Continuous shufflers revisited

Many casinos have installed continuous shuffling machines (CSM) on their blackjack tables. These machines are a combination shuffler and dealing shoe that contain 4 (or sometimes 5) decks of cards. The dealer deals the cards from this device and then after one or several rounds picks up the discards and places them back into the CSM, where the cards are randomly mixed with the unplayed cards in the shoe (i.e., think of it as one shoe of cards that are continuously in play). This is quite different from the conventional manual or automatic shuffler where a cut card is used, most of the cards are dealt, and all the discards and unplayed cards are shuffled together.

Two independent studies were recently done to look at the effect of the CSM on the casino's edge against the basic strategy player. Michael Shackelford (www.wizardofodds.com) took the first crack at this and published his results in issue #8 of Blackjack Insider Newsletter (www.casino.com/newsletter/blackjack/archive/) and later published his result in an article in Casino Player Magazine (April 2001). This was followed by another study by Dan Catlin that appeared in the 2001 summer issue of The New Chance & Circumstance Magazine.

This is what these mathematicians concluded from their studies.

1. The average number of 10s per hand is slightly higher with a CMS game than with a game that uses a cut card.
2. The probability of getting a blackjack is slightly higher with a CSM game than it is with a game using a cut card.
3. The casino's edge over a basic strategy player is actually slightly less in a CSM game vs. a game using a cut card.
4. Overall the player in a CSM game will stand to lose about 20 percent more money because they will be dealt 20 percent more hands per hour in a CSM game.

Confusing? The key to understanding all this is a phenomenon in blackjack called the cut card effect. It works like this.

Suppose you take a single deck of cards and place the cut card two-thirds of the way into the pack of cards (at card 36). Assume there are 5 players and a dealer. The average number of cards dealt per hand in blackjack is 3, therefore you would expect 6 x 3 or 18 cards used per round. You would expect to reach the shuffle card after 2 rounds of play (18 cards per round x 2 rounds) and the cards would be reshuffled.

But let's assume for the moment that the first two rounds contain a disproportionate number of high value cards (10s through aces) so that there would be a lot of 20s and some blackjacks dealt in the rounds leading up to the shuffle card. This means that the players would be standing and not drawing a third or fourth card, therefore the number of cards per hand in this situation will be less than the expected three. So after the second round is finished, there will be fewer than 36 cards played and since the shuffle card did not appear, the dealer will deal a third round. Since a lot of 10s and aces (player-friendly cards) were already dealt, the remaining unplayed cards contain a lot of small, player-unfriendly cards. From the player's perspective, dealing the third round is not good.

Now let's look at the reverse situation, namely, during the first two rounds of play there is a disproportionate number of small cards played. When this occurs players will most likely average more than 3 cards per hand and the dealer will most certainly reach the 36th card (cut card) after two rounds and reshuffle. In this situation the remaining unplayed cards will be rich in player-friendly 10s and aces, but these cards would not be played because a third round would not be dealt. Not dealing a third round when the unplayed cards are rich in 10s and aces is also not good from the player's perspective.

Now what does the cut card effect have to do with a CSM? Without going into a lot of technical details, Shackelford found that in a CSM game (which is like playing against a freshly shuffled shoe every hand) you'll draw disproportionately more high cards out of the deck. But when a cut card is introduced, the cut card effect introduces more small cards in the last hand and neutralizes the player-friendly bias in the CSM game.

Catlin did a similar study and found that the probability of a player getting a blackjack is slightly higher with a CSM game compared to a game that uses a cut card for the same reason (cut card effect). Shackelford estimated the casino's edge decreases in a CSM dealt single-deck game by 0.113%. However, the more decks used, the smaller the effect (the casino's edge only decreases by 0.020% in a six-deck game).

On the surface, it appears that a basic strategy player would be better off playing a CSM game with its slightly lower casino edge compared to a game that uses a cut card. However, the lower casino edge is more than offset by the greater number of hands that will be dealt per hour (Catlin estimates 20 percent more hands per hour). Remember with a CSM game, there is no manual shuffling. The game is dealt continuously from the four decks of cards with no break in the action. A basic strategy player is therefore betting more money per hour in which the casino has the edge and therefore will lose more money (about 20 percent more) on average per hour.

To summarize, even though the casino's edge is slightly lower in a CSM game, this is more than offset by the faster speed of the game, resulting overall in a greater hourly loss for the basic strategy player. My recommendation to basic strategy players is to stick with the good old hand-shuffled game or a game where all the cards in the shoe are shuffled by an automatic shuffler and avoid games dealt by a CSM.