Two Dice Challenge

You have two dice in a shaker. You ask a friend to shake the dice and peek at the outcome, which he does. You ask him, "Is at least one of the dice a two?" He says, "Yes." What is the probability both dice are a two?

In this video, a challenger accepts my offer to pay 8 to 1 odds for two 2's, as long as there is at least one two. Watch to see who wins, after over 300 shakes of the dice.


Here are three threads where this problem has been discussed at Wizard of Vegas, for over nine years.