What are the odds?

Just got back from Atlantis in Nassau, Bahamas and had the following event at a blackjack table. What are the odds of this happening?

Played at a single deck game with just me and the dealer. New shuffle and of the first 4 hands, the dealer had 3 blackjacks. I was floored!

your cutcard was 1 card away from the exact opposite... :p

Aren't there only 2 black jacks in a deck? You sure it's a single deck? Seems suspicious..

4 aces and 12 cards 10 or higher. Does that equal 4 black jacks in a deck? The color of the cards is irrelevant. I may be wrong.

Quote: mason2386

...The color of the cards is irrelevant. I may be wrong.

I'm confident that your chain was being yanked.

This was a serious question but I'm glad you guys are having fun with it! This really happened and I wish I knew how to calculate the odds of this happening. They must be astronomical.

bummer man

were you betting 100+per hand?

did you get any 10/J/Q/K during the 3 rounds? If not, and assuming the burn card wasn't an A or a 10 value:

It's been a while since I've had to do this kind of probability math.. but isn't it something like:

[(4/51)*(16/50)] * [(3/47)*(15/46)] * [(2/43)*(14/42)]

Something like 1 in 123470

My starter bet is $50 - fastest $200 I ever lost.

Quote: paigower

did you get any 10/J/Q/K during the 3 rounds? If not, and assuming the burn card wasn't an A or a 10 value:

It's been a while since I've had to do this kind of probability math.. but isn't it something like:

[(4/51)*(16/50)] * [(3/47)*(15/46)] * [(2/43)*(14/42)]

Something like 1 in 123470

I only remember my first hand, which was a 20 (2 faces - thought this was going to start out nicely!). I really don't know the math, so I can't comment, although by the seat-of-the-pants method, it seems that the odds should be higher than that.

This will be 'close' but a sloppy approximation because you could easily look these numbers up. For a rough estimate, you basically want to know what the odds of the dealer getting 3 blackjacks in a row are... Same odds as the player getting 3 in a row. Thus, your answer is P(BJ)^3... where P(BJ) is the probability of getting 1 blackjack.

P(BJ) ...for an 8 deck game... = (32/416)*(128/416) + (128/416)*(32/416) = .0473, which is about 1 in 21 hands.

Thus, the probability of getting 3 blackjacks in a row is (.0473)^3 = .000106, which is about 1 in 9,261 (1/21 * 1/21 * 1/21).

DO NOTE: This is assuming a "fresh" deck on every deal. So the odds would be 'slightly' worse if you'd previously removed aces and 10's from the next deals. So ~1 in 20,000 for a close but sloppy approximation (as promised).

Single Deck
For this I'll try to use your information where you had 2 face cards first hand... etc.

The probability of the dealer getting 3 blackjacks in a row would be:
P(3BJ) = P(1BJ) * P(2BJ) * P(3BJ)

where

P(1BJ) = (4/52)(16/52) + (16/52)(4/52) = .0473 (1 in 21)
P(2BJ) = (3/48)(13/48) + (13/48)(3/48) = .0339 (1 in 30)
P(3BJ) = (2/46)(12/46) + (12/46)(2/46) = .0236 (1 in 42.5)

*P(2BJ) is 3/52 because we removed an ace from the first hand, and 13/52 because you said you had 2 face cards when the dealer blackjacked with one too.
*P(3BJ) is assuming we don't know your cards on the 2nd dealer blackjack... so only removing 1 ace and 1 10 from the 3rd round calculation.

therefore:

P(3BJ) = .0473 * .0339 * .0236 = .0000378, which should be 1 in the product of the denominators... 1 in 26,775

Bruce, a few of the responses have covered the probability of the dealer getting blackjack 3 of the first 3 hands. I believe you were asking about 3 bjs in 4 hands.

In an infinite deck, the probability of 3 bj in 4 hands is 4choose3*(P(bj))^3*(1-P(bj))^(4-1)=~4*(1/21)^3*(20/21)=~ 1 in 2431

In a single deck, the removal of the aces lowers the chance considerably. I think we can take Romes' 0.0000378 and multiply it by our 4*(20/21) from the above equation to reach about 1 in 7000 shoes, maybe once a week at Atlantis.

Sorry about your luck, but Atlantis only has 6 to 5 blackjack, so perhaps your $200 was doomed from the start. I don't think we still have the 'Gulf' regional forum, but we'd love to hear about your overall experience there, maybe in the 'Mississippi' forum.

Quote: studmuffn

Bruce, a few of the responses have covered the probability of the dealer getting blackjack 3 of the first 3 hands. I believe you were asking about 3 bjs in 4 hands.

In an infinite deck, the probability of 3 bj in 4 hands is 4choose3*(P(bj))^3*(1-P(bj))^(4-1)=~4*(1/21)^3*(20/21)=~ 1 in 2431

In a single deck, the removal of the aces lowers the chance considerably. I think we can take Romes' 0.0000378 and multiply it by our 4*(20/21) from the above equation to reach about 1 in 7000 shoes, maybe once a week at Atlantis.

Sorry about your luck, but Atlantis only has 6 to 5 blackjack, so perhaps your $200 was doomed from the start. I don't think we still have the 'Gulf' regional forum, but we'd love to hear about your overall experience there, maybe in the 'Mississippi' forum.

Great post... On a side: It's no fun if you do ALL the math for them, how will they ever learn? ;)... I like to do the math for something close, so if they just want an answer they have one, and if they want a more exact answer/understanding of how to get the answer they should be able to use my numbers and process slightly tweaked (as you did) =).