That's what you say it is, at least
This is a very fun game to be played with someone who either has a) no common sense or b) someone you can coax into doing something extremely stupid. Whichever you choose, your opponent should have a good sense of humor...or you should be able to run very fast
Okay, so you have your subject. Tell them to place their elbow on the table in normal arm wrestling postion. Tell them to make a fist. Turn their hand so their knuckles are pointing directly at their nose, and tell them the object of the game is to touch your knuckles to your nose. It is best to turn their hand toward their face yourself so you can avoid saying "Okay, now make a fist and point it at your face." This usually gives it away.
Now the hard part is done. If they haven't realized they are on the path to chipped teeth, a bloody nose, or a bloody lip, thats their problem. Take their hand and pull it toward the table, and they should pull back their fist towards their face. Try to really get into it. Strength shouldn't be a factor because the muscles you are using are much stronger then the muscles your oppenent is using, but try to butter it up.
If you havent figured out what to do next, you should be the one about to punch himself in the face. Get their hand at a 45 degree angle to the table, make sure they are pulling hard, and let go. If all goes well, they have just hit themself in the face. Congrats, you just won a game of Polish Arm Wrestling! (This is the point where you either run like hell, or laugh hysterically, depending on the general size of your opponent).
If your opponent lost enough brain cells after this hit, you might be able to convince him you accidentally let go and try for another round. This also works if the person is just plain stupid or if you are especially charismatic.