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How a live baccarat shoe runs, from the shuffle to the last hand
A baccarat table works through one shoe at a time. Step through it below: the shuffle, the burn, the cut card, one hand with its third cards, the roads and the last hand. Every figure on screen is computed from a shuffled eight-deck shoe. This is an explainer, not a game: there is nothing to bet and no balance.
Eight decks, 416 cards, are shuffled together and loaded into one shoe.
A baccarat shoe usually holds eight standard decks, although some tables use six. Eight times fifty-two gives 416 cards. They are shuffled together so that no deck keeps its order, then stacked and slid into the shoe, a box the dealer draws from one card at a time. From here on, every card that leaves the shoe is final: none goes back until the next shuffle.
The first card is shown; its value says how many more are burned face down.
Before the first hand, the dealer turns over the top card. Its value decides how many further cards go face down into the discard, unseen. An ace counts as one, two to nine as printed, and a ten, jack, queen or king counts as ten here, not zero as it would in a hand. The live providers' published game help does not describe a burn; this model follows New Jersey's published casino rules as an example. In this shoe the first card is a seven, so seven more cards are burned.
The cut card goes in near the back: in this model, 14 cards from the end.
A plastic cut card is pushed into the stack near the back. The cards behind it are never played. The live providers' published help does not say where it goes. New Jersey's published casino rules, given here as an example, ask for at least fourteen cards behind it; other houses place it elsewhere. This explainer assumes exactly fourteen, which leaves the number of cards shown in the panel in front of the cut.
Bets are taken for a set time; then the dealer calls no more bets.
Every hand starts the same way. Bets on Player, Banker or Tie are accepted while the betting window is open; at a streamed table the time left is shown on screen. When the window closes, no more bets are taken and the deal starts. No card leaves the shoe while bets can still change, so nobody bets on a card already seen.
Four cards come out in turn: Player, Banker, Player, Banker.
The dealer draws four cards in a fixed order: the first to Player, the second to Banker, the third to Player and the fourth to Banker. Each hand is then counted. Aces are worth one, two to nine their face value, tens and court cards nothing, and only the last digit of the sum counts. Here Player has two and Banker has three.
The drawing rule decides any third card; nobody at the table chooses.
A third card is never a choice. Player draws on a total of nought to five and stands on six or seven. Banker then follows a fixed chart that looks at Banker's total and Player's third card. Here Player draws a five and reaches seven; Banker, on three against a five, draws a two and stops on five. Player wins seven to five.
A squeeze shows a card slowly. It changes the pace, never the result.
Some tables reveal cards slowly, bending or peeling them before showing the value. It is theatre. The card was fixed the moment it came out of the shoe, in the order the shuffle put it there, so a slow reveal cannot change what it is. A squeeze table simply runs fewer hands in the same time than a table that turns cards straight over.
The roads record every result. They are a record of the shoe, not a forecast.
Beside a live table, scoreboards called roads log the shoe so far. The bead plate fills one mark per hand, column by column; the big road starts a new column whenever the winner changes and marks ties on the last entry. Both only describe what has happened. The next hand still comes from the shuffled cards, and a run of one result does not make the next hand more likely to follow or to turn.
The cut card comes out: live tables end on that hand; this model deals one more.
At a live table, the providers' published help makes the hand in progress the last hand of the shoe: the dealer completes it and deals no more cards until the shoe is changed. Some casino rules, New Jersey's for one, deal one more hand after it, and this model follows that example. The rest of the cards are set aside and a freshly shuffled shoe comes in. In this shoe the panel shows which hand reached the cut card.
Across 20,000 simulated shoes, one shoe gave 81.5 hands on average, from 76 to 88.
To see what one shoe yields, the same procedure ran on twenty thousand shoes, each shuffled from its own seed: eight decks, the burn, the cut card fourteen cards from the back, the drawing rule, one hand after the cut card. The count varies because the burn takes two to eleven cards and a hand uses four to six. Nine shoes in ten gave 79 to 84 hands.
Over 1,629,572 hands, Banker won 45.87 %, against an exact eight-deck value of 45.86 %.
Counting every hand of every simulated shoe gives Banker 45.87 %, Player 44.64 % and Tie 9.49 %. The exact values for a full eight-deck shoe, worked out by enumerating every possible deal, are 45.86 %, 44.62 % and 9.52 %. The gaps are the size that chance leaves over this many hands. The burn, the cut card and the roads change none of the odds.
How the numbers were made
The worked shoe is one eight-deck shoe shuffled with a fixed seed, so the same cards come out every time the page loads. The decks, the cut card and the end of the shoe follow the live providers' published game help listed below; the burn and the cut card's depth, which that help does not describe, follow New Jersey's published casino rules as an example: the first card shown and its value burned, the cut card 14 cards from the back, the standard drawing rule, the hand that reaches the cut card completed and, as in that example, one more hand dealt. For the last two steps the same procedure ran on 20,000 further shoes, each shuffled from its own seed, 1,629,572 hands in all. The exact shares come from enumerating every possible deal from a full eight-deck shoe. Limits: at a live table the hand that reaches the cut card is the last, so a live shoe gives about one hand fewer than shown here; a streamed table may also place the cut card elsewhere or burn in its own way. A deeper cut card means fewer hands per shoe; the win shares do not move.
Sources
- Baccarat (Wikipedia): shoe size, the burn, the cut card, the roads
- Pragmatic Play Live's baccarat game help, as published by licensed operators: eight decks, the cut card, the last hand
- Example: N.J.A.C. 13:69F-3.5 (New Jersey), the burn and the cut card's depth
- Example: N.J.A.C. 13:69F-3.8 (New Jersey), one more hand after the cut card
- Exact eight-deck odds: our full enumeration of the shoe