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July 21st, 2018, 07:53 AM  #1 
Newbie Joined: Jul 2018 From: twin cities mn Posts: 1 Thanks: 0  Can Someone Please Help Me?!
Analysis? Variable? Probability? IDK, But I am writing some casino industry related papers and I am totally stuck about how to figure something out concerning a casino game called baccarat. Here it is. The game of baccarat with simple rules. It is a no decision game for the person playing, unlike blackjack, so once the cards are set in the shoe, the order never change throughout the shoe. The person playing chooses either the banker or the player side, for the sake of these questions, forget about the tie or the side wagers available in the game. My questions are (and i will be grateful for any help or direction or even approximates given for any or all of them): 8 decks of cards are used, no jokers. Each shoe starts with 416 cards, for the 8 decks combined. All aces count only as 1 point. All 10's and all Face cards are worthless, counting as a zero. So a 10 and a 9 is a value of 9. Or a 8 and 5 are a total of a 4. Only count as high as 9, nothing over. Dealer has to burn the amount of cards at the beginning of a shoe determined by flipping the first one over. So a ten flipped will burn the next ten cards before the start of the shoe. An ace flipped will burn the next 1 before the start, etc. Each hand can only be 4 or 5 or 6 cards totaled, never less than 4 and never more than 6. Casinos vary, but they place the stop card at varying amounts at the rear of the deck before placing into the shoe. Most do 14 cards, some might do less and many do more, maybe 20 or so. No rock solid rule on that one. Here are the rules in a nut shell: __________________________________________________ __________ Rules of Baccarat: Baccarat is a card game that is dealt from a shoe that holds 6 or 8 decks of cards. Two hands are dealt by the house dealer, the "banker" hand and the "player" hand. Before the hands are dealt, bets may be placed on the banker hand, on the player hand, or on a tie. Winning bets on banker or player are paid 1:1, but a commission of 5% is charged on bank bets making the net odds on such bets 0.95 to 1. Some casinos may charge a lower commission (e.g., at this writing, Binion's Horseshoe in Las Vegas charges 4%.). Some sources report that tie bets are paid 8:1, while others claim that tie bets are paid 9:1, so this may vary from casino to casino. If there is a tie, bets on the banker or player are returned. Once a bet has been placed, there are no opportunities for further decisions  both the banker hand and the player hand are dealt according to fixed rules, resulting in final hands of either two or three cards for each. The value of a hand is determined by adding the values of its individual cards. Tens and face cards are counted as zero, while all other cards are counted by the number of "pips" on the card face. Only the last digit of the total is used, so all baccarat hands have values in the range 0 to 9 inclusive. The hand with the higher value wins; if the hands have the same value, the result is a tie. Rules for the player hand: If the player's first two cards total 6 or more, then the player must stand without drawing a card. If the player's first two cards total 5 or less, the player must draw one additional card. Rules for the banker hand: If the banker's first two cards total 7 or more, then the banker must stand without drawing a card. If the banker's first two cards total 0, 1, or 2, then the banker must draw one card. If the banker's first two cards total 3, 4, 5, or 6, then whether the banker draws is determined by the whether the player drew, and if so the value of the player's draw card, as shown by the table below. Bank Drawing vs. player's draw Bank N 0 1 2 3 4 5 6 7 8 9 < player's  draw card 9            8            7            6        D D   5 D     D D D D   4 D   D D D D D D   3 D D D D D D D D D  D 2 D D D D D D D D D D D 1 D D D D D D D D D D D 0 D D D D D D D D D D D  D = draw, N = no card drawn by player The probability distribution for a hand dealt from a complete shoe is as follows: Probability Probability of Probability of bank win of player win of tie  6 decks 0.458652719 0.446278570 0.095068711 8 decks 0.458597423 0.446246609 0.095155968 This implies the following house advantages: Bet bank Bet bank Bet player Bet tie Bet tie decks 5% vig. 4% vig. 9:1 8:1  6 1.05585% 0.59720% 1.23741% 4.93129% 14.43816% 8 1.05791% 0.59931% 1.23508% 4.84403% 14.35963% __________________________________________________ _________ What I need to know, my questions: 1) How many combinations can there possibly be when the shoe is set? There will always be between 76 and 84 hands/chances presented by the shoe, the dealer. Remember, each hand reduces the remaining hands of the shoe by discarding 4, 5 or 6 cards. (How many possibilities is a player wagering looking at with 416 cards, 2 to 11 removed and 7 to 20 remaining in the rear as stop cards?) 2) One of my main goals is to disqualify so many beliefs that a system can be invented to implement a schedule of wagers prior to dealing a hand(s) so the person playing could match up certain types, etc. That is why I want to know how many combinations or a total count of combos are possible with the 416 cards in the shoe. Meaning, wager on the Banker side because so many Players came out or any other event happened prior. 3) The other question is about the automatic casino shufflers or the outside vendor companies that legally provide preshuffled sealed decks of cards to the casinos, where they unlock the seal on the plastic case, burn the first card and whatever number of cards by the rule I mentioned, as well as a random cut by a customer/player, etc. Many people say, those automatic shufflers or the outside vendor companies can set up a shoe to be in the casino's best interest, so there are no long streaks or other patterns and trends that the players spot and wager heavy with, etc. Is it possible to have a preset deck of cards that are purposely set up in a certain order that could achieve this, even with a random cut by a player and then an undetermined amount of cars from 2 to 11 being removed from the beginning of the shoe? Thanks You for any help! A few other notes if it matters. More frequently than not, the ending total of the shoe will be relatively close, meaning 35 bankers, 35 players and approximately 10 ties. Rare instances will have a difference of about 10 or more winning hands for one side versus the other. 
July 21st, 2018, 06:36 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,112 Thanks: 1002 
Good luck buddy...I got a headache after reading about 1/4...
