"I'll bet you $10 I lose this bet."

Here's an attempt to unravel this...1

Every bet is posed by a bettor to a bettee(for want of a better word), and consists of a stake, and a condition. When the condition is proved or disproved, the bet resolves, and if the condition is true, the stake is given to the bettor; if not, it is given to the bettee.

In this bet (B), the stake is $10.
The condition is that the bet B resolves, and that the condition is false.
The condition, therefore, depends on its own resolution in order to resolve, and will therefore never resolve. If it were to spontaneously resolve, it would start a 'this sentence is false' paradox. Thankfully it doesn't come to this.

So feel free to take this bet, for whatever stakes you like... You'll die long before you'd have to pay up.

1 - With apologies to the magic: the gathering errata team