Even if their kicker is 100%, it’s still the right play if they are 40% to succeed with the two-point conversion attempt. You assume you will score another touchdown (and that you are even money in overtime) and go for one the second time if and only if the two-point try worked. I’ll show the calculation in the lengthier explanation, but you should try to work it out for yourself.
The situation is that you score a touchdown late in the game and find yourself down by eight points. And by late in the game, I mean that it would be nearly impossible to win if the opposition scores again. Depending on time outs left, that would be in the neighborhood of three or four minutes. (Actually, my strategy is probably correct if there is quite a bit more time left than that, but it is harder to prove.) In almost all cases the correct strategy is to try for a two-point conversion and if you make it, you obviously go for one if you manage to score another touchdown and go for two (which would give you a tie) if you miss the first time. If you assume that you will in fact score again, assume you are 50% if it goes to overtime, assume a two point try works 40% and a one point try is 100% your chances move from 50% to 52% (of those times you do actually score again). The math is simple.
If you go for one after the first score you obviously go for one the second time and pin your hopes on an overtime win which we have defined as 50%. If you go for two, you have two ways of winning. 40% of the time you “win” instantly, assuming the second score. But you can also win if you fail on the first conversion attempt, succeed on the second one, and go on to win in overtime. That is 60% x 40% x 50% which is another 12% that you can tack on to the 40%. In real life the calculation is even more clearcut since two-point conversions are a bit higher than 40%, and one-point tries are a bit lower than 100%. The only legitimate argument against my suggested strategy could only come up if your team is so much better than your opponent that its chances of winning in overtime is well over 50%. (Some try to claim that the second score becomes significantly less likely after a failed two-point conversion attempt because the team is “demoralized”. Invariably those who put forth this argument are not people who were aware of the mathematical conclusions regarding the strategy mentioned here and are just trying to hide their ignorance by putting forth a theory that almost certainly even if true at all, could not overcome the mathematical argument. See # 69.