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Strategies & Market Trends : The Art of Investing -- Ignore unavailable to you. Want to Upgrade?

To: Sun Tzu who wrote (848)	1/27/2000 12:34:00 AM
From: Greg S.	Read Replies (2) \| Respond to of 10713

OT - Theory of runs There is actually such a thing as "theory of runs" which applies equally to gambling and trading. Something interesting to consider if you're willing to bear with a little math (but what good gambler isn't?): When you have a series of N independent success/failure trials with equal probability of success for each, the probability that the series will contain a run of length greater than log2 N tends towards 0.0 as N gets larger. This means that if I toss a coin 8 times in a row, the probability that I get more than 3 heads or tails in a row (log base 2 of 8) is not so great. And if I toss a million coins, the probability that I get a run of length longer than 20 (log base 2 of a million) is pretty dang small. Think that's cool? Oddly enough, the probability that that the series contains a run of length equal to or less than log2 N actually tends towards 1.0 as N gets large. So when tossing a million coins, 20 heads in a row is actually quite probable (probably on the order of 85%), but a run of length 21 is not very probable at all (probably about 25%). Now imagine that the trial here is not the flipping of a coin but whether or not the dealer wins a hand of blackjack. I'm not sure how well this property holds when the two outcomes (success/failure) are not equally probable, as in a blackjack game, and when the outcomes are not independent. Outcomes of a blackjack game are dependent but in such a complex way that I will throw mathematical rigor aside and say the dependence is insignificant for this exercise. So, let's say a dealer is dealing 25 hands and in each hand he has a 50/50 chance of winning. If you actually work out the math (which is horribly complicated but can be found in advanced statistics books), here are the probabilities that he will have a winning streak of each length: P(2) ~= 1 P(3) = 0.992764 P(4) = 0.847665 P(5) = 0.549631 P(6) = 0.299667 <-- critical point P(7) = 0.150781 P(8) = 0.0732273 P(9) = 0.0349884 P(10) = 0.0165758 P(11) = 0.00780916 P(12) = 0.00366181 P(13) = 0.00170898 P(14) = 0.000793457 P(15) = 0.000366211 P(16) = 0.000167847 P(17+) ~= 0 Notice that the probability of a run of length 6 dips significantly below the 50% mark. The stretch of course is in adapting this model to the real blackjack odds, and to figuring out just what N to use when you're watching the table. Also, these same rules could be adapted to the wins/losses of a player .. you're streaks can't last forever! ;) This is an oversimplified and decidedly unrigorous model, but I think it does lend a little abstract credence to Sun's particular style of blackjack play. -G