The Market for Lemonade

Jack of Spades(I was just reminded of this story by oscarmc).

"On the day I left home to make my way in the world, my dad gave me some advice. 'Son,' he said, 'I'm sorry I am not able to bankroll you to a big start. But I am going to stake you to some very valuable advice. One of these days, a guy is going to show you a brand-new deck of cards on which the seal has not yet been broken. Then this guy is going to offer you a ridiculous bet - perhaps that he can make the jack of spades jump out of this brand-new deck of cards and squirt lemonade in your ear.

Whatever you do, son, don't accept this bet. Because as sure as I'm standing here in front of you, you're going to wind up with an ear full of lemonade."

This is a nice illustration of a common fallacy in reasoning, and it is quite common in poker as well. We can view it is a simple failure of Bayesian updating. Unlikely though an event may be, if someone has indicated that they have a strong belief in it, the event becomes far more likely. Given that the other fellow had just as unlikely a prior belief that some deck of cards would act in this strange manner, he must have seen some amazingly strong evidence to make him willing to bet on it. Hence we should consider his willingness to bet as amazingly strong evidence in its own right.

The same concept is quite important to playing poker well. The a priori likelihood of getting a very strong hand beat is quite low. But when the betting and raising indicates that you have a very strong hand, and your opponent is still raising you, that must be taken as very strong evidence that you are in fact beaten. Yet it's common to shrug, and think "But it's so unlikely!" and call anyway. (Plus, when you lose, you get to curse your bad luck.)

Of course, there are advantages to this behavior. By discounting the evidence of other's opinions, and needing to see evidence for ourselves, opinions are more independent, and the crowd is more wise, as James Surowiecki teach us. Perhaps that's why our brains tend towards "seeing is believing", even though in some situations this heuristic performs poorly.

Anyway, the take-home message is that people who believe strange things, when such a belief has a cost, often have good reasons. Disbelieve them at your peril, lest you end up with a wet ear. Unless it's me of course, in which case you should never stop raising with the second nuts.

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Great quote. I use it in

Great quote. I use it in class when explaining the concept of asymmetric information. In the version I've heard (attributed to Damon Runyan), the Jack spits cider.

Marlon Brando tells that

Marlon Brando tells that story in _Guys and Dolls_. Then he takes a sucker bet and calls out to heaven "Dad, I got cider in my ear!" once he realizes it. Good gambling movie. Also features a floating craps game and Sinatra singing "Luck Be A Lady Tonight".

Patri, Your general point is


Your general point is well taken. It presents an interesting puzzle, though, since, as Stephan alludes to, the strategy that you suggest works for poker might also lead us to accept claims of alien abduction, snake handling, and personal visits from Jesus.

What, then, is the limit of this sort of thing? Sometimes it is the case that perfectly rational people believe things that have some cost because they have good evidence for believing those things, and you're right that it's a bad idea to ignore such individuals. But many, many people believe strange things that have some cost without any good evidence for believing those things.

What do we want to say about the person who ardently believes in God but who can offer no evidence, no justification for her belief? For that matter, what do we say about the lunatic who believes something that is clearly false? Generally, I hold the view that the wackier a belief is, the more evidence you have to provide before I'm going to take your belief seriously. So personally, you'll probably have to give me an ear full of lemondade before I'll believe you.

That, of course, is a different question entirely from betting on things. I'll have to leave that part of the discussion to people who are better at it than I.

This is why I always will

This is why I always will give the benefit of the doubt to those expressing abnormal beleifs or fixations. If they believe what they do despite strong opposing currents of thought, then they most likely have a good reason.

What about people who derive

What about people who derive benefit from believing things that contradict the common wisdom? I know many people believe outrageous conspiracy theories (like say aliens at Area 51) simply because it grants them happiness to know "secrets," to be on the "inside."

" What do we want to say about the person who ardently believes in God but who can offer no evidence, no justification for her belief? ... That, of course, is a different question entirely from betting on things."

What about Pascal's wager? :)

One important thing about

One important thing about the example was that the believer in question was a gambler, meaning someone who makes a career out of being right. Unfortunately, not everyone is a gambler, and hence they more easily fall into believing silly things.

Patri, What about the

What about the Heaven's Gate folks? They had a pretty strong belief, and there was significant cost associated with it.


Several commentators make

Several commentators make the good observation that belief does not always indicate good evidence. And that is certainly true. Alex gives one good response - stated belief is sometimes quite different from "heart of hearts" true belief.

Another part of the answer is that people have reasons other than evidence to believe things. That was why I was careful to say "when such a belief has a cost", since costless beliefs (ie voting) obviously don't need evidence. And there are certainly reasons other than evidence that people choose to believe strange propositions - those must go into your calculations as well.

But when someone has a strong belief in something very unusual, and there aren't clear alternate reasons why they would believe should begin to wonder if it is true.

Brian and Crazycow, I think

Brian and Crazycow,

I think a big distinction is being made here between what you SAY you believe, i.e. what you're betting on, and what you ACTUALLY believe in your heart of hearts (but may not actually act on or tell anybody), and the Jack story is talking about the former.

Incidentally, for you fans of Pascal's Wager, which of the above do you think God is really seeking to reward?

Belief is involuntary. At

Belief is involuntary. At every point in gathering and analyzing evidence, you either believe a proposition or you do not. Or you don't care.

Brian, Sorry for the vague


Sorry for the vague pronoun reference. The 'that' in the last paragraph was supposed to refer back to my claim about what sorts of things I'll be willing to believe. There are lots of things, though, that I believe but wouldn't be willing to bet on. I believe, for example, that the Hokies will play for the national championship in football this fall. I'm not looking for a bookie to take my money, though.

I'm never quite sure what to make of Pascal's wager. As Vache points out, belief is involuntary. I've never yet met anyone who could persuade herself to adopt theism based on Pascal's wager. Besides, the wager really only works if one accepts a specific set of theological claims, namely, that heaven is infinitely good and hell infinitely bad. One would, however, need to offer some justification for those claims, too.

There's also the problem that I can rewrite the wager to show that I ought to be a Satanist, but that's another problem entirely.

is it not just an alegory of

is it not just an alegory of people being set up in a rigged game? theres a difference. if some one is hyping something, its rigged, is the message i get. the promoter does not actually have to believe it. thats why they give long odds.

What do we want to say about

What do we want to say about the person who ardently believes in God but who can offer no evidence, no justification for her belief?

...That, of course, is a different question entirely from betting on things.

Well, surely it's no coincidence that devout Christians tend to be opposed to gambling... :grin:

(though, curiously enough, which exact part of the Bible forbids gambling is a matter of much confusion...)

Brian, I got your Pascal's

I got your Pascal's Wager right here. :grin: