Have you ever heard of the Martingale Technique for playing Roulette? The idea is that you sit near a table and wait for it to red or black a certain number of times, then bet on the opposite color. The longer it lands on one or the other, the more likely it will flip.

But wait! This is based on the human conceit that the odds get better over time. They do not, the odds of the table going red or black at any given time are always 50% (slightly less for roulette). You're no better off waiting.

So you see, the odds of the cops catching up to you were always 50%, even though it seemed like over time things had swung in your favor.