It was quiet at Morty's last night ...
Until Matt the Mathematician proposed a game.
Alex and Davey would both put their billfolds on the table,
and Matt would count the money in each.
Whoever had more would forfeit his money to the other player.
"Think it over," Matt said, and he ordered another frosty one.
Alex thought to himself,
"There's no reason to believe I have more money than Davey
has, or less, for that matter; so my chances of winning are 50%.
Now if I lose, I'll lose whatever's in my wallet.
But if I win, it'll be because Davey has more money than I.
So on a tossup bet, my winnings are more than my losses."
"I'm in," he finally announced.
And Davey thought the same.
He figured his chances of winning were as good as Alex's,
and he'd either lose the amount in his wallet or win
an amount greater than that.
"You're on," said Davey with a smile.
If the boys were thinking clearly, how could the game favor both of them?
Or if not, where is the flaw in their reasoning?