Learn / Finite Shoe vs Continuous Shuffling

In a finite shoe, every card dealt changes the cards that are left.

A continuous shuffling machine keeps putting used cards back into play. That changes what the cards you have already seen can tell you about the cards to come. OddsOfBlackjack is built for finite-shoe games.

The finite shoe

Shuffled once, dealt down to the cut card, then shuffled again.

In a shoe game, the decks are shuffled together, a cut card is placed in the stack, and the cards are dealt round after round. In the usual procedure, when the cut card comes out, the round in progress is completed and the cards are then shuffled again, according to the table’s rules. Until that shuffle, every card dealt stays out of play.

Because nothing is put back, the cards that remain are the full shoe minus every card dealt so far. Each round changes that remainder, so rounds dealt from the same shoe are not independent of one another. This dependence is what card-counting research studies: Edward O. Thorp showed in 1961 that the player’s prospects change with the cards that have already been played.

Between shuffles
Dealt Cards Stay Out
Cards played in earlier rounds are not available again until the next shuffle.
Composition
The Remainder Drifts
As the shoe is dealt, the mix of cards left can move away from the starting mix, in either direction for the player.
Depth
Penetration Sets the Limit
How much of the shoe is dealt before the shuffle decides how far the remainder can drift.
Automatic shufflers are not all continuous.
Some tables use an automatic shuffler that shuffles a complete shoe, or a batch of cards, between shoes. That replaces the hand shuffle, but the game is still a finite shoe: it is dealt to the cut card and then reshuffled.
Continuous shuffling

The used cards go back into the machine while the game goes on.

A continuous shuffling machine (CSM) supplies the cards for each round and takes back the discards during play, mixing them in with the cards still waiting to be dealt. Once the discards are loaded back, the cards you saw in earlier rounds are no longer excluded from the rounds that follow. A record that subtracts every card seen does not follow those reinsertions.

Limiting what earlier cards reveal was the stated purpose of an early design: a patent issued in 1986 describes its apparatus as making card counting “virtually impossible”. How often the discards are loaded, and how many cards wait inside the machine, depend on the model and on the casino’s procedure. This page makes no claim about what the history of a particular machine can or cannot reveal.

Finite shoe Continuous shuffling machine
When used cards return At the shuffle, after the round in which the cut card comes out During play, as the discards are loaded back
Cards seen since the shuffle Stay out of play Can return to play in later rounds
The remaining cards Full shoe minus every card dealt Replenished with the used cards
Subtracting the cards you record Follows the cards removed from play, as far as you see and enter them Does not follow the cards the machine puts back
Why the recorded composition matters in OOB

OOB calculates from the cards you record. It assumes those cards stay out of play.

In OddsOfBlackjack you record the exposed cards as they are dealt. Each recorded card is removed from the remaining shoe until the shoe is reset with NEW SHOE, and the available actions are evaluated from that remaining shoe. OOB tracks the cards you enter, not a direct measurement of the physical shoe. Record each known removed card once and reset at the shuffle. Unseen cards and entry errors remain limitations.

This page compares two ways of dealing. It does not estimate a house edge for either, and it is not a statement about any particular casino or machine.

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Related pages.

Record each exposed card once: Getting Started →