# Door GameFebruary 22, 2008 1:24 PM   Subscribe

The predictably irrational door game.

The optical illusion demonstrations are also good (scroll down half page).
posted by Rumple (39 comments total) 5 users marked this as a favorite

Anyone else find this to be terribly buggy? I got points every click in the first round, and NaN seemed to be behind every door after that.
posted by base_16 at 1:31 PM on February 22, 2008

More frequent switching when the doors are shrinking is most likely a reflection of an irrational tendency to keep your options open.

This tendency cost you points in the game, but it could have much larger implications in life...

Thanks for the life-tip door game guy.

GTA should do something similar. "You had sex with nine prostitutes and blew the heads off four. This tendency cost you points in the game, but it could have much larger implications in life..."
posted by mattoxic at 1:31 PM on February 22, 2008 [9 favorites]

So... why would you waste clicks to open doors given that the number is random anyways whether you open a door or just stick with one?
posted by edgeways at 1:38 PM on February 22, 2008 [1 favorite]

base_16: Wow! I didn't get a NaN a single time... Strange
posted by larsso at 1:45 PM on February 22, 2008

mattoxic - I got the same message when I never switched doors.
posted by jozxyqk at 1:54 PM on February 22, 2008

Is it random 0-100? I suspect it random from normal with mean of 50.
posted by Rumple at 1:57 PM on February 22, 2008

"So... why would you waste clicks to open doors given that the number is random anyways whether you open a door or just stick with one?"

I thought that the distribution from the mean of 50 was greater in some doors than others. Though I'm not sure what strategy that would argue for, noting that the more times you click on any of 'em, the more you should revert to that mean.
posted by klangklangston at 2:02 PM on February 22, 2008

I switched doors less the second time. I scored fewer points the second time.

I think they all have a mean of 50 but the standard deviations are different depending on the door.
posted by Hactar at 2:02 PM on February 22, 2008

I don't get it. Click a door and get no points, or click an opening and get points. Why do I not want to click a door once and then just hammer the opening?
posted by seanmpuckett at 2:02 PM on February 22, 2008

And each click to open a new door is a wasted opportunity, so I'd imagine that in general, the less switching you do, the closer you'll hew to 2500.
posted by klangklangston at 2:03 PM on February 22, 2008

Playing stupid door switching games is most likely a reflection of a pathetic pursuit to make your life more interesting.

This tendency cost you nearly 2 minutes of your time, but it could have much larger implications in life...
posted by milarepa at 2:04 PM on February 22, 2008 [3 favorites]

So... why would you waste clicks to open doors given that the number is random anyways whether you open a door or just stick with one?

I didn't see anything that went into this explicitly, but this is what I guess was going on:

Each of the three doors is going to generate random numbers according to some random distribution, or to reduce it farther let's say some random range from lowerbound to upperbound. Each door's lower and upper bounds are different, but static for the whole round, so there's theoretically a best choice—the door that has the highest average likely output.

So then the game is about deciding which door to run with, and running with it.

First round: with doors that don't shrink, I decided to give each door five clicks or so to see if any of them seemed to perform particularly well or poorly. One gave me an average of maybe 20-25, the others both seemed to be going around 35-40, so I picked one of those two and blew the rest of my 35 or so click on it. Came out with just over 2000 points for the round.

Second round: door shrinking means I'm stuck with a smaller number of clicks per door if I want to test them all once before committing. I did three clicks each, I think, wagered that the distributions were probably similar (but randomly reassigned) to round one, picked a good performer, and clicked away the other 40 or so clicks. Came out with about 2300 points.

My assumptions could be wrong; I threw together this model as I played on the assumption that the game wouldn't actually be dull enough as to generate numbers in the same distribution from all three doors, but my model could be wrong. And my test data, the initial set of clicks for each door, was quite small, especially in round two, so I may well have picked a less-than-best door in either round anyway.

But clicks spent switching doors are clicks that don't pay, so I wanted to minimize my switching as much as possible. I might go back and do some single-door trials just to see what a no-switch strategy offers.

Is the site more explicit about any of the things I'm making assumptions on, and I just missed it, or are we all this much in the dark as its presented?
posted by cortex at 2:07 PM on February 22, 2008

I don't get it. They tell you to "find the door that gives the most points," but you get back random numbers regardless of the door you click on, and clicking on more than one door "cost you points" and is "a reflection of an irrational tendency."

