The actual issues of my question are complex but can be reduced to the metaphor of a game of texas holdem with a twist. The holder of the queen of spades always looses.
The actual scenario is that there are two players and all the cards are dealt for one hand only and then the players never see each other ever again. Suddenly one player says "you can have every card in the deck but in exchange if you have the queen of spades you must turn it over, which means that you lose"
The other player declines the deal.
My question is how to show mathematically that such declination (assuming the imperative of rational and self-interested behavior of winning) is mathematically equivalent to holding the queen of spades