A standard $6$-sided die is put inside a cup. The cup is shaken and put upside-down, hiding the die.
You are going to guess what is the number on the top of the die.
But, instead of given $6$ options, there are only $2$ options for you:
- It is $6$, or
- It is not $6$ (i.e. it is between $1$ to $5$).
After you choose your guess, the cup is opened, and you will win if the die matches with your guess.
You are going to play this game $600$ times, and you want to win as many as possible.
There are these two possible strategies:
- Always go for the second option (not $6$), or
- You "imitate" the roll: you bring a new die and roll it.
If it rolls $6$ then guess $6$, if not $6$ then guess not $6$.
Which strategy will you choose? Do you have any better strategy?