This is a very poor demonstration of whatever it's supposed to demonstrate.
posted by designbot at 2:19 PM on February 22, 2008 [4 favorites]

Upon some slogging no-switch trials on various doors, it looks like it is indeed three different distributions that all have a mean of 50 or so; a 30s-60s option, a 40s-50s option, and a 10s-80s option.

Which is, you know, pretty goddam boring, and not really even a gotcha except as a metagame thing: if you provide no information about what kinds of distributions to expect but offer the option to switch, drawing conclusion about the switching that occurs is kind of weaksauce.

I also managed to produce the NaN issue on one clicking spree.
posted by cortex at 2:20 PM on February 22, 2008

So... why would you waste clicks to open doors given that the number is random anyways whether you open a door or just stick with one?

Well it says each of the doors has a different distribution. Suppose each of them is a normal distribution with different means. If the means are far enough apart you should be able to suss out which one gives, on average, higher returns. The question is whether you can do it quickly enough to be worth the lost points.

On preview, ack, what cortex said.
posted by juv3nal at 2:21 PM on February 22, 2008

The rules are pretty unclear. They made it sound like some doors were 'worth' more than others. So I tried each door once in the first game, switched back to the one that had scored highest, and then just clicked there until the game was over.

I did the same thing in the second game, but the third door I clicked had the highest score, so I just stayed there.

But they insist that I 'wanted to keep my options open', when in actual fact I just switched back to the highest-scoring door.

This is a terrible test. It doesn't explain enough, and it makes bad inferences from inadequate observation.
posted by Malor at 2:48 PM on February 22, 2008

It's Friday, it's flash... hands up who had any fun?
posted by Chunder at 2:55 PM on February 22, 2008

Read Elbow Room by Dennett and play some other flash game instead.
posted by MillMan at 3:05 PM on February 22, 2008

I stuck with one door and wound up with 2428/2497. I haven't learned anything at all, and now I'm bored.
posted by boo_radley at 3:23 PM on February 22, 2008

Those two numbers, 2428 and 2497, are in fact the two totals I kept seeing for most of my brute force runs. The former corresponds to the 30s-60s door, the latter to the 40s-50s. So it's not even random numbers according to a distribution; it's fixed sets (in, at least, it appears, random order) matching their given distribution.

Not that that should really matter if it's being treated as a single trial, because, hey, what tiny shred of a point there is to be made here is about evaluation strategies and the cost of avoiding commitment, and if you've only got one shot at the whole thing and presumed ignorance of the mechanics driving the numbers, it doesn't really matter as much what the mechanism actually is. But still, blech.

What would be interesting would be to build a more flexible version that actually did produce random, distinct distributions, and then use that as a basis for developing an evalutative strategy to maximize points over a fixed number of trials. Put some real math into it, see what sort of breaking points would develop.
posted by cortex at 3:35 PM on February 22, 2008

Every click that opens a door gives you no points. So the point is to pick one door and run with it. Irrationally we switch doors looking for a payoff but every time we switch that is a click that gets us zero.

It isn't a game, just something to show us how stupid we are.
posted by konolia at 4:19 PM on February 22, 2008

Reading this makes me wonder very seriously about the value of multi-armed bandit models.
posted by ~ at 4:23 PM on February 22, 2008

You switched 14 times less when the doors were shrinking.
More frequent switching when the doors are shrinking is most likely a reflection of an irrational tendency to keep your options open.
This tendency cost you points in the game, but it could have much larger implications in life...

Well, since I switched less often when the doors were shrinking, and got a higher score as a result, I can't see a tendency that cost me points in the game.

The reason I switched less often when the doors were shrinking is because that was the second round of the game that I'd played. Having used the first round to explore, and having come to the same conclusion as konolia, in the second round I just picked the right-hand door and clicked it until I ran out of clicks.

Lolshrinks.
posted by flabdablet at 4:28 PM on February 22, 2008

But konolia, the problem is that a model where every choice has exactly the same associated value represents close to zero analogous real-life situations. Worse yet, it's a model that loosely implies that there will, in fact, be non-identical results from the different doors.

