I think that Las Vegas is based entirely on the fact that people don't understand probability. "I have a feeling that I'll get 7's again!"
That's not actually how it works.
Say you're on a game show. You get to pick one door out of three. One door has money behind it, the other two have men with squirt guns.
You pick a door. The chance of you picking the door with the money is easy, right? It's 1/3. Three doors, one guess.
The game show host decides to fuck with you. She says that one of the other doors definitely has a dude with a squirt gun, and asks him to come on out.
Then she asks you if you want to stick with your original choice, or if you want to switch to the other door.
You're down to two doors now, right? One with money and one with a squirt gun dude. You've already selected one.
Do you switch?
Intuitively, I would say no. Why would you switch? You picked a door, stick with it, yo! Gut instinct and a desire not to get squirted won't lead you wrong!
Mathematically, yes. You switch.
Why? Because you started with a 1/3 chance. That means that you had two chances to pick the wrong door. Even though you know, after the first squirt gun fella reveals himself, that you didn't pick that wrong door, it's still more likely that you chose wrong. If you switch, you end up with a 2/3 chance of winning. If you don't, you're stuck with your original 1/3 chance.
I hope that one day you'll use this.
And then you'll send me ten percent of your winnings.