We have no idea what the odds are, but they are certainly better than the odds of winning a billion dollars by picking all the NCAA tournament winners.
A math class we took about 25 years ago tells us that we *think* the chances of at least lining up all 16 games properly would be one in 16! (Sorry, that's not 16 exclamation point. That's 16 factorial. Which means 16*15*14*13 and so on. So that's like 1 in 20 trillion). But the Rams play three teams twice, so that's probably not right. Also, it's quite possible we have forgotten something about the maths in all those years.
But then you also have to guess what day the game is on, whether it is home or away, plus the bye week.
In any event, it's probably a lot harder than it sounds. But if you want to try, here is the link! The Rams are happy for your patronage!