What are the odds of this happening?

Ladies & Gentlemen,

I was playing at a LV casino over the weekend and something occurred at the table I have never seen. There were three players at the table plus the dealer. A shuffle just happened and on the first round post shuffle, every player AND the dealer all were dealt a Blackjack. I have been playing casually for almost 20 years and was amazed at what I saw (so were the other players & dealer as well). I am curious as to what are the odds of 4 participants all being dealt a Blackjack on the first hand? The game was using two decks.

I don't know if that will ever happen again in my lifetime, but I was so awestruck I had to ask those in the know how "rare" of an occurrence it was. Thanks so much!

Depends on the number of decks. How many decks in the shoe?

For a single deck the chances are very slim as there are only four aces in the entire deck.

( 52 4 ) = 270725

Only one of those ways is four aces you need (one per each player).

From there, the chances that you get all faces for the remaining four card is

( 16 / 48 ) * ( 15 / 47 ) * ( 14 / 46 ) * ( 13 / 45 )= 1/106.912

The for a single deck game, I'm coming up with 1 in ( 270725 * 106.912 ) = 1 in 28.943 million.

For more than a single deck, it's much more common. I apologize if my math is wrong, and I would be surprised if it were right. I'm not a math guy! Get ready for the ridicule!

Assuming I'm wrong, the chances are very likely more common than this, but this at least is a ceiling for how remote this is to occur.

Quote: unlvhotrod

Ladies & Gentlemen,

I was playing at a LV casino over the weekend and something occurred at the table I have never seen. There were three players at the table plus the dealer. A shuffle just happened and on the first round post shuffle, every player AND the dealer all were dealt a Blackjack. I have been playing casually for almost 20 years and was amazed at what I saw (so were the other players & dealer as well). I am curious as to what are the odds of 4 participants all being dealt a Blackjack on the first hand? The game was using two decks.

I don't know if that will ever happen again in my lifetime, but I was so awestruck I had to ask those in the know how "rare" of an occurrence it was. Thanks so much!

happens all the time.

Assuming Ahigh's math is right, remember that the results he got would be the odds for that result on one specif hand. Multiply by the thousands of hands you've seen, and the odd that you see it in that lifetime becomes much more likely.

Maybe not quite the "happens all the time" frequency that Alex is implying, but not at all that rare either.

Put another way: Shit happens.

Not quite 4 hands as the OP, but I was playing 2 hands from third base on a full table when I got BJ on both of my hands in the same deal. Naturally, the dealer also had BJ, so that was 3 hands dealt in sequence that had a BJ.

On an infinite deck game, odds of Blackjack for one hand is 1/13 * 4/13 * 2 = 4.7337%

So the odds of 4 blackjacks in an infinite deck is .047337^4 or .00000502126

In 8 decks it is 32/416 * 128/415 * 2 = .047451344 for the first one.
Then 31/414 * 127/413 * 2 = .046051631 for the 2nd one
Then 30/412 * 126/411 * 2 = .044646021 for the 3rd one
and 29/410 * 125/409 * 2 = .04323454 for the 4th one.

Put them all together to get 0.000004218005 for four blackjacks in a row on the beginning of an eight shoe deal.

I think the OP mentioned a 2 deck game. Here are the rounded chances for four blackjacks directly off the top for different deck sizes

infinite - 1 in 199,153
8 deck - 1 in 237,079
6 deck - 1 in 252,138
2 decks - 1 in 447,677
1 deck - 1 in 1,808,986

my attempt 4 years ago (Prob and Stats 101)
'1 in' values

all hands	1 deck	2 deck	6 deck	8 deck
1	20.72	20.92	21.06	21.07
2	564.01	496.63	461.57	457.62
3	22,721.56	13,657.31	10,552.37	10,250.00
4	1,808,985.94	447,677.15	252,138.31	237,078.88
5	n/a	18,226,855.26	6,311,131.53	5,669,408.19
6	n/a	983,575,115.55	165,903,550.61	140,352,422.26