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May 15, 2013 at 10:04 comment added Vincent Beffara Good to know, at least my asymptotic analysis gives the right order of magnitude and even the right growth rate. Far from an exact result, but I believe that the approach is more robust than bijective methods like the one suggested by Ori.
May 15, 2013 at 10:01 history edited Vincent Beffara CC BY-SA 3.0
Result of the computation for case 1
May 14, 2013 at 18:22 comment added Douglas Zare Exact calculations for $n \le 100$ give a value of $2^{n-1}-1$ for the expected time to completion from $(1,n-1)$. I haven't yet proved that this always holds.
May 14, 2013 at 17:44 comment added Vincent Beffara (Actually case 1 needs a proper estimate for the exponential rate, which I don't have time to do right now but should be straightforward enough ... sorry ...)
May 14, 2013 at 17:40 history answered Vincent Beffara CC BY-SA 3.0