The current NFL overtime rule makes it possible for games to go on too long, and too often leads to teams playing for a field goal and not particularly caring if they can get in the end zone. I have a proposal to fix this.
The basic rule is that each team gets one play to see if they can score a touchdown. They each get to pick which yard line to start from. But both teams have to choose their starting position simultaneously without knowing the other team's choice.
Each team gets one play to try to score a touchdown, with the team that chose the closer yard line going first. If one scores and the other doesn't, the team that scored is the winner. If both teams score, then the team that scored from further away is the winner. A turnover ends the game immediately with the defense that forced the turnover declared the winner.
An accepted penalty results in replaying the down from the same yard line as before. Obviously, if the team that was not penalized likes the outcome of a play, they decline the penalty, so committing penalties still hurts you.
If neither team scores, then they swap yard lines and try again. If neither team scores a second time, then start over and repick. If both teams pick the same starting position, then the decision is invalidated and they have to repick immediately, without any plays being run.
And that's it. No more playing for a field goal. It will be two snaps of overtime and then game over a large fraction of the time, so TV can quickly show the overtime and not have it drag on forever. No more having out of region games shut off five minutes into overtime. You always get a winner who won the game on the field by making an interesting football play, not just having a long pass interference penalty bring you into field goal range.
Note that there isn't a dominant strategy to picking your starting yard line. If you know that your opponent will choose the n yard line, your best choice is the n+1 yard line, unless n is large enough to justify picking the 1 yard line as the counter. But to mitigate the disadvantage of bad luck in your yardage choice, a second play if necessary swaps the yard lines, giving you the advantage if you had the disadvantage the first time.
This also has the feature that, as soon as someone scores, the overtime can last at most one more play. If the team that started further away is the first to score, the game is over. If the team that started closer is the first to score, then the next play will end the game with a victory for the second team if they also score or the first if their defense holds. That's like having fourth and goal with one second on the clock while down by five, which is a lot more exciting than playing for a field goal.