If someone wants to make a point about irrationality, they should at least keep up their end of the bargain. This thing sucks.
posted by cortex at 4:36 PM on February 22, 2008

But does Monty Hall know which door is optimal?
posted by DanSachs at 4:42 PM on February 22, 2008

Yeah, this sucks intensely. It demonstrates nothing because it uses faulty methods to try arriving at their point. Tried poking around with it, but there's really no point whatsoever.

Pretty much just affirming what everyone else already said.
posted by Stunt at 4:58 PM on February 22, 2008

I think I'm Spock, or I've got some idea how psychology games work
posted by fearfulsymmetry at 4:58 PM on February 22, 2008

Okay, so my wife is looking over my shoulder as I play the game. And yes it's stupid. So then she watches me read this thread, and we chuckle a bit. And the she says, "This is even more stupid than the door game. It's a bunch of people having a conversation about something on the internet that is not interesting, but trying to make it interesting, ON THE INTERNET."

I replied, "You FINALLY GET METAFILTER!"

And then we chuckled again.
posted by Roger Dodger at 5:18 PM on February 22, 2008 [2 favorites]

I think everyone is missing the point here. This is supposed to be a demonstration of a psychological issue, not a probabilistic . The goal (in my opinion) is to demonstrate how the practice of "keeping your options open" can really screw you over. In reality, it's even harder to let options disappear because you can observe them and potentially learn more information (though this is often an illusion). I think they were intentionally misleading (but not lying) about the distributions, leading you to seek an advantage that's not easy to find (due to it not existing).

However, I think that if they had put a window in each door and had the points for each door appear on every click (while you only win the points from the open door), the effect would be much more dramatic. You would find yourself doubting your choice as a door with a high value streak gets smaller and smaller.
posted by ErWenn at 5:29 PM on February 22, 2008

I got predictibly irritated.
posted by kuujjuarapik at 5:34 PM on February 22, 2008

Yes, ErWenn, but it's framed badly enough that the purported psychological "gotcha" isn't nearly as clearcut as it would be in a presentation that made rational behavior possible to pursue. You have to provide sufficient information to the player before you can actually claim their behavior is rational or irrational, and this model approaches EPIC FAIL on that front.
posted by cortex at 5:38 PM on February 22, 2008

Was anyone else hoping it would be one of these door games, or am I really that big a dork?
posted by Cat Pie Hurts at 5:59 PM on February 22, 2008

So.... You get the most points if you just keep clicking on the same door.

What the hell kind of personality is this supposed to reward?
posted by Afroblanco at 6:00 PM on February 22, 2008

One that knows the difference between zero points and more points?
posted by konolia at 6:37 PM on February 22, 2008

konolia, they don't really give you enough information to draw the conclusion that you drew (i.e. "since opening a door is zero points, the best strategy is to open a door and stick with it". Or, if they did give you enough information to draw that conclusion, I certainly didn't see it.

For example, let's say that one of the doors gives you 40-60 points, another 40-70, and the third 40-10000.

You would be silly, if you knew this to be the case, to claim that you should always open only a single door, since opening another door doesn't get you any points for that click.

And they didn't provide enough information to you to know that distributions like that are not what's actually there.
posted by Flunkie at 8:00 PM on February 22, 2008

I switched doors 3 times in the first game, then when the doors were shrinking I switched ZERO times.

The damn game still berated me, even though by its metric I picked the optimal strategy. Fuck off, stupid game.

FWIW, the middle door has the narrowest distribution. I don't like seeing those 30's and 20's so I just kept clicking it.
posted by ikkyu2 at 8:05 PM on February 22, 2008

You switched 4 times less when the doors were shrinking.
More frequent switching when the doors are shrinking is most likely a reflection of an irrational tendency to keep your options open.
This tendency cost you points in the game, but it could have much larger implications in life...

That doesn't even make sense. I switched 4 times less, so why are they lecturing me on my irrational tendency to switch "more?"
posted by jcruelty at 9:02 PM on February 22, 2008

I am the most irrational of all.

I got zero points on the first round, because I failed to notice you needed one click to "open" the door and kept clicking all the doors in succession wondering why none of them ever gave me any points.
posted by lastobelus at 11:13 PM on February 22, 2008

I saw it the same way as konolia. On the second round, I chose one door and just stayed with it the whole time.

Interestingly, I would say that I *am* obsessed with keeping my options open. Which just shows that this test sucks.
posted by bingo at 5:53 PM on February 24, 2008

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