Edit: I just did a little bit of research - the average team kicked approximately 26 FG's this year and scored approximately 38 touchdowns. That's 64 scores per year which conveniently works out to 4 per game. That means the average game has 8 scores. So even if a safety occurred in EVERY game, there's only a 1 in 9 chance that it would be the first score of the game, and a 1 in 18 chance that it would be a chosen team doing so. So the odds Vegas gave that guy were as if a safety occurred more often than once every 3 games. The guy got lucky that he won, but he got HOSED on the odds.
Also, if you adjust it by looking at the scoring tendencies for the Pats and Giants specifically, the Pats had 61 touchdowns and 28 FG's while the Giants scored 47 touchdowns and 19 FG's. That's 89 scores for NE and 66 for NYG. That's 155 scores - 9.7 per game. Considering they both have considerably below average defenses, by playing each other, you'd expect AT LEAST 10 scores (actually more, but 10 is a nice round #). That means, even if a safety were guaranteed to occur, it would be a 1 in 11 chance of being the first score, and a 1 in 22 chance of being scored by a chosen team. That means the odds Vegas gave that guy were based on the probability that a safety occurs nearly every other game. Again, completely hosed. Even Vegas usually gives more fair odds than that.
Think about it for a second, Vegas gave 50-1 odds that the first score would be a NYG safety, meaning they'd only give 25-1 odds that the first score would be a safety period (by either team). So if you put $20 down on the first score being a safety, and it was, you'd only win $500. Just absolutely ridiculously low odds.
[ Edited by andes14 on Feb 6, 2012 at 2:24 PM ]