Side Bet Shuffle

Some years ago I received an e-mail from a perplexed casino boss asking why he was losing so much money at the Super 7's game. Three successive jackpots had been hit.

I replied that I did not usually assist casino personnel, but since his request was courteous and the answer could not harm advantage players, I told him that Super 7's is rather a volatile proposition that, while favouring the house in the long run, would see dramatic fluctuations along the way during which the house could be hit quite hard.

Now I'm not so sure. Or rather I am sure, but for different reasons than I initially suspected.

It's well established that adjacent cards tend to remain in close proximity with greater frequency than pure chance would suggest following a shuffle. At regular blackjack this does not usually matter a great deal. The effect on the raw mathematical odds of the game is fairly minimal.

However, when you start introducing large payouts for infrequent card combinations, as with Super 7's, it matters a great deal. The mildest shift in the true odds of being dealt these combinations can shift the odds massively in favour of the player.

Unless there is some kind of systematic bias in the ordering process, the shuffle bias is just as likely to shift the odds in favour of the house as it is away from the player. However, the short-term fluctuations will hit the house much, much harder. Every time, for example, that a player receives three suited 7's in one shoe, the odds drop significantly that another player will receive this hand in the subsequent shoe and also that a player will receive one of the smaller payoffs associated with this bet. This can lead to double trouble for the casino.

To illustrate what I'm talking about, let's look at a more fashionable game, the new lucky ladies sidebet.

The jackpot on this wager is 2000-1. That's for receiving two queens of hearts while the dealer is dealt a blackjack. The raw math odds of this are 115,000 to 1. You are playing heads-up. Now let's assume that you see the two QH's go into the discard tray together. With this shuffle, there is an 8% chance that these cards remain together with a 1-card separation (the 1 card going to the dealer, so you get the two QH), a figure typical for the type of game shuffle-trackers go after. The odds of hitting the jackpot are now 15,000 to 1, a sevenfold increase!

When you take into account the revised overall payout schedule, you will find that the player has a significant positive expectation for this shoe. Not even I am so incredibly indiscreet as to spell this out in dollar terms, but it should be obvious that the player who has mastered the sequencing strategies presented in "Get The Edge At Blackjack" could attain an overall advantage well in excess of 100% at this type of game (though this type of advantage is ameliorated to some extent by the extreme volatility, which requires conservative betting).

This phenomena is not confined to blackjack. A year or so ago Frank Scoblete passed along a contribution from one of his readers asking if sorting pairs and triples together at Caribbean Stud, which is apparently a popular practice, changed the odds.

In the US these games use continuous shufflers which thoroughly randomize the cards, so my answer was that I did not think this was likely. However, in Europe such a strategy could be very effective: this game is almost universally hand-shuffled there.