Chapter 7. Blackjack Variance and Volatility Data

" May you live in interesting times" — reputed ancient Chinese curse

What are long and short runs?

There are four charts on this page displaying results starting with the short term (1,000 hands) and moving through successively longer terms (up to a million hands). We start with a chart displaying the total won or lost for a card counter playing 1,000 hands. The 1,000 hands are displayed in 100 groups of ten hands each. Each group of ten hands is a vertical line showing the minimum and maximum overall result from the start of the chart during those ten hands. So the last bar in the chart shows that in hands 991 through 1,000, our results varied between  -220 to -226 units. We can see a few large swings denoted by the long vertical lines. This is not a surprise. Most of the time we make small bets. But when the count rises, we can make several max bets and experience a large swing. This chart shows these occasional large swings and the fact that we can easily end up behind in 1,000 hands.

Now we move to 10,000 hands in groups of 100. The y-axis has been expanded to a larger range. We see some very large swings. The tenth line shows a range from about 1,300 to 1,800 units in 100 hands. At some point in those 100 hands we were 1,300 units ahead and at another point we were 1,800 units ahead for a swing of 500 units. Although we ended up winning in this particular set of 10,000 hands, the volatility is obvious and we clearly could have lost. Although winning is more likely, we do see some punishing downturns and do not end the chart at our highest point.

Let's expand this to 100,000 hands in groups of 1,000. We see the y-axis has expanded again as our results in this section range from 2,000 units ahead to 7,000 units ahead. The line is starting to look smoother. But we still see long flat periods and dips. And we can see that at one point we were ahead 7,000 units but ended up a bit over 5,000 units. At least the overall trend is up.

Finally, 1,000,000 hands in groups of 10,000. Here we start at zero units won and end up with 60,000 units won. The line is much smoother, although there exist clear downturns. If we expanded this to one billion hands we would then see a nearly straight line.

There is a lot of talk about the long term and short term in Blackjack. Basically the only difference is that the more you play, the more likely your actual play will match theoretical advantage. The fewer hands you play, the more random your results. Which is to say that short-term results have no meaning. You cannot project advantage or long-term results from short-term results.

Sim details

• Six decks, S17, DAS, LS, 4.8/6 penetration, 4 players, 1-15 spread, Hi-Lo, truncate, full indexes, half-deck resolution
• One million rounds