One of the things I learned from playing backgammon is that it is often better to try to win quickly than it is to let yourself die slowly. That is, going for it all on a single good percentage play often gives you a better chance than just letting things drag on and on and on.
This is a good way to explain why the 2-PAT is the optimal strategy without getting into the math.
realize that you have already beaten the odds once to tie at regulation and every successive iteration will present you with the same underdog odds. your likelihood of beating the odds in a repeated game gets smaller and smaller each iteration (overtime period).
Then consider that to guarantee victory, you are going to have to score a two-point conversion at some point. There is no other strategy that in a repeated game will ensure your victory. College football makes this convenient for us by forcing us to play the optimal strategy (and, alternatively, penalizing the favorite) after the second iteration (third, technically, since regulation was a game as well.)
So if you had a 33% chance to win the game, and you have a 45% chance of successfully completing the 2-PAT, take into account then that your overall odds will be reduced by the percentage of that iteration. Overtimes are non-timed periods so you would have to calculate what that constant modifier would be (what percentage of a game does one overtime period constitute) and the that would be how much your overall expected value would be.
Fortunately the dynamics of football make this even easier to illustrate. I said that to guarantee victory you will at some point have to score a 2-PAT. But what condition creates the decision path for the PAT? You have to score a touchdown, first.
Your 45% (i am making that up, there is an actual number that I looked up for the North Texas game when I explained this the first time because, assuming we and North Texas were even in ability (debate that as you may) we were the road team and thus the edge was with the home team. Anyway, that 45% is a far, far, far higher expected value than the likelihood of scoring a touchdown from the 25 yard line.
The same rule applies in a regular game situation if you're at the same point on the field. If your likelihood of reaching the end zone is 45%, and say we'll just give Matt Weller the benefit of the doubt and say he will make a field goal from that spot every time, the field goal is worth 2.9 points when compared against the expected value of going for the touchdown on fourth down.
You are helping your team lose by kicking the field goal. Obviously the pure points strategy only applies early in a tied game. The closer you get to the finish, based on the score, you can calculate whether to go for it or to kick. You'd like to think the football coaches would be aware of these basic odds -- a game of strategy and luck demands attention to them, as every good poker player knows the odds of every single decision he or she makes at the table -- but from what I've read they are woefully ignorant of them. One economist made a handy card that explains the odds for all game situations but it didn't get many takers.
Sports pundits argue today over the value of advanced statistical research in baseball over "gut feelings" and "trusting your eyes." But baseball is hundreds of years ahead of football when it comes to making decisions based on expected returns.