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SOLUTION

Posted By: Bob Koca
Date: Wednesday, 10 January 2024, at 4:38 a.m.

In Response To: SOLUTION (Timothy Chow)

Here are the two ways I did it:

A) Roll until you get an odd number or a 6. Since those are 2/3 of the rolls it takes 3/2 turns on average for that to happen. 1/4 of the time you got a 6 and the game is over and 3/4 of the time you have a restart.

So we have the equation E = (1/4)(3/2) + (3/4)E. Solving gives E = 3/2.

B) I suspect this may be really the same as your explanation but I think it is a bit nicer:

Generate the list of random numbers backwards. When you get to a 6 it will take 3/2 rolls on average to get another 6 or an odd number. That number of rolls is how long it took to get the 6 looking at it forwards with the odd numbers resetting the count.

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