The efficient-market hypothesis (EMH) stipulates that you can't, on average, "beat the market" by picking better stocks or timing the market. According to the EMH, all information about the market is immediately available to every market participant in one form or another, and it is immediately reflected in asset prices, so investing is like playing a game of cards with all the cards revealed. The only way you can win is by betting on very risky stocks and getting lucky.
The French mathematician Bachelor developed a test for the EMH around 1900. The test examines consecutive occurrences of negative and positive price changes. We don't count events during which the price didn't change and only use them to end a run. These types of events are relatively rare anyway for liquid markets.
The statistical test itself is known outside finance and goes by the name of the Wald-Wolfowitz runs test. If we denote positive changes with '+' and negative...