## Tuesday, June 9, 2009

### Predictable "Random" Distributions

Opposed to academic principles, I notice predictable elements within “random distributions” via theory and empirical evidence. Exploiting these alleged aspects or “inefficiencies” then could open doors to profitable betting.

Normal Distribution basics

“In probability theory and statistics, the Normal or Gaussian distribution is a continuous probability distribution that describes data that clusters around a mean or average.” (Wikipedia) This theory applies to most assumed independently random statistics today (e.g. coin tosses, roulette spins, blackjack hands, individual lifespan, and etc.), where the law of large numbers states larger sample groups produces more stable (relatively narrow) distributions.

Empirical observations (Blackjack)

Purely independent events like a string of blackjack games while the player applies the “basic strategy” would results in a win/loss distribution with the mean somewhere a bit left of 50%. Understanding and knowing this, several assertions become possible.

Theory

Due to independent randomness, any arbitrary sample group W/L distribution exhibits Stationarity. This means with any string of games, you KNOW a rough range of resulting winners. You simply do not know when they will occur, only that they come sometimes earlier than later.

Instances where winning hands come later, preceded by strings of losers, a window of profitable opportunity then arrives. Mean reversion works! Yeah this completely disengages from academic philosophy, which is reassuring considering how flawed existing academic financial economic theories still flourish today.

An example stock return distribution

This is a daily return distribution of US stocks from Dec. 31, 1999 to April 09, overlapped with a Normal Bell Curve. (Similar to the century long return) The distribution, though not exactly normal, clearly suggests stock prices tend to fall harder (given large enough trading days). It also hints that each period of rallying presents a higher probability of a coming decline. After all, we care more about the immediate future than the immediate past.