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 .
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.
This post received a 1.8% upvote from @randowhale thanks to @team-leibniz! For more information, click here!
Hey I didn't know you were posting again. Welcome back!
Thanks! Was off for a bit because my job caught up with me and had to stop. Happy to be in a better place and posting again!
very good. follow you
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As a former steemcleaner myself, terribly sorry. Just tagging what I've observed have been common tags for posts like these. I will remove in future posts.
I never use the side bet.
Nice to see I inspired some more complicated math! More complicated than what I'm teaching my kids about blavkjac.. Your complex solution deserved it's own post!