Chapter 8. Bankrolls, Goals, Risk Data

Fortunately formulae exist to aid us in planning for the inherent volatility of Blackjack card counting. Chapter 8 charts the relationships between bankroll, risk, goals and time, in several manners.

"Time washes clean" — Linda Ronstadt, 1970

What is my risk of ruin?

Risk of Ruin refers to the chance that you will lose your entire bankroll. The charts on this page display three views of risk using formulae from Don Schlesinger's Blackjack Attack. For all charts, we are playing six decks, S17, DAS, 5/6 penetration, Hi-Lo, betting optimally from $10-$180.

Let's start with simple risk of ruin. This is the risk of ruin with no limit on the number of hands and no quit point. We continue playing forever unless we go bankrupt. Along the x-axis you will see bankrolls of $1,000 to $20,000. At the above betting level with a $1,000 bankroll we can see an enormous risk of 82% that we will lose our entire bankroll. We can see that larger bankrolls dramatically reduce our risk. At a bankroll of $20,000 we see a risk of about 1.8%. At a bankroll of $18,000 (100 times the max bet of $180) the risk is 2.75%. Obviously, changing the rules, penetration, strategy, unit size or bet spread will significantly change this chart.

What is my Trip Risk of Ruin?

Now let us look at one trip. Trip Ruin is much the same except there are a limited number of hands in one trip. In this chart we are playing the same game, but we will play 5,000 hands, unless we go bankrupt first. The curve is dramatically different here as it is highly unlikely that we will lose an entire bankroll above a certain size in that short a period of time. The risk is now below 1% with a $10,000 bankroll.


What happens when I include a goal?

Let's throw in a goal. This is called a double barrier formula because we quit playing if we win or lose specified amounts. We are calculating the risk of bankruptcy before hitting a goal. In this chart a goal of $20,000 is selected. We are looking at the risk involved attempting to end up with $20,000 given bankrolls of $1,000 to $20,000. The risk at $1,000 is nearly the same as in the first chart, which had no goal. But the risk with a $20,000 bankroll is obviously zero and all risks in between are a bit lower.

Clearly bankroll is an important aspect of risk. But you can also lower risk by finding better games, reducing the betting level, or using a better strategy.


Sim details

  • Six decks, S17, DAS, Heads-Up, Hi-Lo, truncate, Sweet 16 indexes, half-deck resolution, penetrations 5/6 penetration, Spread $10-$180
  • Two billion rounds each, all sims use optimal betting


copyright © 2007, Norm Wattenberger, All rights reserved