simulating probability

♔: Hey, have you heard the Monty Hall problem? Turns out if there's a prize hidden behind one of three doors, and you choose one, and someone who knows where the prize is eliminates one of the remaining doors by opening it to reveal no prize, and they let you switch your guess if you want, you should switch your guess!

♛: Oh? Seems like it wouldn't matter..

♔: No no, it matters because blah blah, bs, probability mumbo jumbo somethingorother...

♛: Whatever. Let's simulate it.

♔: Hey, did you know that if you want to roll a six on a die, you'll need to roll it an average of six times? This is easy to calculate with an infinite series of blah blah bs probability mumbo whatnot...

♛: Whatever. Let's simulate it.

♔: Hey, imagine that someone's rolling dice. They'd expect to see a six once every six rolls. But if you show up at some random point between rolls and wait for a six, it will probably have taken the guy twelve rolls to get that six.

♛: Oh? Seems odd, since it's usually six rolls to get a six...

♔: No no! It's because of sampling bs blah blah mumbo probability... blah...

♛: Whatever. Let's simulate it.