As a D&D fan and GM, I often deal with probabilities. People often think that if they roll a "One" 100 times, they will be lucky on the 101st roll. Unfortunately, this is not the case because the probability of rolling any number is always 1/20.
This is why casinos always win. Be aware that the chance of losing all your money is higher than the chance of winning. For example, let's run a simple simulation: a player bets everything on "zero" every round in European roulette, where the probability of winning on a single round is 1/37. He keeps playing until he loses.
There are two events:
Each round is independent, meaning the outcome of one round does not affect the next. However, if we consider the probability of winning multiple rounds in a row, it decreases exponentially with each round because the player keeps playing until a loss occurs. So the probability of winning i rounds in a row is:
PAi = (1/37)i
If the player wins in the first round, it is usually best to take the money and run, because the probability of winning multiple rounds in a row is extremely low.
In D&D, every roll is independent because skill checks never end. You can roll a "One" thousands of times, and it is normal. This works theoretically with infinite trials, but we live in the real, finite world. The guy in New York who rolled a "One" cannot help a player in Vladivostok.
These examples show that our intuition can fail us. I like "The Monty Hall Problem." A player has three doors. Behind the doors are two goats and a car. When the player chooses one door, one of the other doors opens to reveal a goat. The player can then change their decision. What do you think the player should do to maximize their chances of winning?