🚀 go-pugleaf

As promised, here is the solution:

The probability of surviving one round (interesting choice of
words there) is 5/6.  The probability of surviving N rounds
is           N
    p = (5/6)

The probability of surviving N-1 rounds and being killed on the
Nth round is
                N-1
   p = 1/6 (5/6)


The average lifespan of someone who plays Russian roulette is

                      N           i
   L = lim            Sum [i (5/6) ]/6
       N-->Infinity   i=1

                               N
     = lim            1 - (5/6)
       N-->Infinity (------------) / 6
                               2
                      (1 - 5/6)

     = 6.

My thanks to all who submitted solutions.  As you can see, I have
left out some steps, and the last limit expression presumes that
the limit of a derivative is the same as the derivative of the
limit.  I didn't verify that this is always true, but it turned
out to be true in this case, so I didn't type in the more complicated
limit expression that would have resulted by taking the derivative
first, then computing the limit of the result.

John Blanton
blanton@lobby.ti.com