 to one. The most precise calculation would be (5/311)(5/309)(5/307)(5/305) which, since I'm doing this all in my head, I am not inclined to do at the moment :)

A perfect pair is a sidebet on blackjack where you get dealt two cards exactly the same eg a pair of 8 hearts. From what I remember It pays 30-1 in the UK.

You also get paid 12-1 for a coloured pair (two red/black cards of same value eg 8 heart and 8 diamonds) and 5-1 for a mixed pair (any pair eg 8 hearts and 8 clubs)

Quote: Croupier

A perfect pair is a sidebet on blackjack where you get dealt two cards exactly the same eg a pair of 8 hearts. From what I remember It pays 30-1 in the UK.

You also get paid 12-1 for a coloured pair (two red/black cards of same value eg 8 heart and 8 diamonds) and 5-1 for a mixed pair (any pair eg 8 hearts and 8 clubs)

Let's see: you have a 62:1 shot at the identical pair, a 52.5:1 shot at the colored pair (why do you Brits always misspell that word--sheesh!) , and a 26:1 shot at the mixed pair. Outcomes:

5 identical-card winners x 30:1 payout= 150
6 same-color winners x 12:1 payout= 72
12 mixed winners x 6:1 payout= 72
288 losers= 0
Total 311 outcomes= 294

So the net return on the bet is 294/311. This solves to .94, so this bet has a house advantage of about 6%. Pretty decent as side bets on table games go; pretty lousy as far as bets in general go.

(I also did all the above math in my head, so there's a high probability of an error in there somewhere. I also rounded where laziness dictated that.)

Quote: DJTeddyBear

What's a "perfect" pair?

Angelina Jolie; Dolly Parton; Pamela Anderson; etc.

Quote: jonfourtwenty

...I was playing blackjack on a table with 3 other players when the dealer amazingly dealt a perfect pair to each of the 4 boxes.

What are the odds of this occuring? We play using 6 decks here in the UK and I have calculated this to be aprrox 1 in 15 million...

Our results agree. I get approximately 1 in 14,854,387.

Quote: ChesterDog

Our results agree. I get approximately 1 in 14,854,387.

OOOOOOOPSY. My calculation in my previous post was...wrong!!! Looks like we all basically agree.

Thanks everyone.

Still can't believe I saw that happen!

Quote: mkl654321

OOOOOOOPSY. My calculation in my previous post was...wrong!!! Looks like we all basically agree.

I don't understand, mkl. I thought your previous post was a suggestion that "Angelina Jolie; Dolly Parton; Pamela Anderson; etc." presented a perfect pair. Where was the miscalculation?


Edit: Or did you miscalculate that those perfect pairs were presented to YOU?

Quote: Doc

I don't understand, mkl. I thought your previous post was a suggestion that "Angelina Jolie; Dolly Parton; Pamela Anderson; etc." presented a perfect pair. Where was the miscalculation?


Edit: Or did you miscalculate that those perfect pairs were presented to YOU?

It was my failure to calculate the chance that they would all be presented, as the OP stipulated, AT THE SAME TIME.

Quote: mkl654321

It was my failure to calculate the chance that they would all be presented, as the OP stipulated, AT THE SAME TIME.

I still don't see a problem. ;-)