Thread: Shoes Distribution

This thread is continued by Baccarat system design on the topic of Card Shoe and Result Shoe.

Let me repeat the statistics here:

(1) Total 500,000 shoes (1-deck):
Total hands: 5075866 (10.15/shoe)
Player: 2268293(44.688%) Banker: 2332781(45.958%) Tie: 474792(9.354%)
Total Shoes: 1.459E+42

(2) Total 500,000 shoes (half-deck):
Total hands: 2450623 (4.90/shoe)
Player: 1093333(44.614%) Banker: 1130165(46.117%) Tie: 227125(9.268%)
Total Shoes: 1.954E+19

Galo thinks the Card Shoe vs. Result Shoe distribution will obey Gauss distribution. I try to find it out. If the object is a 8-deck shoe, I have no idea how much samples should I run to get a close result because the whole set Card Shoe of 8-deck is 416!/[(32!)^9*128!]=1.6494E+376. So I better start it from a 1-deck shoe because not only the Card Shoe is much much less but the Result Shoe is about 2^10.15=1136. I would make the Result Shoe set 2^12=4096 and see how are the pigeons go into the pigeon-cages.

First I label the shoe from 0 to 4096 as followed. For example, a result shoe is PBPPPPBBPB (recorded from left to right, first hand is P last hand is B); convert it to 1011110010 (P=1, B=0) then take it as a Bin number and convert it to Dec number 317. Hence, this shoe is labeled 317. By this way shoe from 000-000-000-000 to 111-111-111-111 has the only individual label number from 0 to 4096. Note that the power order is from left to right; and the shoes are eliminated the Tie; and I do not delimit fixed hand shoe, i.e. there are shoes are 7 hands, there are shoes are 10 hands, etc. So all Banker shoes will have the same label 0, and some Result Shoe will overlap too, particular those shoe adding Banker after Player, e.g. shoe 0011101 has same label as 0011101-000 has. I will think about this label system later since I have already ran 5 million shoes.

See the curve and the output data. I can see the curve is not a Gauss curve, is it? Probably it is.

The shoe label method has drawback, any idea better one?

Since I start this 1-deck Card Shoes distribution topic, let me finish it. I redo the Result Shoe label with its own result, e.g. a result shoe 112212 (1=P, 2=B) is labeled with an integer 112212. Thus there are no more result shoes overlap issue. Also I put them in order from 1-hand shoe to 12-hand shoe (please refer to the Result Shoes.txt) by giving the shoe number from 1 to 8190.

The curve I upload does not tell good infornation regarding system design. I don't think the entire Card Shoes obeys Gauss distribution vs. Result Shoes. Card shoes (50-million sample) cluster here and there merely represent they are 8-hand shoes, 9-hand shoes, 10-hand shoes, etc. Within a certain hand shoe, say 9-hand shoes, I can't see any good information; nor they obey Gauss distribution.

This is 1-deck Card Shoes distribution look like. I guess 6 or 8-deck shoes may have similar look. If you can find any useful pattern from the curve please share here, thanks.