How much money would you put up for a 50% chance to win $1000? A coin toss... Heads you win, Tails you loose. If you win, you only get the $1000, not yor original bet back.
How would your bet be different if you get the $1000 AND your original bet back if you win?
Taking the problem at face value;
I'd bet 1c in both cases.
(Unless I could bet even less than that)
In case 1: if I win, I'm down 1c and up $1000. If I lose, I'm down 1c.
In case 2: if I win, I'm up $1000. If I lose, I'm down 1c.
Betting more gains me nothing if I win, it just adds to my potential losses.