If a College Football game finishes regulation tied, the two teams go to overtime. Overtime in College Football is different than in Pro Football. In college football, "if the score is tied at the end of regulation, there is a coin toss followed by a series of overtime periods. In an overtime period, each team gets one untimed possession starting at the opponent's 25-yard line (plus a try if the possession culminates in a touchdown). In the first overtime period and in all subsequent odd-numbered overtime periods, the winner of the coin toss can choose whether to have the first or second possession. The coin-toss loser gets the choice in the even-numbered overtime periods. Play continues until, at the end of some overtime period, the score is no longer tied."
Almost any team that wins the first coin toss at the beginning of OT chooses to play defense first. This is because most people perceive that there is an advantage in going last. The advantage is that if your opponent scores a TD, you know that you have to score one on your possession, so on 4th and 4, you will go for it instead of kick the Field Goal. How much is this worth, according to one analysis, the coin toss winner will win the game 52% of the time (in pro football they win 57% of the time which shows that the college version is fairer), but nonetheless, blind luck is now playing a part in who wins the game. But this can be fixed.
All we need to do is modify the choices until they are actually even. What if the team who plays offense second starts on the 27 instead of the 25? That would give them a slight disadvantage over the other team because they'll be starting on the 25 and it may counter the slight advantage they have from going second.
I'm not sure how far back the second team would have to start to balance it out. We could try to figure it out mathematically, or we could ask college coaches "How many yards would you be willing to give up to go last?" but regardless we probably won't get it totally fair. It won't be totally fair until coin-toss winners choose to play each defense and offence about 50% of the time.
Basically this is form of using bidding to decide who goes first. Straight up bidding would be better.