of losing all 4 bets which you have already placed, assuming the line perfectly splits the probabilities, 1/16 as Fishead stated.
However, if you say, I'm going to place 64 bets in a row, what are the odds I'll lose X number of bets in a row, that's a totally different bit of math (which I don't have the capability to do right now). Plain probability would say you'd lose 32 and win 32 but you could have unusually long win or loss streaks within the 64 due to variance.