# Does my insurance company commit Gambler's Fallacy, or do I?

I would not be able to put this into symbols, but I ask here because I think it's the correct place to ask.

Would the chance of my parked car getting damaged (bumped or scraped) by other cars parking nearby increase over time?

Gambler's fallacy says: if something happens less frequently than normal during some period, it will happen more frequently in the future. (wikipedia)

For every time I leave my car parked, there is a chance it will get damaged. If I don't want to commit the gambler's fallacy, I should consider the chance of damage the same every time I park.

But if I park at the same spot every day for many years, the chance that my car would have been damaged after all those years, would surely be greater than if I just parked there one day, right? How does this not contradict the gambler's fallacy?

My insurance company asks a higher premium if I park on the street all year round, than in a garage, so somehow they must figure that the chance is higher than if I just park on the street one day. How does this not contradict the gambler's fallacy?

If you for example let the probability of the car being damaged be $0.01$ on any given day, independently of what happened in the past, then the probability that you will avoid damage over the next year is $0.99^{365}\approx 0.025$. So obviously, the longer the period, the higher probability of getting damage.
Now, let it be the case that you have had no damage for the last $10$ years. Using the independence of events, the probability of avoiding damage in the course of the next year is still $0.025$. Committing gambler's fallacy here would be to say that this probability is lower than $0.025$ because of the long stretch with no damage. On the other hand saying that the probability will decrease if you take a longer time period, is not gambler's fallacy.