What solution do you give to this puzzle?

I give three different formulations, if that can help.

The original one is supposed to be the last one here...

In this game there are two people, labelled Dealer and Player. The Dealer writes two different numbers down on two slips of paper, and seals them in envelopes. It doesn't matter what the numbers are. They can be 0, 5, 4081922, -382.393193, pi, anything. They just have to be different numbers. The Dealer then hands the two envelopes to the Player in any order they please. The Player then selects one envelope to open. They then must decide whether the number in the other envelope is greater or less than the number in the envelope that was just opened. Obviously it's easy to win 50% of the time. The challenge of the game is to come up with a strategy which wins more than 50% of the time. Can you think of a strategy?You are on a game show. The host has chosen two different whole numbers (integers) and has hidden them behind doors A and B. He allows you to open one of the doors, thus revealing one of the numbers. Then, he asks you: is the number behind the other door greater or smaller than the number you have revealed? Your task is to answer this question correctly with probability strictly greater than one half.I give here my own view on this, hidden to not influence anyone...Alice secretly picks two different real numbers by an unknown process and puts them in two (abstract) envelopes. Bob chooses one of the two envelopes randomly (with a fair coin toss), and shows you the number in that envelope. You must now guess whether the number in the other, closed envelope is larger or smaller than the one youâ€™ve seen. Is there a strategy which gives you a better than 50% chance of guessing correctly, no matter what procedure Alice used to pick her numbers?

EB