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How calculate combinations in baccarat?

April 28th, 2011 at 9:33:51 AM permalink
Josephine2705
Member since: Apr 28, 2011
Threads: 1
Posts: 2
Hello,

I wonder how to calculate combinations in baccarat (8-deck shoe). For example , what is the combinations when player has 2 cards with total 1 scores and banker has 2 cards with total 9 scores. The answer is 45,033,013,641,216 based on Wizard (his site is just amazing) How to get this number?
here is the link:
http://wizardofodds.com/baccarat/baccaratapx.html

For example total combinations in baccarat is 416*415*414*413*412*411., it`s easy to calculate,
but when I am trying to figgur out portions like above, I lost in some patterns.

Can anybody help? Thank you.
April 28th, 2011 at 1:19:20 PM permalink
pacomartin
Member since: Jan 14, 2010
Threads: 547
Posts: 6211
Usually the Wizard is good about showing formulas if they are algebraic. He clearly wrote a computer program to do those tables.

The numbers do not look like they are easy to calculate. For instance if you prime factor the first column you get almost nothing.
28979901420544 = 2^10*29*107* 9,120,427
24291119898624 = 2^13*3* 988,408,199
26957461020672 = 2^13*11*23* 3,559
46033607532544 = 2^13*23*571*1929* 2,839,483
46171612971008 = 2^16*7*47* 2,141,407
etc.
Wine loved I deeply, dice dearly -Edgar, betrayed son of Gloucester in King Lear
April 30th, 2011 at 9:01:30 PM permalink
Josephine2705
Member since: Apr 28, 2011
Threads: 1
Posts: 2
Thank you. But even that numbers were figur out by a computer program. Formula exists. Like all this 9,120,427 ; 988,408,199 and so on... can be calculated. It should be "+" in formulas for partial numbers of combinations as well I guess... Thanks...

 

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