You'll lose more than half the time. If you try a more complicated betting structure than "Bet you $5", you'll have to explain it to them, which will make them suspicious.
Let's assume the data in the article is perfectly representative, or that it is chosen "almost 18" percent of the time. I'll say an even 18 to make this easier:
"I'll bet that if you pick any random number from 1 to 20, I can guess it. If I miss, I give you a dollar. If I get it right, you give me ten."
Over 100 trials, you would lose $1 92 times, but gain $10 18 times: net gain of $88. It works almost all the way down to getting $5 per correct guess.
Intuition would tell the guesser that they've got a nineteen-to-one chance of gaining a dollar. You know (in theory) they've got only slightly better than a one-in-five chance of winning.
