Random Walk, Gambler’s Fallacy and Gambler’s Ruin

Burton Malkiel has written a book called “A Random Walk Down Wall Street” in which he proposes that in efficient market past trend of share prices cannot be used to predict future price. There is no connection between two.

The share price movement is like walk of a drunk fellow, it is random, hence cannot be used to predict future. Like drunkard’s random walk, stocks take a random and unpredictable path.

But there are others who feel that past trends can be used to predict future.

“A blindfolded monkey throwing darts at a newspaper’s financial pages could select a portfolio that would do just as well as one carefully selected by experts.”

-Burton Malkiel

Random Walk can also be used to explain Gambler’s Fallacy or Monte Carlo Fallacy.

The gambler’s fallacy is when an individual erroneously believes that the onset of a certain random event is less likely to happen following an event or a series of events ex. if you get 25 heads in a row by flip of coin, than in 26th attempt chances of getting tail is very high. But this is not correct every time you flip coin chances of getting head or tail are 50%. What happened in past has does not influence current event.

Gambler should be aware of not just gambler’s fallacy but also Gambler’s Ruin.

Suppose there are two gamblers and both are betting Rs.100. Chances of winning for each gambler is 50%. Now if one gambler has Rs.200 to bet while other can bet only Rs.100, then chances of winning for second gambler are lower. Now suppose first gambler has not just Rs.200, but say 1000 or 10000 or 100000… while second gambler still as Rs.100, then chances of second gambler winning will keep going down, finally it will zero. In other words, if you have finite wealth and other person has infinite wealth, then you will eventually lose all your wealth if you keep gambling.

 

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