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 |
