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Interesting Brainteaser

Posted By: Bob Koca
Date: Monday, 7 March 2016, at 5:46 p.m.

In Response To: Interesting Brainteaser (AP)

I am getting (SQRT(5)-1)/2 which is approximately .61803 and is better known as reciprocal of the golden ratio.

Having obtained that answer I will guess there is some elegant explanation.

A summary of how I did it is:

Suppose opponent switches at A and you switch at B.

Then i) with probability AB you both switch and in this case you win 1/2.

ii) with probability (1-A)(1-B) neither switch and in this case you win (B-2A + 1)/ 2(1-A)

iii) with probabity (1-A)B you switch and opponent does not and in this case you win (1-A)/2

iv) with probability A (1-B) you do not switch and opponent does and in this case you win (1+B)/2

Adding up all the cases gives that you win with probability

(1/2) (-A + B +AB - B^2 + A^2B - AB^2 +1]

Considering A a constant we can find the value of B that maximizes the win chance. Then set that equal to A and solve.

Messages In This Thread

• Interesting Brainteaser
  AP -- Monday, 7 March 2016, at 2:15 p.m.
  • Interesting Brainteaser
    Bob Koca -- Monday, 7 March 2016, at 5:46 p.m.
    • Interesting Brainteaser
      AP -- Monday, 7 March 2016, at 9:21 p.m.
      • Interesting Brainteaser
        Bob Koca -- Monday, 7 March 2016, at 9:53 p.m.
  • Interesting Brainteaser
    Igor -- Monday, 7 March 2016, at 11:08 p.m.