Almost no one likes the current sudden-death-overtime NFL rule for breaking ties after four quarters have been played.
The problem is that the winner of the coin toss in OT gets a HUGE advantage. If they score on their possession, the game ends without the other team having a chance to score on a similar possession (a variation of which is used in college football).
The problem with extending the game is that the longer the game is played, the more chances there are for injuries by players whose play gets sloppier with exhaustion as the game goes on.
The college football variation also creates a ridiculous amount of scoring that plays havoc with statistics - both real and fantasy. (Don't think gambling/fantasy football doesn't drive significant profits for the NFL and sports media - it does and they know it.)
So here's how to deal with the problem of luck governing overtime.
NEW RULE - The team that FORCED THE TIE (i.e. scored last) KICKS OFF IN OT. Pure strategy; no coin flips involved. It will also give incentive to go for the win over the tie by the team coming from behind in regulation.
Example #1 - A team trails 24-17 and scores a TD with 5 seconds left in the game. The odds are now better to go for two and the win in regulation than to go for one and kick off in OT.
Example #2 - A team trails 24-21 with three seconds to go on at the opponent's 3-yard line. The odds now favor going for the TD rather than the FG to tie.
Example #3 - A team has driven to the opponent's 15-yard line with under a minute to play trailing 24-21. No longer will you see three line plunges or kneel-downs to bring the clock to three seconds and kick the short FG to tie. The odds strongly favor a team actually trying to win the game instead of (yawn) killing the clock. If they score quickly, you'll have the added excitement of the other team desperately trying to score in the last seconds of the game.