Soft 17

What are the odds that the dealer gets a soft 17 in a 8 deck shoe?

On the first hand of the shoe, I think it's (32/416)*(32/415)=.005631. So, about 1 in 169.

Quote: sport

What are the odds that the dealer gets a soft 17 in a 8 deck shoe?

In infinite deck, which is reasonable close to 8 decks, it is 0.018038227

Quote: rdw4potus

On the first hand of the shoe, I think it's (32/416)*(32/415)=.005631. So, about 1 in 169.

Don't know the answer, but your calculation presumes a soft 17 is only A,6. But it can be comprised of more than two cards. (A,3,3 etc.).

So a soft 17 is A-6, A-5-A, A-4-2, A-3-3, A-4-A-A, A-3-A-2, A-3-A-A-A, A-2-2-2, A-2-2-A-A, A-2-A-A-A-A, and A-A-A-A-A-A-A and all combinations thereof.

One would have to calculate the number of combinations of each, keeping in mind that the combinations can cope out in any order.

For example, A-6 can also be 6-A. The odds of getting an A is 1/13 and the odds of the next card being a 6 is 1/13. Multiply result by 2 because a soft 17 in two cards is an A-6 and a 6-A, which is 2/169 or .0118343 on an infinite deck.

A-A-5 or A-3-3 is 1/13 x 1/13 x 1/13 * 3 or .001365.
A-4-2 is 1/13 x 1/13 x 1/13 * 6 or .002731.

Overall a 3 card soft 17 then is 12 x 1/13 x 1/13 x 1/13 or .0054620

A four card soft 17 is (1/13) to the fourth power x (4 + 4 + 12) = .0007002

A five card soft 17 is (1/13) to the fifth power x (5 + 10) = .0000404

A six card soft 17 is (1/13) to the sixth power x 6 = .0000001

A seven card soft 17 is 1/13 to the seventh power = .00000002

Add it all together and you get .01803823 as the total probability on an infinite deck. The probability is reduced as the decks are lowered.

Inotherwords, what Mango said.

Quote: rdw4potus

On the first hand of the shoe, I think it's (32/416)*(32/415)=.005631. So, about 1 in 169.

You have to double this for the first two cards as you can get either A-6 or 6-A.

I wish Sport would come back to this thread and clarify.

If it were me asking, I would be wondering the odds of a soft 17 where the dealer's up card was a 6. After all, that's the only combination where it, and the house rule, would affect my own decisions.

Quote: DJTeddyBear

I wish Sport would come back to this thread and clarify.

If it were me asking, I would be wondering the odds of a soft 17 where the dealer's up card was a 6. After all, that's the only combination where it, and the house rule, would affect my own decisions.

I was so sure that was the intended question, I didn't even think twice before providing my answer this morning.

Sorry guys I should have explained more. The casino I live next to just switched from not hitting soft 17 to hitting soft 17. I understand that the house edge changes but was curious as to how many times does this event actually happen. Seems like they think that are going to make more money but I dont see it. I think they are going to loss thier players to another casino. I my question should have been what are the odds of any combination of soft 17 occuring in a 8 deck shoe?

Quote: sport

Sorry guys I should have explained more. The casino I live next to just switched from not hitting soft 17 to hitting soft 17. I understand that the house edge changes but was curious as to how many times does this event actually happen. Seems like they think that are going to make more money but I dont see it. I think they are going to loss thier players to another casino. I my question should have been what are the odds of any combination of soft 17 occuring in a 8 deck shoe?

Again, it is reasonable close to 0.018038227. That is 1 out of about 55.4 rounds.

Quote: rdw4potus

I was so sure that was the intended question, I didn't even think twice before providing my answer this morning.

The answer to that question would be 1/13 though ;)

Another way to answer the original question, with exact values for 8 deck, we look at https://wizardofodds.com/blackjack/appendix2b.html

For 8 deck, Stand 17, we get probability of 17: 0.145215
For 8 deck, Hit 17, we get probability of 17: 0.133409

The difference is 0.011806.

Quote: weaselman

The answer to that question would be 1/13 though ;)

No it wouldn't.

For infinite deck purposes, the answer is ( 1/13 ) * ( 1/13 ) = 0.59%

I.E. It's the chance that a six is the top card and an ace is the hole card.

Well, the way I read your version of the question was what was the chance of soft 17, provided that the top card is 6 (since that would be the only situation that affects your actions)