Blackjack Streaks and Shuffles

Fred Renzey writes:

In the end it all comes down to the randomness question. Until it's determined positively whether shoe-dealt blackjack is more streaky than its theoretical probability dictates, the contention that progressive blackjack wins will remain a hotly debated controversy. Me? I seriously doubt it works.

A number of studies have been conducted into the effects of shuffles over the years by a series of highly respected theorists: Arnold Snyder, Bryce Carlson, Ken Fuchs, Mason Malmuth and Stanford Wong. The findings are interesting. Firstly, though each study produced different results, the universal opinion was that extreme forms of shuffling do produce some differences in player expectation that theoretical probability would contradict. Further, as a practical matter in most casinos, these effects were negligible or non-existent. A final consideration is that, even though their results produced strange effects on player expectation, they do not increase or decrease the probability of a streak beyond that predicted by theoretical probability.

In fact, I believe some shuffles may produce very minor increases and decreases in streaks under special conditions. This is because of the casino practice of setting minimum cut-card limits, a factor ignored or downplayed in the above studies.

The reason is simple and can be illustrated by a thought experiment. If the cards located behind the cut-card are low in value, the player will receive a higher than average number of high cards. Because high cards are good for the player, he is likely to win more money than expected. If the cards located behind the cut-card are high in value, the player will receive a higher than average number of low cards. Because low cards are bad for the player, he is likely to lose more money than expected.

Now, what happens to the cards behind the cut-card after the shuffle? Depending on the particular shuffle, some of the cards may be shuffled back into the pack, and some cards remain roughly where they are. Unless you are a skilled shuffle-tracker (a very powerful form of advantage play used by advanced card counters) who can follow the discards, you don't know where they go so it doesn't matter, right? Because the deck will be cut at some random point and the cards will be dispersed?

Not quite. Most casinos do not allow the pack to be cut from less than a deck away from the end of the pack. This means that a bias exists which can mean that, depending on the particular shuffle, cards located behind the cut-card tend to remain there, or tend to appear in front of the cut-card with more frequency than chance suggests. This would create a situation in which you could say that if you made a profit after playing a particular shoe, you know that the winning meant you received more than your fair share of high cards. You know that for this shuffle that means a significant proportion of those cards may end up behind the cut-card after the shuffle. This would create an anti-streaky effect. If the shuffle tended to redistribute the played cards in front of the cut-card, you would get to play those money cards again. This would create a streaky effect.

Now, this is all very well, but this is really just an interesting theoretical curiosity. It's not exploitable as a practical matter. The correlation between winning and losing shoes is very weak indeed, certainly not the basis of a practical winning system, gaining no more than a few tenths of a percent, unless you do something dramatic like bet table minimum and then table maximum when you think you have a hot shoe. Moreover, to determine what type of bias a shoe has is not easy unless you are a skilled shuffle-tracker, in which case you can beat the game easily anyway. Still, it's a fun way to annoy card-counters (Hey, I'm one of them!) who drone on about the law of independent trials whenever they sniff something vaguely unscientific.