Hi,

The cheques are k and 2k, for a strict positive value of k. Since you don't know the value of k, actually looking at the cheque has no influence whatsoever.

You pick one of the cheques:
- 50% chance to pick k
- 50% chance to pick 2k.

If you were to switch, they continue as:
- 50% chance to pick k, and then switch to 2k, winning k
- 50% chance to pick 2k, and then switch to k, losing k

As you can see, the winning and losing values of switching are equal, so switching is not worth the bother (but does no harm either).


How is this different from the initial approach? There, the extremes of two separate cases are compared:
Case 1: Choose one of 2k and k
- 50% chance to pick k, and then switch to 2k, winning k
- 50% chance to pick 2k, and then switch to k, losing k

Case 2: Choose one of k and 0.5k
- 50% chance to pick 0.5k, and then switch to k, winning 0.5k
- 50% chance to pick k, and then switch to 0.5k, losing 0.5k

This is incorrectly combined to
- 50% chance to pick k, and then switch to 2k, winning k
- 50% chance to pick k, and then switch to 0.5k, losing 0.5k
by considering the read value k in both cases. However, the knowledge of the problem shows these to be separate cases.


It's that knowledge that makes this different from the quiz master who says:
- You! have won! k! But!! You may open! the Joker! box.! If you do?, the amount is either halved?? or doubled!!!
If the winner could reasonably assume the chances to half and double are equal, then indeed it would be advantagous to open the box.


Nice one; really had to think this one through.

Bye,
                                                                Mysha