You keep the money. Use it to buy a couple of t-shirts. One for you (that says "I was right") and one for him (that says "I was wrong).
Honestly, if you'd have lost the bet, would you have paid up? If so, keep the cash. You're both grownups.
I have an uncle that is constantly saying stupid, stupid things and gets really obstinate when the viewpoint is challenged. He inevitably does the "Let's put money on it" thing, and I always keep the money when I inevitably win.
A fool and his money are soon parted.....
And Vlad nailed it the post above!