Most Gamblers Underestimate the Effects of Luck

My imaginary friend Eddie has been playing blackjack for many years. He's a pretty good basic strategy player, but not perfect. Eddie still has trouble playing his soft hits and soft doubles correctly, and he's foggy on some of the trickier splits. Based on the overall caliber of his game though, I'd say Eddie plays at about a 0.75% disadvantage to the house.

Still and all, Eddie does make some decent wins for himself here and there. It's not that unlikely, you know. After all, it's called "gambling", and three quarters of one percent is a pretty small disadvantage to buck.

Since Eddie is a fairly regular once-a-week player, I've been after him to plug the holes in his basic strategy and at least start using the Ace/10 Front Count to erase his disadvantage altogether. But he's been running pretty well lately and is happy just doing what he's been doing.

Eddie is basically a "quarter" player. He varies his bets between $25 and $50, but probably averages about $35 per hand. Year to date, he's actually ahead of the game.

How can this be, you ask, when Eddie has a small but definite disadvantage? Well, it's all about something that gamblers call the "luck factor" and math geeks refer to as "standard deviation". The only difference between the two is that standard deviation can be measured, but the luck factor can't. When you gamble, your actual result will fall within one standard deviation from normal, two times out of three. Here's a simple example of how standard deviation affects the flip of a coin.

If you toss a balanced coin 100 times, it would be perfectly normal and average to get 50 heads. But due to the luck factor, aka standard deviation, you might happen to get more or fewer heads than that. How many more or fewer? The standard deviation for 100 coin flips works out to be 5. In other words, two times out of three you'll get between 45 and 55 heads.

Now let's use standard deviation to show you what Eddie's outlook at blackjack will be for the next year. If he plays his regular old game for, say, three hours a week at the stakes mentioned above, his average outcome would be an expected loss of about $3500. But he's by no means locked into that. That's because his standard deviation for that amount of play is $4500. So two times out of three, Eddie will show a result somewhere between a win of $1000 and a loss of $8000. One extreme is just as likely as the other.

Now you can see that being $1000 ahead after a one-year period is not a rare outcome for a player like Eddie. Unfortunately, neither is losing eight grand! But gambling is a long run thing and the more you play, the closer to the true odds your results will be. Ten years from now, playing this way Eddie will be hopelessly buried.

On the brighter side, what if Eddie did take up the Ace/10 Front Count to eliminate the house edge and replace it with a 0.25% advantage of his own? Then, after a year, his average outcome would be a net win of $1200. His standard deviation, however, would be about $6000. So it would actually be no big deal to find him anywhere between $7200 up and $4800 down.

I wish I could tell Eddie that he'll be a guaranteed winner next year if he does use the Ace/10 Front Count and will be a dead meat loser if he doesn't -- but that's not necessarily so. Volatility is the nature of gambling.

The best I can say is that he's likely to come out about $4700 better over the next year if he takes that next step in his game. Either way it's still a gamble. But if he's going to be playing blackjack in the coming years anyway, it's an easy step over the line from underdog to favorite.