You’re guaranteed to lose if you precommit to giving Omega $1k, if this scenario ever comes up, yes.
However, a precommitment to giving Omega $1k if you lose, and gaining $1M if you win, has positive expected value, and it necessarily entails the precommitment to giving Omega $1k if you lose the coin toss. If you just precommit to giving Omega $1k (and also to refusing the $1M if he ever offers it), then yeah; that’s pretty dumb.
You’re guaranteed to lose if you precommit to giving Omega $1k, if this scenario ever comes up, yes.
However, a precommitment to giving Omega $1k if you lose, and gaining $1M if you win, has positive expected value, and it necessarily entails the precommitment to giving Omega $1k if you lose the coin toss. If you just precommit to giving Omega $1k (and also to refusing the $1M if he ever offers it), then yeah; that’s pretty dumb.