777
777
Joined: Oct 7, 2015
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January 26th, 2021 at 8:36:43 AM permalink
On Wizard of Odds site there is a table on Power 8’s Baccarat side bet listed a Three Suited Eights event with 666,369,134,592 combination.

https://wizardofodds.com/games/baccarat/side-bets/power-8s/

I want to know and to understand how the 666,369,134,592 combination was derived.
Wizard
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Wizard
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MrCasinoGames777
January 26th, 2021 at 11:13:24 AM permalink
Looping through all the way the cards come out that cause three suites eights to win.
It's not whether you win or lose; it's whether or not you had a good bet.
777
777
Joined: Oct 7, 2015
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January 26th, 2021 at 12:25:45 PM permalink
So you apply the traditional Baccarat drawing rules, go through 6 loops each representing 52 cards in a deck (52^6 iterations at a minimum). Am I correct so far? What I would like to know is the mathematical formulation or procedure that would yield the necessary 8-deck combinatorial combinations when the looping iterations are at the “three suites eights” events.
ThatDonGuy
ThatDonGuy
Joined: Jun 22, 2011
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777
January 26th, 2021 at 12:27:35 PM permalink
I think I can clarify.
There are 416 cards in the deck, and the table is counting all 416 x 415 x 414 x 413 x 412 x 411 possible ways to deal six cards in a particular order.
The deals have to be divided into four groups:
1 - neither the player nor the banker draw a third card; count the number of deals where the 4 dealt cards include 3 suited 8s and no other 8s (of any suit - otherwise, it would be counted as 4 8s In Initial Deal instead), and multiply by 412 x 411 (the number of possible permutations for the fifth and sixth cards).
2 - the player draws a third card, but the banker does not; count the number of deals where the 5 dealt cards include 3 suited 8s and no other 8s, and multiply by 411 (the number of possible cards that can be the sixth card).
3 - the banker draws a third card, but the player does not; count the number of deals where the 5 dealt cards include 3 suited 8s and no other 8s, and multiply by 411.
4 - both the player and the banker draw a third card; count the number of deals where the 6 dealt cards include 3 suited 8s and no other 8s.
Add up those four numbers.

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