Is the six due?

Question

You are rolling a fair six-sided die and you need a six. You have rolled ten times and not one of them was a six. On your next roll, is a six more likely than 	frac16?

Accepted Answer

No. Each roll of a fair die is independent, so the ten sixless rolls have no effect on the next one. The probability of a six on the next roll is still \frac{1}{6} \approx 16.7\%. The feeling that a six is "overdue" is the gambler's fallacy. The die does not track how long it has been since a six, and it has no mechanism to correct a drought. A long stretch without a six is simply a mildly unlucky sequence, and the die approaches its expected frequency over time by diluting the past with many future rolls, not by suddenly producing sixes to catch up. Ten sixless rolls is not even especially r…

Is the six due?

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