A release-checked easy problem for training Games.
Question
You are on death row presently. The judge offers you the following game: You have $50$ white balls, $50$ black balls, and $2$ empty urns in front of you. You can distribute all $100$ balls between the $2$ urns in any way you please. Then, you are blindfolded and must pick one of the urns to select a ball from. If you pick a white ball, you are free. However, you are executed on the spot if you draw a black ball. Assuming optimal strategy, what is your chance of survival?
Practice focus
This Probability problem is tagged Games. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.