Taking People's Money

By now pretty much everybody has heard of the Monty Hall Problem, even if they generally don't know the right answer. It has a long history of pissing people off, and ranks right up there with the airplane on a treadmill as being one of the most hotly contested thought experiments ever.

My current concern is using this problem (and people's insistence on misunderstanding the answer) in order to trick people out of their money, because that's just how I roll.

First, just in case you're not familiar with the details, we'll re-cast the problem as something you can screw people over with in real life, where you hopefully would have some trouble coming up with a goat on short notice:

1. Obtain a napkin, two pennies, and a quarter.
   
2. Tear the napkin up into three pieces.
   
3. The "host" places each of the coins under a separate napkin, making sure that the "contestant" cannot see where each one is.
   
4. The contestant picks a napkin, aiming for the quarter.
   
5. The host uncovers one of the pennies, without telling the contestant whether he's picked correctly or not.
   
6. The contestant has a final opportunity to switch his choice.
   

The problem is, it's a little difficult to exploit the game as it stands. People intuitively think that the contestant has a 1/3 chance of winning, whether or not they switch sides. They assume that they would be completely indifferent to switching, and if you offered them what they would perceive as "fair" 1/3 odds, you'd lose money in the long run because they will occasionally switch. If you offer something closer to the true fair odds (1/2), they're not going to play because they see it as extremely weighted in your favor.

So let's switch things up. Allow the mark to play the host. Now we can take the role of the contestant, and assuming our mark is a good target, they will feel like they are getting a "good deal" when you offer to put up $5 for every $6 that they throw into the pot. After all, they should win "2/3" of the time, right?

And now you're +10% expected value each time you play the game. Only real problem now is finding someone sober enough to sit down and listen to the rules of the game and think about it enough to "realize" that 5:6 are odds that they should take.

Perhaps even simpler is the two coins game. Here's the way this one works:

1. Host flips two coins, hides the results from the contestant.
   
2. If both coins are heads, host shows the coins (so contestant knows the host isn't lying) and starts over.
   
3. If at least one is tails, the host announces this fact.
   
4. Contestant guesses what the other coin is.
   
5. Contestant wins if his guess is correct.
   

Now, the scam here is that most people think "fair" odds for this game are 50/50. Obviously, right?

Well, that's wrong. In reality there's a 2/3 shot that the other coin will be heads. See Jeff Atwood's blog for a lot of discussion. Many people won't believe this even after it's been explained to them.

The nice thing about this version of the problem is that people have a real affinity for 50/50. Flip a coin? Even bet, obviously. A lot simpler than having to think about an ostensible 2/3 bet and decide whether 6:5 odds is giving them value or not.

With this one, we again want to take the contestant side. We can play the host as well, but it's harder to explain and sell the extra conditions we need to add to make this a +EV play (these changes will (correctly, for once!) make the mark think the game is tilted against them), so it's simpler to stick with playing the contestant. It also puts the coins in the mark's hands (let them use their own!), so they feel more comfortable that they're not being swindled.

Offer them odds slightly better than 50/50, but don't go further than 2:1, that's your break even point. $6 of yours to every $5 of theirs should do the trick, though $11 to $10 is even better, if you can sell it. You always go for heads, and you're set.

A tip: try to specify the number of rounds you're going to play beforehand. A lot of marks will stop once they've lost a little bit, and this option has value. That won't hurt you in the long run, so you won't end up in the red if you don't do this (the ability to stop playing is more like a stop loss order in the stock market; it is only worth anything in this case because the game has -EV for the mark), but if you can lock someone in to 10 rounds, go for it!

A bit of advice: people that feel confident about probability estimates can often make great marks here, because once they've arrived at the wrong answer they are absolutely certain that it is correct. Think poker players, mathematicians, etc. - overall they tend to be only slightly better than average at figuring out the right answer, but they end up far more committed to their answers, so they'll really dig in and chalk the losses up to "variance."

And that's what we refer to as "getting our lulz."