I'm going to try this one more time.  I created another thread on this topic but I realize that my original post might not have been as clear as it should have been.  It was my fault because I included too much math and made it confusing.

This is an important point and I think you'll see football in a whole new light if you get it.  Similar situations pop up a lot and about 95% of the time the coach gets them wrong.

Dallas was down by 18 and on the 6 yard line with 12 minutes to play.  Nearly all coaches would have kicked the field goal in that situation.  Phillips went for it.  The announcers couldn't contain themselves talking about how stupid he was.  15 points is two scores.  11 points is two scores.  You should in no circumstances ever risk being down three scores when you could be down only two.   The number of times you need to score from here until the end of the game is the only thing that matters.

Phillips was right.  They were wrong.  I'm going to explain why.  Hopefully, I'll be clearer this time.

I think most people agree that there was really only one way to win involving the field goal.

Kick the FG
Hold NY scoreless
Score 2 TDs
Convert 2 pt Conversion
Win in OT

Do all of that and you win.  Miss a single piece of it and you lose. 

If Dallas went for the touchdown, their path to victory would be:

Make the Touchdown
Hold NY Scoreless
Score 2 TDs

Compare the two options and you see that "Score 2 TDs" and "Hold NY Scoreless" are in both of them.  Is there any particular reason to think that in either case, it is more likely that you'll be able to make 2 TDs and hold NY scoreless just because you kicked or went?  Not really.  Obviously, doing this is unlikely, but its unlikely whether you go for it or not.  Whatever probability you want to assign to this, you need to assign it to both scenarios.  Since the probability is the same, you can just remove it from the equation.

So ultimately the decision comes down to

Make the touchdown or Kick the FG + Convert the 2 point conversion + Win in OT

Sports bettors should recognize this scenario.  Wade Phillips was basically offered a choice between a straight bet and a teaser.  One low probability event vs having to complete all 3 higher probability events.  You can go ahead and place your own probabilities in there but I think you'll see that the teaser was the wrong choice.

But the analysis doesn't end there.  Both of those scenarios involve making both TDs and holding NY scoreless.  There was no realistic way that Dallas could have won without doing this if they kicked. There are several ways Dallas could have still won the game even without 2 more TDs and holding NY scoreless if they got the initial TD.  They could have won in OT with two TDs and a NY field goal.  They could have won in OT with one TD, a 2 point conversion and a field goal.

When you add these scenarios back in to the straight bet, the teaser that Wade Phillips was offered became even less attractive.

I'm sure some of you won't get this.  Some will just throw up their hands and say "two scores is always better than 3".  Some just don't want to accept that 95% of coaches routinely make the wrong decision.  The crowd can't be wrong.  The one guy that goes against it must be.  But others might get it. If you look closely at what I'm saying and you aren't instantly dismissive, I think you'll eventually come around. 

I know its counter intuitive but you'll gain a whole new understanding of football strategy if you really think about it.