An invisible target on the integer line starts at $0$. On each round it stays put, moves to the left or moves to right by $1$ with probability $\frac{1}{3}$ each. You are then asked to guess the location of the target and told whether your guess was correct or wrong.

What is the optimal strategy to maximise the number of correct guesses, say in $N \geq 2$ rounds?

An invisible target on the integer line starts at $0$. On each round it either stays put, moves to the left or moves to the right by $1$ with probability $\frac{1}{3}$ each. You are then asked to guess the location of the target and told whether your guess was correct or wrong.

What is the optimal strategy to maximise the expected number of correct guesses, say in $N \geq 2$ rounds?

An invisible target on the integer line starts at $0$. On each round it moves either to the left or right by $1$ with equal probability, then you are asked to guess the location of the target. You are then told whether your guess was correct or wrong.

What is the optimal strategy to maximise the number of correct guesses, say in $N \geq 2$ rounds?

An invisible target on the integer line starts at $0$. On each round it stays put, moves to the left or moves to right by $1$ with probability $\frac{1}{3}$ each. You are then asked to guess the location of the target and told whether your guess was correct or wrong.

What is the optimal strategy to maximise the number of correct guesses, say in $N \geq 2$ rounds?