Mileage, of course, is the modifier (m).

Okay. So, there are four states in this arrangement.

First, it's your turn, and you're contributing. This is assigned a value of p.

Then, it's not your turn, and you're receiving. This is preferable, and is assigned a value of -p.

If it's not your turn, but you must contribute, this is less preferable, and given a value of p+q, where initially, qp, the arrangement ends. Since the goal is to keep the total time (t) of the arrangement as large as possible by keeping ∆p=0, we shall deal with small values of t(q).)

And, if it is your turn, but you have no one to contribute to, you must still participate. This isn't preferable, and since no contribution = no arrangement, let us say this value is approximately (q).

Now, if all players (n) take their turns (d) equally, then ∆p = p•d - (-p•d/n), so then, if you replace p with (p+q)•d for the number of turns missed... then divide that by n...

Argh.

This is exactly why the key to happiness at work is finding an easy-going carpool. So that when your vacation days overlap your days to drive, you can just settle everything with rock-paper-scissors.