Solved

# Game show envelope conundrum

Posted on 2011-02-28

so the game show gives you a choice of prizes, two sealed envelopes, all you are told is one envelope has twice the amount of money in it as the other, but you've no idea what it is.

So you take envelope A and it has $100 in it - the host asks if you want to swap. What is the value in swapping to envelope B? It is 50% it has $200 and 50% it has $50 in it - so it is worth

.5 x 200 + .5 x 50 = $125

so it has to be worth swapping - but you would therefore always decide to swap. or would you not swap? Would you swap before seeing the envelopes contents? It seems to be a contradiction