It's not just Wikipedia - Google "gambler's fallacy" and you'll see what I mean. I chose Wiki because I thought it summarized the rationale as well as anywhere else.
Here's something to consider. Suppose you've tossed 50 heads in succession, so you believe that tails is now the more likely bet? But why should the most recent 50 tosses of that one particular coin carry more weight than any other coin toss? What about the tosses that preceded those 50, or in fact the results of every other coin toss that's ever occurred in history? Or in fact every toss that's going to occur in the future?
Or let's put it another way. You toss 50 consecutive heads, and then 20 consecutive tails. Is heads now more likely (due to the most recent run of tails), or tails more likely, because 50 of the last 70 tosses were heads? Surely it's completely arbitrary as to which batch of tosses we choose to consider.
Here's another possible angle. The greater the number of tosses, the greater the probability that the ratio of heads to tails will be closer to 50/50. But to reach the point where there is 100% certainty of an exact 50/50 result would require an infinite number of tosses, which is the requirement for the "law of averages" to become effective. But no matter how many times we toss that coin, "infinity" will always lie beyond our grasp.
BTW, I agree that if I draw an Ace from a card deck, the probability of drawing a second Ace decreases. But that's because the original Ace isn't replaced. But each coin toss is a completely independent event. The key word is independent: in a random event, the past has no bearing on the future. People either see that or they don't.
Anyway, trading results are not necessarily random. A system can perform brilliantly one year, and badly the next. As an example, a trend-following system might string together a sequence of winners while the market is trending. Then the market moves sideways for a while, and a sequence of losses occurs. While the market is trending, the probability of it's continuing to do so is greater than 50% (all of the "let profits run", "cut losses short" and "trade with the trend" maxims depend on that assumption). So if our sequence of winners reflects that fact, then the probability of adding a further winner to the sequence is always > 50%.
If a boxer has won his last 10 fights, is he more or less likely to win the next one? I would say more likely, because his track record suggests that he's a good fighter. The "skill" factor creates a bias that overrides any "law of averages" or "gambler's fallacy" considerations. If - and only if - it can be shown that trading wins and losses tend to cluster together in a statistically significant manner, then we also have a bias.
David
.......Just like blackjack players should be allowed to count, the dealer is allowed to shuffle after every hand
