How often are NHL games all Over or Under in 1 night?

I was looking at the scores last night and there were 4 games. The 3 early games were under (or were halfway done and looked like they would end up under) and I thought that betting over on the late game (LA vs Carolina) would be smart. Of course it was too late as the game had just started, but it did end up going over.

Anyone have stats on how often that all games on a single night are all over or all under, if all are one way then betting the opposite on a late game could be a good bet.

I am also curious about bets for all home teams vs all away teams and if there are any patterns to this that anyone has found? I know home and away wins/losses are pretty close to 50% but when home teams win do they tend to score more goals? (or vice versa)

I don't have the stats but its like asking what are the odds on flipping heads 10 times in a row if the previous 9 times it came up heads.  Well the odds on the 10th are 50/50.  I don't think the previous 3 games on the board can have any effect on the outcome of the last one.