Imagine starting this conversation during lunch then have it go on until work ends.

I wrote something to simulate this (1,000,000 times each run as specified) rather than try to solve it algebraically.

I assume the first day if he loses the roulette he lives 0 days since he does this first thing in the morning. My first 5 runs:

Min 0 Max: 80 Avg (EV): 5.00518
Min 0 Max: 78 Avg (EV): 5.003595
Min 0 Max: 81 Avg (EV): 4.992225
Min 0 Max: 77 Avg (EV): 4.999014
Min 0 Max: 73 Avg (EV): 5.002547

Answer: Life Expectancy is 5 days

Edit: and if we start on day 1 then it's 6.

Edit2: What Bruce said

lol

Interesting that the max life range is that tight at 73 to 81 days for 1 million sessions. Not much variance, but on such a long long shot, seems like more variance would be expected. I come up with a 1 in 2.2 million shot at living 80 days.

Looks right to me. In a million trials, a 1 in 2.2 million shot will occur with probability of about

1 - 1/e^(1/2.2) ≈ 36.5%.

If occurred in 2 of the 5 runs of a million, that's 40%. Living 73 days has a probability of about 1 in 600,000. In a million trials, that would occur with probability of about

1 - 1/e^(.6/2.2) ≈ 81%.

So the probability of it occurring in each of the 5 runs of 1 million would be about 35%.

Don't you need to combine that 35% probability (of living at least 73 days sometime within all 5 runs) with the probability to not live more than 81 days in any of the runs? I guess that's trivial, but it's the part that struck me as odd, that the high max was so close to the low max. I guess we would need more runs to have more chance of an outlier run.

The point is that there is a big difference in probability between living 73 or more days and living 82 or more days in a million runs, so it's reasonable that we live 73 or more days in each of the 5 sets of runs, and it's reasonable that we don't live 82 or more days in any run. The probability of living 73 or more days is about 81%, and the probability of living 82 or more days is about 27.5%, so subtracting we get the probability of living between 73 and 81 days is about 53.5%. The probability that happens in all 5 runs is only about 4.4%, but I don't think that's very meaningful because it's after the fact and too specific. You could ask about the probability of getting each of those 5 exact numbers too, and the probability would be near zero no matter what the results were. You could run another 5, and if it happened again with that same range, I'd be suspicious.

I just ran 5 and got 80,77,82,88,81.

Calculated distribution.

The distribution is helpful, thanks. Looks like 70 to 90 would cover over 90% of the runs.

Very interesting results guys.

Obviously, I wouldn't ask this person to write a simulation and figure it out himself, though I'm kind of sad that I didn't bother to write my own sim and check some of this stuff out.

If he can program *at all* the simulation is trivial. If he can't, he can probably READ a simulation someone else has written. The sim I wrote was like 6 lines or something like that.

Can someone explain the fundamental difference between russian roulette and bunjee-jumping to me, except that you have to pay to jump?

I suspect one fundamental difference is life expectancy. According to ask.com there have been 18 recorded fatal accidents due to bungee jumping since 1986.

This website says it is 1:500,000 against having an accident: http://xtremesport4u.com/extreme-lan...bungy-jumping/

I'll bet they are biased, but I doubt they are off by a factor of 100,000 (i.e., in traditional russian roulette with a 6 shooter, you are 1:5 against shooting yourself in the head.

That 1:500,000 figure probably includes people who don't go to organized events, but just get some bungee cords and huck themselves off a bridge. I read that at organized events it's as safe as roller coasters.