In a study of online gamblers, those who had won several bets in a row were found to have a higherchance of winning their next bets, say Juimin Xu and Nigel Harvey of University College London. Losing streaks had the opposite effect, decreasing gamblers’ chances of winning the next bet. The apparent reason is that after winning, gamblers tended to place safer bets, believing (falsely) that they were “due” to lose; losers believed they were due to win and placed riskier bets. The effect was to create good luck for the already lucky and bad luck for the unlucky.
SOURCE: A Self-Fulfilling Fallacy?