This question came up in another thread and I thought it would be worthy of its own post. Apparently, many casinos offer a 10:1 side-bet for a suited blackjack when it occurs. Is this profitable over time?

Let's start with an Ace first blackjack, for a pattern.

Consider a one deck shoe.

The probability that the second card is a 10 point card is 16/51. So the probability of an ace first blackjack is (4/52)*(16/51). Multiply this by 2 because the ten could just as easily be the first card and the answer is

2*(4/52)*(16/51)= 128/2652 = 0.0482655, or about 1 in 20.7 .

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Now the suited blackjack

Same logic, different situation. Let's shift to a standard casino six deck shoe.

2*(4/13)*(6/311)= 0.0118723, or about 1 in 84.2.

Which, breaks down as:

• (4/13) - A reduction of (96/312) K, Q, J, or 10's in a 6 deck shoe.
• (6/311) - Six aces of the same suit of the previously drawn K, Q, J, or 10 in a 6 deck shoe. There are 311 cards in the denominator because 1 was drawn for the first. There are 312 cards in a six deck shoe.
• 2 - A multiplier because the Ace could have just as easily been the first card.

Just for Funsies

How about a suited blackjack on an N deck shoe.

N-Decks	Probability	Percent	1 in:
1	0.012066365	1.20664%	82.875
2	0.011949216	1.19492%	83.6875
3	0.01191067	1.19107%	83.95833333
4	0.01189149	1.18915%	84.09375
5	0.011880012	1.18800%	84.175
6	0.011872372	1.18724%	84.22916667
7	0.011866921	1.18669%	84.26785714
8	0.011862836	1.18628%	84.296875
9	0.011859661	1.18597%	84.31944444
10	0.011857122	1.18571%	84.3375
20	0.01184571	1.18457%	84.41875
100	0.011836596	1.18366%	84.48375
300	0.011835078	1.18351%	84.49458333
1000	0.011834547	1.18345%	84.498375

So, that bet that pays 10:1 ?

Yeah, pretty terrible. Has an awesome house edge.