Two events are independent when knowing the result of one tells you nothing about the other. Roulette spins, dice rolls and slot spins are independent. The chance of two independent events both happening is found by multiplying their individual chances. Treating independent events as connected is the root of the gambler’s fallacy. Cards drawn from a deck without replacement are not independent, because each card dealt changes what is left.
Example
The chance of red twice in a row on a European wheel is 18/37 x 18/37, about 23.7%. The chance of red on the second spin, given red on the first, is still 48.65%.