What is an equitable method for having six partners take turns picking game dates from 61 baseball games?

In a strict repeating 1-6 order the earlier pickers have a permanent advantage to take the most popular games before the final pickers get their turns. So the sixth picker finds the best games gone before he can make even a few picks. How can we vary the picking order to make it more equitable?

Interesting question...

The only way I can think of doing this is by making it a game of chance.

Draw numbers 1-6 and go in that order. Redraw for each new round.

Another idea I just had, not a game of chance, but an auction. Each person would get a certain number of points based on pay in (if everyone contributes equally, they all get the same number of points). Then let them bid points on each game. Those that win high value games in the auction would spend more but may not get to go to as many games. Those that bid on lower value games would get to go to more games.

hhmmm, seems like you would need an auction type program to make idea 2 work easily. Don't know if there is a program like that or not. I'll look around and see if I see something like that later on this evening.