Editing Gambler's fallacy (section)

===Other examples===
The fallacy leads to the incorrect notion that previous failures will create an increased probability of success on subsequent attempts. For a fair 16-sided die, the probability of each outcome occurring is {{sfrac|1|16}} (6.25%). If a win is defined as rolling a 1, the probability of a 1 occurring at least once in 16 rolls is:
:<math>1-\left[\frac{15}{16}\right]^{16} \,=\, 64.39\%</math>

The probability of a loss on the first roll is {{sfrac|15|16}} (93.75%). According to the fallacy, the player should have a higher chance of winning after one loss has occurred. The probability of at least one win is now:
:<math>1-\left[\frac{15}{16}\right]^{15} \,=\, 62.02\%</math>

By losing one toss, the player's probability of winning drops by two percentage points. With 5 losses and 11 rolls remaining, the probability of winning drops to around 0.5 (50%). The probability of at least one win does not increase after a series of losses; indeed, the probability of success ''actually decreases'', because there are fewer trials left in which to win. The probability of winning will eventually be equal to the probability of winning a single toss, which is {{sfrac|1|16}} (6.25%) and occurs when only one toss is left.