How to Get Wizard’s Number of Combinations ?
February 10th, 2022 at 1:56:06 PM
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Recently I was asked by a friend to calculate the return of the blackjack side bet ‘Blazing 7s’.
I checked my results with the wizard of odds section: /games/blackjack/side-bets/blazing-7s.
Surprisingly I found differences in the numbers. Reason could be that Michael Shakleford uses a different model.
Can anybody explain me how wizard of odds got the combinations in the four tables ?
My actual understanding is, that the total combinations in the first two tables is the product of comb(309,2) * perm(312,3).
How did wizard get the combinations of the relevant subsets ?
mpower
I checked my results with the wizard of odds section: /games/blackjack/side-bets/blazing-7s.
Surprisingly I found differences in the numbers. Reason could be that Michael Shakleford uses a different model.
Can anybody explain me how wizard of odds got the combinations in the four tables ?
My actual understanding is, that the total combinations in the first two tables is the product of comb(309,2) * perm(312,3).
How did wizard get the combinations of the relevant subsets ?
mpower
February 10th, 2022 at 2:12:30 PM
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Link to WoO Blazing 7's:
https://wizardofodds.com/games/blackjack/side-bets/blazing-7s/
edit: link provided for convenience only; it does not address the question in the first post
https://wizardofodds.com/games/blackjack/side-bets/blazing-7s/
edit: link provided for convenience only; it does not address the question in the first post
Last edited by: Dieter on Feb 11, 2022
May the cards fall in your favor.
February 13th, 2022 at 3:26:56 PM
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I tried to get the Wiz to correct a typo on his Blazing 7's page back in 2018, but so far no luck:
https://wizardofvegas.com/forum/questions-and-answers/math/32019-typo-on-woos-blazing-7s-page/#post686945
Dog Hand
https://wizardofvegas.com/forum/questions-and-answers/math/32019-typo-on-woos-blazing-7s-page/#post686945
Dog Hand
February 13th, 2022 at 6:25:54 PM
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Looking at the first one
Player
(i) Player gets any 7 : 24 (312/13)
(ii) Player then gets identical 7 : 5
(iii) Player then gets third identical 7 : 4
Dealer
Total perms = 309*308/2 = 47586
Ways to get BJ = 24 Aces then 96 Pictures = 2304, so non-BJ = 47586-2304.
So total = 24 * 5 * 4 * 45282 = 21735360.
Similar logic for others, except when you have two or fewer sevens you need to cater for the fact that your (second and) third card wasn't a 7 so it could affect the BJ odds.
(I'm guessing you can only draw to two sevens if the dealer doesn't have BJ. It may be that if the Dealer does have BJ you still get paid on the first two sevens. If so this would mean you need to add up the various possibilities 77x non-dealer-BJ and 77 vs BJ etc.)
Player
(i) Player gets any 7 : 24 (312/13)
(ii) Player then gets identical 7 : 5
(iii) Player then gets third identical 7 : 4
Dealer
Total perms = 309*308/2 = 47586
Ways to get BJ = 24 Aces then 96 Pictures = 2304, so non-BJ = 47586-2304.
So total = 24 * 5 * 4 * 45282 = 21735360.
Similar logic for others, except when you have two or fewer sevens you need to cater for the fact that your (second and) third card wasn't a 7 so it could affect the BJ odds.
(I'm guessing you can only draw to two sevens if the dealer doesn't have BJ. It may be that if the Dealer does have BJ you still get paid on the first two sevens. If so this would mean you need to add up the various possibilities 77x non-dealer-BJ and 77 vs BJ etc.)
February 13th, 2022 at 10:39:26 PM
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Thanks charliepatrick !
The BJ for dealer explains properly my missing link.
.
@DogHand: I am a AP from Switzerland and recognized back in 2018 the error of wizard in the section of Blackjack Zurich Progressive. Shackleford corrected 2019 from BJ to AJ only for the Minor/Major jackpot. Unfortunately the side bet amount is still wrong. It should be 5 francs instead of wizard’s 10 francs.
The BJ for dealer explains properly my missing link.
.
@DogHand: I am a AP from Switzerland and recognized back in 2018 the error of wizard in the section of Blackjack Zurich Progressive. Shackleford corrected 2019 from BJ to AJ only for the Minor/Major jackpot. Unfortunately the side bet amount is still wrong. It should be 5 francs instead of wizard’s 10 francs.
