Check out my books on Amazon (paid link): https://amzn.to/2SiQjlp Two players are each given 10 marbles. They will take turns playing a guessing game. In each round, one player is designated as the hider and the other as the guesser. The hider hides any number of marbles from their stake in their hand. The guesser also selects a number of marbles from their stake and guesses whether the hider has hidden an odd or even number of marbles. If the guesser guesses correctly, the hider must give marbles from their stake equal to what the guesser has in their hand. If the guesser guesses incorrectly, the guesser must give marbles from their stake equal to what the hider has in their hand. The roles alternate each round, and play continues until one person has run out of marbles and therefore loses. Can you figure out how to play this game optimally? 0:00 Rules of the Game 2:13 Example 3:18 The Puzzle 3:49 Hints 4:29 The Solution 4:56 When the Guesser Guess Correctly 6:04 When the Guesser Guesses Incorrectly 8:49 Why This Game Is Actually Matching Pennies 9:31 Why the Hider Shouldn't Choose Small Numbers 10:53 Why the Guesser Shouldn't Choose Small Numbers