Each drop is an event independent of the others. The Law of Large Numbers does apply here, but to the other poster who mentioned picking straws out of a bag, that analogy is incorrect, since that blank straw is "put back into the bag" with each attempt.

The idea that ones chances improve after multiple failures is a fallacy that casinos, for instance, rely on heavily for driving some of their games (e.g., roulette). You could hit red five times in a row, but you still have a 50/50 chance of hitting red instead of black on your 6th attempt, since the "red squares" are not removed from the equation just because they've been hit before.

I hope that makes sense.