500
The emperor offers you a chance to live. He gives you 50 black marbles and 50 white marbles and 2 empty bowls. He says,'divide these 100 marbles into these two bowls however you like. Then I will blindfold you and mix the bowls around. You can choose one bowl and pick one marble. If it's white you live, but if it's black you die.'
How will you divide the marbles?
Place 1 marble in one bowl and the rest in another bowl (49 white and 50 black)
This way you begin with a 50/50 chance of choosing the bowl with just one white marble. But even if you choose the other, you still have almost a 50/50 to picking a white marble.