# Expected rolls until a 6

Suppose I roll a fair, six-sided die repeatedly until I get a 6. It is well-known that the expected number of rolls is exactly 6.

Now, suppose instead that I roll a fair, six-sided die repeatedly until I get a 6, and I tell you that every time I rolled the die, an even number (2, 4, or 6) came up. What is the expected number of die rolls that I made?


Clarification: For example, I could have rolled 2-4-4-2-4-6, 2-6, 4-4-6, or just 6.

Source: Gil Kalai's blog

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