Three boxes sit in front of you. One contains two gold coins, one contains two silver, and the third has one of each. You pick a box at random, reach in without looking, and draw a gold coin. What's the chance the other coin in that same box is also gold?
The intuitive answer is 50%. The correct answer is ⅔. Play the game below, or run the simulation to watch the accuracy converge on ⅔ over thousands of trials. Wiki →
Select a box, draw a coin, then guess the other coin. Your guess is tracked below.
Once you've drawn a coin, the box you're holding is more likely to be the same-colored box than the mixed box. Always guess the same color as the one you drew and you'll be right ⅔ of the time.
Simulate N trials. Each trial: pick a random box, draw a random coin, guess the same color for the remaining coin. Watch the accuracy converge on ⅔ ≈ 66.67%.