The Two Jars and Marbles Puzzle

A king gives you two jars and 100 marbles—50 white and 50 black. He will randomly select one jar, then pick one marble from it.

How should you distribute the marbles to maximize your survival?

Put 1 white marble in one jar and the remaining 99 marbles (49 white + 50 black) in the other jar.

The king has a 50% chance of picking either jar.
If he picks Jar 1 (1 white marble) → 100% survival.
If he picks Jar 2 (49 white + 50 black) → You have a 49/99 ≈ 49.49% chance of survival.

50% × 100% + 50% × 49.49% = 50% + 24.75% = 74.75%

✅ This setup gives you a 74.75% chance of survival, the highest possible.