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Luck: The difference between measured and expected value.

Posted By: Moose
Date: 5 Nov 01, 3:28 pm

In Response To: Luck (lucky in love)

Plain and simple. If your expected profit after 1,000 hands is \$X, and your ACTUAL profit is greater than \$x, then you got lucky. If it is less than \$x, you got unlucky.

Luck is completely quantifiable. The unit of luck is the Standard Deviation. I have even gotten my friends talking like this, so when one of them discusses their bad luck playing a fantasy hockey game, or Dungeons and Dragons, they use phrases like "I was really unlucky tonight, about 3 standard deviations worth" - they have a rough idea that 1 standard deviation of luck represents 2:1 odds (either for or against, depending on which direction), 2 standard deviations represents 19:1 odds, and 3 standard deviations represents 199:1 odds.

Note that luck is not an element of games of chance, but an element of situations where the exact likelyhood cannot be known, and has to be approximated with probability. If I have a 70% chance of beating Don S. in a chess game, and I win, then I got lucky, since my measured result - 100% of games won - was higher than my theoretical result - 70% of games won. Even though chess is devoid of CHAOS, it is by no means devoid of LUCK.

This last point is an important one to remember. Even in strict games of skill, even if we have an advantage, we still need luck to win in the short term, and people aren't always prepared to accept this. After all, if I beat Don S. at chess, it was through skill, because I'm a 70:30 favorite. If he beats me, by god, did he EVER get lucky!

Once you get over this hump, thinking that the one with the advantage wins with skill and loses due to luck, then you're on your way to having the criminal mind needed for this stupid game (or any other stupid game).

Something sobering to do: After every blackjack session where you have a big win or a big loss, do your calculations to find out how many SDs + or - you were, then convert your blackjack action to an equivalent amount of craps action, and see how that result would have been. Winning \$1400 playing blackjack for the first time was sure intoxicating until I realized that, hey, if I were playing a DISADVANTAGE game, and had the luck I had, I'd still have made \$1000.

Moose's Universal Theory of Luck: If Mike Tyson is a 999,999:1 favorite to beat Mihkal Barishnokov, and Tyson wins, he got lucky.

(Not VERY lucky, mind you. But all the same, Tyson's theoretical result was 99.9999% and his measured result was 100%)

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