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.
click here!This post received a 1.8% upvote from @randowhale thanks to @team-leibniz! For more information,
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
Using irrelevant tags, especially popular tags, makes it hard to find good and relevant content.
Please try to use only relevant tags when posting!
#steemit
Please only use the “steemit” tag for articles distinctly related to Steemit, the website, itself.
#steem
Please only use the “steem” tag for articles distinctly related to the steem blockchain itself.
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!