by the Green Baize Vampire

In the past few years a new countermeasure has emerged from the casino laboratories to foil blackjack card counters-the dreaded shuffling machine.

The premise behind the creation of such a device is simple-a machine can randomize a deck of cards more quickly and effectively than a human . Shuffle time is wasted time that could be spent dealing extra rounds. A round or two extra in an hour will make a staggering difference to the casinos annual profit margin. But casinos generally shuffle up with at least 25% of the cards remaining owing to the fear of card-counters, who benefit greatly from seeing many cards dealt out.

The casinos must strike an effective balance between the two to optimize their profits. Except that the shuffle machine changes all that,effectively they eliminate shuffle time.

How this is achieved depends on the variety of shuffler. There are two distinct forms-the garden variety autoshuffler, and the exotic continuos shuffler.

The autoshuffler does away with "down-time" by using two sets of cards, one set is being shuffled while the other is being dealt. Whenever the house wants a new shuffle it just inserts unshuffled cards into the machine and removes the freshly-shuffled pack.

The continuos shuffler is rather different: cards are taken out of play and directly reinserted into the machine, usually before the round itself has been completed. There is no break in the action at all.

News of these machines created an almost hysterical response in the card-counting community. The implications were clear: without a significant % of cards dealt out card-counting is ineffective. In the past the casinos were forced to deal out may cards because increased shuffle time would result in loss of action from ordinary players. Now they could eliminate shuffle time altogether, with the happy side-effect of making their games uncountable.

Except, it was'nt that simple. The first generation of continuos shufflers were introduced at the Mirage several years back.Two teams of professional card-counters, one led by Stanford Wong, burned out the game, making off with tens of thousands of dollars before the casino removed the machines.

How was this possible?

The problem is that their is a latency of redistribution. In layman's terms this means cards played on one round probably won't appear on the next. Exactly when they will find their way back into the shuffle depends on the number of players, the speed of play, and most importantly the variety of machine itself. The exact figures can only be derived by peeking inside the machine or by statistical anlysis.

How do you do this?

This is no big secret though few card-counters actually know how to do it. Any statistics text book will tell you how to go about doing this. Basically you memorize a card on one round and look to see if it appears on the next. The chance of a card of any value being dealt is 1 in 52 with a single-deck. The chance of it being dealt on the following round is 0 if it has not been redistributed into the pack. So if the card repeatedly fails to turn up on the following round, it is a very strong indication that the cards of the first round are not redistributed in time for the second round.

Now, most modern continuos shufflers use more than one deck. This brings up the problem of distinct cards. How on earth do we tell one ace of spades from another? Surely this means we cannot work out the redistribution frequency?

In fact it is not that big a problem. We can use a simple method to determine whether or not cards are recycled immediately.

First, memorize the first three cards dealt on a round.

On the next round, look at the first three cards (the first three cards only). Add 1 to a running total in your head if any of these three cards match the three cards you memorized from the previous round. You must play basic strategy and bet the table minimum while doing this.

The chance of a match not occuring is 196/208*195/207*194/206 or roughly 83%. This assumes that the cards from the previous round have been redistributed into the shuffle.

We can test this by calculating the standard deviation.

This calculated by taking the number of hands (say,1000 ),multiplied by the probability of the first card being the first card of the subsequent round (17%), assuming a full shuffled deck and multiplying again by the probability the cardwon't appear again (83%). Finally we press the square root button on our calculator to get the standard deviation. The figure we get is 11.87.

The most likely outcome if cards from the previous round are redistributed immediately is that we will get 170 matches . We test for randomness by seeing if three standard deviations separates our actual from our projected results (35.61). Therefore we have a fairly good ideathat if the actual number of matches we get is less than 135 then there is a >99.7% chance that the cards from previous rounds are not available for play.

If the actual number of matches is between these two figures then more clocking is required for certainty.

