Hi Matt.

All the rolls are independent, so rolling double sixes twice in a row is the same as rolling a six (on one die) four times in a row. Since there are six choices, then each time there is a 1/6 chance of rolling a six.

The fact they are entirely independent of each other means we simply multiply each roll's probability together: 1/6 × 1/6 × 1/6 × 1/6 = (1/6)⁴ = 1/1296 = 0.00077.

Now let's say you had already rolled double sixes. What is the probability of rolling double sixes on your next roll? The answer is 1/36. The past rolls are entirely independent of future rolls, so history doesn't matter.

Stephen.