I agree, and I don't think that people understand what you are saying. If you kick an extra point to go up by 8, the other team will have to score a TD and get a 2 point conversion to tie. If you miss the extra point, the other team only needs a TD and an extra point to tie. Unless you're Jack Del Rio, nobody is going for two to win the game. If you go up by 9, the game is essentially over. The counter argument is the about the best odds. What has better odds? Attempting a two point conversion to potentially go up by 9 or the opposing team scoring a TD and either kicking an extra point or a two point conversion depending on if you miss the extra point attempt? I am going with going for two.
I did the problem under the assumption that the other team will kick the XP if given the chance. If they'd rather go for 2 instead, I would have to redo the entire problem under the new assumption. The probability of winning/losing if we go for 1 is the same as before. The probability of losing if we go for 2 is then 0.53*p*0.47 = 0.2491*p because they have a 47% chance of making their 2 pointer. In the original universe, if we assume our probability of winning in OT is 50%, 0.53*p*0.94*0.5 = 0.2491*p. So it doesn't matter whether they choose to go for 2 or 1, and it doesn't change the fact that it doesn't matter for us whether we go for 1 or 2 either.
