Just so I understand, the loser gets to keep the bitcoins?
how is the issue resolved if one of the participants don't have enough bitcoin to double the current amount? Is one a "loser" in the game of flinch for being less wealthy than a challenger?
You don't know how much BTC your opponent has, or how much he's willing to risk. Don't accept a challenge if you're afraid of being outclassed. Or accept it and, if you get outspent, at least you'll have his coins as a consolation prize. Or maybe he's playing you. The only way to find out is to accept the challenge.