Jay Jacobs has some fun with roulette simulations and explores the odds of winning for different bets. Above shows a simulation of 250 spins 20,000 times. Or to put it differently, it's like simulating the play of 20,000 people, who each took 250 spins and always bet on a single number.
I'm not sure why it doesn't start to get red until you're $500 in the hole, but bottom line: the longer you play, the higher probability you will lose all your money. That was my main takeaway from Probability 101 in undergrad. The rest is a blur.