1000 hands played at $5 will cost the player $50, so this is not without cost. It will also require ten hours of play. The best way to clock a shuffle machine is of course while not playing, but this is obviously impractical for long periods.

The above figures are calculated on the basis of a hypothetical four-deck game with a player who memorizes three cards. You must alter the calculations if the conditions you are playing under are different, or you can easily memorize more cards per hand. Obviously the more you can memorize the fewer trials are needed.

In face-down games we can eliminate the need for a large number of trials. We can do this by exploiting the asymmetry of certain cards. If you look at the six of spades and turn it upside down you will see it is not symmetrical, ie it is recogniseably different depending on which you turn the card. Therefore, if you turn it one way, and turn every other six of spades the other way, then you will know when that particular six of spades has been redealt.

Once you have determined how many rounds it takes for cards to reenter play, you can count on a round by round basis. For example if it takes three rounds for discards to renter play then you have to keep the count of the last three rounds in your head at all times.If the first three rounds you play are +2,-1 and +3, you now have a "total" count of +4. If on the next round you get a count of -3 then you rub out the first round count of +2, and now have a total count of -1, +3 and -3, which is -1.

Generally, it does not take that long for cards to return to play. This is not the same as counting a game with shallow penetration, since you are effectively playing the last hand of a game with shallow penetration, which is mathematically more attractive.

The other advantage of playing a continuos shuffler is that there is no heat, because casino personnel think these machines are unbeatable. You will be able to obtain very large bet spreads with no attention.

I have heard rumours that new machines are under development which will virtually eliminate the latency of redistribution. Qualified sources have already told me there are machines in existence which will have a ready-to-deal stack only five cards short of the full pack.

Would these machines be unbeatable? No. In fact they can be spectacularly profitable.

With these machines there is the possibility that cards taken out of play may return on the same round. If a player to my left is dealt the jack of spades and busts, those cards will be returned to the discard tray and I may receive a jack of spades as one of my hit cards on the same round.

It can be seen that a team can exploit this. A high-roller could be stationed at third base. Small bettors can take up the rest of the table. The small bettors play in order to maximize the value of the high-rollers hand.

For example, a high-roller is dealt 16 against the dealer's six, and stands. A table minimum bettor to his left is also dealt a ten and a six. If the small player hits and busts those two cards are returned into the continuos shuffle machine which increases the chance of a dealer bust. The small player has made a play contrary to basic strategy, but the team as a whole benefit because the high-roller now stands a greater chance of winning the hand.

A prototype strategy I devised would give such a team a 3% edge over the casino. This did not include plays that could not be made for cover reasons, and included the losses of the small players, assuming a 1:50 ratio between high and low-rollers.

Finally, what about the auto-shufflers used to make up shoes? Could a casino set these machines to say, 20% penetration and eliminate the threat of card-counting?

Currently, to the bemusement of card-counters, tables with these machines are set to deal approximately the same % of cards as the human-shuffled tables.

The reason for this is simple. These machines tear up the cards. The cost of replacing cards may eliminate much of the profits from low-limit tables. So, the casinos keep decks in play too long. There is so much card entrophy the card backs become distinguishably warped if shuffling is frequent.

It takes visual acuity and a good memory to recognize the non-uniform characteristics of a card back, but it can be done if the cards are truly mangled. The gain from recognizing when an ace is to be dealt as your first card is 2000 times that of a card-counter on each hand, assuming optimal betting. We are not talking about a minor edge. You could seriously threaten the casinos profitability in any short space of time.

In at least one instance, this type of coup has been successfully executed for over $100,000 dollars (eqv.).

Theoretically, the casinos could use these machines at the high-limit tables where the card cost is comparatively unimportant. But high-rollers are quite resistant to these machines, as they are with any procedural change.

Consider, for example the unneccessary ceremony of baccarat, where typically thirty to forty hands are dealt per hour. On a mini-baccarat table as many as six hundred hands could be dealt. Yet, the casinos will not consider alienating their most valuable customers by replacing the big table game.