Here's a tough one!

So, the probability of obtaining a suited blackjack with a six-deck shoe is 0.0118723. I'm assuming that if I wanted to determine the probability of obtaining a specific suit, I would multiply(?) that by four. NOW... how would I go about figuring the odds of obtaining a suited blackjack, then obtaining another suited (any suit) BEFORE obtaining another blackjack? And the real mind-blower: How could I figure the odds of obtaining a suited blackjack, then obtaining another one of the same suit before obtaining any other blackjack? (Assuming double-deck and six-deck shoes)

"Never tell me the odds" -Han Solo

Quote: D3thd33lr

So, the probability of obtaining a suited blackjack with a six-deck shoe is 0.0118723. I'm assuming that if I wanted to determine the probability of obtaining a specific suit, I would multiply(?) that by four.

Er, I get the probability of any blackjack in a 6-deck shoe as 0.0118724. The probability of a suited one is 1/4 of that, or 0.0029681. The probability of a blackjack in a specific suit is 1/4 of that, or 0.000742.

Quote: D3thd33lr

NOW... how would I go about figuring the odds of obtaining a suited blackjack, then obtaining another suited (any suit) BEFORE obtaining another blackjack?

Another suited what before obtaining another blackjack?

Sorry. Suited Blackjack

Another clarification: once you get your "first" suited blackjack, which I assume has to be on your next hand (otherwise the probability is greater than 0.0118723), does the suited blackjack that comes before the unsuited blackjack have to be on the next hand after that, or is it just that when you get your next blackjack, it has to be suited, even if it's 200 hands later?

Quote: ThatDonGuy

Er, I get the probability of any blackjack in a 6-deck shoe as 0.0118724. The probability of a suited one is 1/4 of that, or 0.0029681. The probability of a blackjack in a specific suit is 1/4 of that, or 0.000742.

0.0118724 is right for a suited blackjack.

You have a 1/16 chance of your next blackjack being a specific suit.

It does not have to be the next hand; just the next blackjack, even if 20-200 hands later

Quote: CrystalMath

0.0118724 is right for a suited blackjack.

Let me see where I got this wrong, then:
A 6-deck shoe has C(312, 2) = 312 x 311 / 2 2-card hands.
A suited blackjack has one of the 96 10-cards and, for each of those, one of the 6 Aces of the matching suit.
The probability is (96 x 6) / ((312 x 311) / 2) = 0.011872372

That's strange - yesterday I got 1/4 of that for some reason...

Anyway, as for the probability of your next blackjack being suited, let's assume that your previous blackjack was in spades.
There are 23 Aces, of which 5 are spades and 6 are in each of the other suits.
There are 95 10-cards, of which 23 are spades and 24 are in each of the other suits.
Of the 23 x 95 = 2185 different possible blackjacks, (23 x 5) + (24 x 6) x 3 = 547 of them are suited, so the probability of the next blackjack being suited is 547/2185 = 0.25034235.
As for a blackjack of the same suit as before, there are 5 Aces and 23 10-cards, so the probability = 115/2185 = 1/19 = 0.052631579.

In a 2D game:
After a blackjack in spades, there are 7 Aces, of which 1 is a spade, 2 are hearts, 2 are clubs, and 2 are diamonds, and 31 10-cards, of which 7 are spades and 8 each of the other three suits. Of the 7 x 31 = 217 blackjacks, 7 + 16 + 16 + 16 = 55 are suited, so the probability is 55/217 = 0.25345622, and the probability of a blackjack the same suit as before = 7/217 = 1/31 = 0.03225806.

Note that these do not take into account the likelihood of more (or fewer) Aces than 10-counts appearing before the next blackjack. That probably needs to be simulated rather than calculated.

My 1/16 number did not account for deck composition. It may very well be that your next blackjack is two or three shoes from now.

Nicely done! It's funny-I've been dealing for years and people always assume I'm a math prodigy. I stink at math. I tell them it's more like reading at this point; For example, you don't sound out R-E-D: you look at "red" and just know that it says "red", in the same way I see a 9,5,7 as 21. This question has been bugging the hell out of me for a while, now. Thank you so much!