I wrapped a probability distribution around this very phenomenon a few years back: https://statisticsblog.com/2013/05/30/uncovering-the-unreliable-friend-distr

I wrapped a probability distribution around this very phenomenon a few years back: https://statisticsblog.com/2013/05/30/uncovering-the-unreliable-friend-distribution-a-case-study-in-the-limits-of-mc-methods/ https://statisticsblog.com/2013/05/30/uncovering-the-unrelia... The expected duration converges to exactly double your wait time so far. I've found the "unreliable friend" distribution to be very useful in my modeling!