If you mean the Monty Hall paradox, this is how I've recently been able to understand it.

You start with a 1/3rd chance of being right. That's a 2/3rds chance you are wrong. Your first pick is likely wrong.

The host now must open a losing door. Since you likely already picked a losing door, the host likely only has one option for which door to reveal.

So since chances are best that you first picked a wrong door, then the host picked the other wrong door. Which means the one that hasn't been picked by anyone yet is likely the winning door.

Edit: Monte Carlo paradox is a thing. My bad.

The gambler's fallacy, also known as the Monte Carlo fallacy, occurs when an individual erroneously believes that a certain random event is less likely or more likely to happen based on the outcome of a previous event or series of events.

For this one I like the example: "The surgery fails 9/10 times. The last 9 patients have died. Does that mean you in the clear?"