One more thing about two-point attempts

With the scores level late near the end of an NFL game, your side scores a touchdown.  You've worked out that the chance of success with a two-point conversion, for either side, is a little over 50%.  So you should try for two?  No.  It makes a difference only if your opponents are going to score a touchdown of their own.  Then if you've failed with a two-point attempt, they're certain to win by kicking a single point (under the simplifying assumption that these kicks always succeed).  Whereas if you've succeeded, they can still tie the game with their own two-point conversion.  In fact, to make your two-point attempt the right strategy the chance of success has to be more than (2 - sqrt(2)), about 58.6%.