Daily reminder: pigeons are smarter than people

[Cain]

When first presented with the Monty Hall problem an overwhelming majority of people assume that each door has an equal probability and conclude that switching does not matter (Mueser and Granberg, 1999). Out of 228 subjects in one study, only 13% chose to switch (Granberg and Brown, 1995:713). In her book The Power of Logical Thinking, vos Savant (1996:15) quotes cognitive psychologist Massimo Piattelli-Palmarini as saying "... no other statistical puzzle comes so close to fooling all the people all the time" and "that even Nobel physicists systematically give the wrong answer, and that they insist on it, and they are ready to berate in print those who propose the right answer." Interestingly, pigeons make mistakes and learn from mistakes, and experiments, Herbranson and Schroeder, 2010, show that they rapidly learn to always switch, unlike humans.

http://en.wikipedia.org/wiki/Monty_Hall_problem#Sources_of_confusion

One day, I'm going to use a variant of the Monty Hall problem and conquer the whole damn world.

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That's quite remarkable. I wonder why humans are so prone to this particular error.

Also, I've always inexplicably liked pigeons.

[Captain Utopia]

If you run iterations of Monty Hall, it becomes clear what the correct strategy is - with a 2/3 probability of a payout for switching, and 1/3 for not switching.

But the humans only get to play once.  If the Nobel physicists quoted who are so insistent upon their answer, actually ran through an few iterations, they'd see that their prediction was faulty quick enough.

[Jasper]

Yeah, no fair giving the pidgeons as many tries as they need! 

[Requia ☣]

If you run iterations of Monty Hall, it becomes clear what the correct strategy is - with a 2/3 probability of a payout for switching, and 1/3 for not switching.

But the humans only get to play once.  If the Nobel physicists quoted who are so insistent upon their answer, actually ran through an few iterations, they'd see that their prediction was faulty quick enough.

I know too many people who fall for the gamblers fallacy even after its failed them year after year to believe humans will actually learn statistics from experience.

[Captain Utopia]

I'd argue that there's a different factor in play there - that gamblers have invested into that lifestyle, and are searching for that "big win" to justify it all.  The pigeons are (presumably) getting a minor food reward if they pick the right door.

Let's make the comparison more equal.  If you sat a human subject in front of a computer running a Monty Hall simulation, and gave them $1 for every correct guess, they would quickly deduce that not-switching was giving them less than the expected 50-50 payoff - "20 rounds, and I've only made $6, wtf?".

[Cain]

Deal or No Deal, which is essentially a Monty Hall problem writ large, seems to suggest not.

[Requia ☣]

Deal or no Deal isn't Monty Hall, its the other case, where the person eliminating other possibilities has no special knowledge of the doors.

[Doktor Howl]

Pigeons are rats with wings.  They should be wiped out, ESPECIALLY if they show signs of intelligence.

[Requia ☣]

Good point.

Do I need to do anything special for the tannerite spray paint trap besides disposing of the nozzle safely?

[Cain]

Deal or no Deal isn't Monty Hall, its the other case, where the person eliminating other possibilities has no special knowledge of the doors.

I was thinking of the final round because I don't believe for a minute that the host on such a show isn't informed as to which box contains the prize at some point during the game.

[Rumckle]

From wikibooks:
http://en.wikibooks.org/wiki/Introduction_to_Game_Theory/Deal_Or_No_Deal

When only three cases remain, Deal or No Deal might seem like a version of the Monty Hall problem. Consider a Deal or No Deal  game with three cases (similar to the three doors in the Monty Hall problem). The contestant has one case. Then, one of the two other cases is opened. Finally, the contestant is given the option to trade his or her case for the one unopened case remaining.


The Monty Hall problem gives the contestant a 2/3 chance of winning with a switch and a 1/3 chance of winning by keeping his or her case. However, there is a critical difference between Let's Make a Deal and Deal or No Deal. In the Monty Hall problem, the host has used his secret knowledge of what lies behind each of the three doors to cause a bad choice to always be revealed. This non-random selection of a bad choice is what causes the difference in odds of winning between switching and not switching on Let's Make a Deal.


In Deal or No Deal the odds behave exactly as you would instinctively expect them to: 2 boxes with a fifty-fifty chance of the top prize being in either of them.

[Cain]

Fair enough then