# Stoplight Theory

Say you are going to travel a route with some stoplights. If you don't know the stoplight schedule, then no matter what time you leave, the average length of your trip won't change. This seems obvious but it means that during preparations, you will get to the destination exactly as much earlier as you leave. This is assuming that traffic is random, and doesn't consider acceleration.

## Leaving 1 second later will on average get you there a second later.

This only works if you don't know the schedule of the traffic lights.

Another related theory is that even with traffic, leaving later can never make you arrive earlier - at best, it can get you there at the same time.

## Acceleration effects

Without acceleration effects (cars at all times move at 0 or max speed), even with known traffic light schedules, leaving later can never get you there earlier. However, with acceleration, leaving later can help you (say on trip A, you come to a complete stop at a light and then go to the destination, but in trip B you leave 1 second later and don't stop at all at the light (say you have a very fast brake and a slow accelerator), - depending on the speed of your accelerator, avoiding that stop could save you more than an entire second).