N people roll a die in turn, following a prearranged list. The first to get a 6 names the drink. The second to get a 6 drinks it. The third, pays! Then the next on the list rolls and so on till the closing time.
The above goes on for 120 minutes, averaging 5 rolls per minute (the time for naming, drinking, plus settling disputes and paying the bills was discounted).
How many times was it the same player that named the drink, consumed it but did not pay for it?
a. Provide your estimates for N=3, N=6 and N=12
b. Please explain the meaning of the results.
Rem: Verification of analytical results by simulation is welcome.
A full cycle goes an expected 18 rolls, and we are rolling an expected 600 times, so we expect 33 1/3 cycles.
What happens when the game ends mid-cycle? Specifically, what if the same player names the drink, and drinks it and then time expires before a payer is selected. Does this or does this not count against our expected target estimate?
I recommend assuming that it does not, because we have no way to determine who pays. In effect, let's assume that the drink is not even available for drinking until it is paid for.
Is that what you had in mind, Ady?