An example of the gambler’s fallacy is when you flip a coin twice in a row and it comes up heads, and then you think the next flip must give you tails. Flips of a fair coin are statistically independent of each other. Market runs are pretty similar.
Dating back to 1896, the last time the Dow Jones Industrial Average had 11 consecutive positive days was February 1, 1955. The Dow has been up one day only to reverse the next day 47.8% of the time, while there have been two positive days in a row 25.8% of the time. Only 13.2% of the time have there been three positive days in a row—we’ve never had 12 in a row. That doesn’t mean it can’t happen, just that it hasn’t.
Statistically, there is no evidence that the market is more likely to fall the next day just because it’s been up.