Posts Tagged ‘Blackjack’

Confusing variance with expectation

Friday, June 20th, 2008

I often encounter gamblers who say things like “What’s $100? I often bet that in a single hand.” Or “Why be so tight with tips? $5 is nothing when I regularly have swings of $2000 a night.”

Though these statements sound plausible, for blackjack they are likely false. The real question isn’t the size of your swings, but the size of your expectation. If your expectation on that $100 bet is $1, then $5 is a lot. If you’re betting kelly, you have to make 9 more such bets (without tipping) just to get back to zero!

Here’s another way to put it. If you win $10000 in a night, don’t get too cocky. Ask yourself, what was your expectation for the play? If it was $500, then don’t be too surprised to lose back $9000 of it next time. That’s just average luck.

Counting cards is just like this. Your short term swings overwhelm your expectation. How much play do you need just to make one standard deviation of your result equal to your expectation? In the blackjack literature, this quantity is known as N0, and greatly depends on the quality of your game, but in almost all realistic cases, it’s a lot, at least a few thousand hands. In fact, if you’re not careful with game selection, it could easily approach 20000, a rather daunting amount. (Assuming 50 rounds/hour, 4*N0 is 1600 hours, an amount almost anyone would be hard-pressed to play in a year.)

If you can’t get N0 hands in in a year, then you really are just gambling, even with an edge. You can’t truly call yourself a professional, because you just won’t get into the long run in that year. Really you want to get at least 4*N0 hands, which would mean a loss for the year would be a 2 standard deviation result, about a 2.5% event on the negative side.

So what is the moral? Simulate your play. Keep your expenses low in comparison to your expectation. To play enough to get into the long run, you probably need to play higher quality games.

An additional fact of importance is that no matter what your risk of ruin, if you do not increase your bankroll, you will eventually be ruined. To take a practical example, if you choose a 5% risk of ruin, and cap your gambling bankroll at that (or, equivalently, always bet at that level), you will likely wipe out at some point in your gambling career.