Here is a puzzle to test your understanding and intuition.
You are faced with a problem in which you need to make a decision. For example, you might be choosing $u_0$. You can choose $u_0=0$ or $u_0=1$. One of these is optimal (better than the other).
There is something "A" which you do not know. It could be either true or false.
If you were to know A is true then $u_0=1$ is definitely optimal (i.e. better than $u_0=0$).
If you were to know A is false then $u_0=1$ is also definitely optimal.
Can you therefore conclude that $u_0=1$ is optimal?
See Answer to the puzzle, Proof by Genie, Coda on the puzzle, and Proof by Genie, continued.
You are faced with a problem in which you need to make a decision. For example, you might be choosing $u_0$. You can choose $u_0=0$ or $u_0=1$. One of these is optimal (better than the other).
There is something "A" which you do not know. It could be either true or false.
If you were to know A is true then $u_0=1$ is definitely optimal (i.e. better than $u_0=0$).
If you were to know A is false then $u_0=1$ is also definitely optimal.
Can you therefore conclude that $u_0=1$ is optimal?
See Answer to the puzzle, Proof by Genie, Coda on the puzzle, and Proof by Genie, continued.
