Sigh…was it possible to approach this too rationally? Or at least too mathematically? This is what too many statistics classes have done to my brain…
In my first round, I clicked on each door five times in a row to obtain a “sample” from which I would determine the approximate mean of each door. It wasn’t until after sampling the third door and choosing the one with the highest mean (the first) that I realized that I consistently didn’t get points until the second click on the door. By then, my plan was sadly foiled, and I only ended up with a 2027.
All these doors…if only this was the Monty Hall problem. I know the answer to that one.
I’m not going to spoiler-box this since if you’ve read this far in the thread you should have played the game already. Otherwise, what’s the point?
A few observations:
[ol]
[li]I made more points on the part where I switched the most, which means that switching is not actually irrational. If giving up clicks made a real difference, I should have gotten a lower score, especially over the course of 50 trials.[/li][li]If the numbers aren’t really random or if you are getting a run of consistently low numbers, it’s not necessarily irrational to switch to something that might give a better possibility. It’s like that classic game theory setup where shunning someone who screws you, but consistently being fair with those who treat you fairly gains you more over the long run.[/li][li]You really have to play the “game” through to the end to actually see whether or not there’s any pattern, or if they’ve changed any other rules than the ones they’ve stated they changed. Up to that point your choices have been based mostly on your uninformed decisions. Playing a second round with no rule changes and no explanation of the principles other than what you deduce would be a better test of rationality vs. irrationality. If, knowing what you know after playing the whole game, you still do things that have a high potential for lowering your score, then you’re irrational. Until then, you’re experimenting and learning, which is highly rational.[/ol][/li]
Dumb game, doesn’t test what it claims to test, and is based on flawed logic.
To double check, I just played through twice again. Knowing what I know about the game mechanics, I switched whenever I got a low payout on the first part, and stuck with a single door on the second part. I got over 50 points higher on the first part where I switched the 7 times, and about 25 points higher when I switched 4 times. My strategy works better over a combined total of 100 trials than their supposedly logical method. So, which is the more logical way to approach this problem?
You’re misunderstanding the experiment and the conclusions. They don’t claim that switching is rational or irrational. Posters on this thread have. They claim that switching more in the “doors shrink” version than in the “doors stay the same” version is “is most likely a reflection of an irrational tendency to keep your options open.” It’s the difference in behavior in the two versions that they are studying. And they randomized the order of version to control for learning patterns.
I’m not sure I understood the test. I’ll post what I did then look at other peoples’ responses…
I just clicked on the middle door each time. Scored 2428 in my first round, 2446 in my second. Does that make me rational or irrational? I have no idea.
The test isn’t testing how many times you switch. It’s testing if you switch a different amount of times under slightly different circumstances. You stayed the same, so you were not irrational (for this test ).
2150 and then 2146. I switched four times when the doors were shrinking, and three times when they were not. It took me those switches to see what was the best distribution. After the first six clicks in each trial I stayed with one.
I switched three times in the first test and zero times in the second. In the first, I was checking the distributions, and switching when a low number came up. I think by the second door, it dawned on me that I was losing numbers when I switched. It also looked like the first door had the best distribution. So for the second test, I tried the first door and decided to stick with that as long as it looked like the same distribution.
I picked and clicked one door each time, since it seemed pointless to switch between them if you wasted a click to open the door. 2416 the first time, 2497 the second.
Folks, you need to say whether you saw the doors shrinking in the first version or not. It was randomized, remember? Not everyone had the same test on the first round.
Really? That seems pretty extreme in the other direction. The reason would be that other doors might have different distributions, giving you more points.
I don’t know if spoilers are still necessary at this point. I went the boring route and clicked on the left door all 50 times the first time. I got 2416. The second time, I clicked on the middle door all 50 times and got 2446.
From having read this thread now, I’m not sure what that says about me, but switching arbitrarily just seemed silly. If it was random anyway, I couldn’t see why it would be advantageous to switch to a different random door, especially after I figured out in the second game that the first click didn’t score anything.
Speaking for no one but myself, I…wasn’t. I just figured that clicking on the same one repeatedly was every bit as “random” as clicking on several different doors. And it made it very easy to report exactly what I’d done, rather than having to memorize a sequence.
No, I’m not misunderstanding the experiment, as I explain in point three of my post, which you omitted when you quoted me. The experiment was to see if you switch, under what circumstances you switch more, and tries to draw a conclusion as to why you switch. The problem is that their game isn’t set up so that their purportedly optimal strategy is actually the best one. They make an assertion that switching hurts you when only a little experimentation shows the participant it actually doesn’t have a negative impact on the score.
That flaw invalidates any bias toward or against switching when the doors are shrinking, because it’s not obvious that the best strategy is to stay with one door and never deviate. The instructions imply that not deviating could be the best course, but it’s only when you actually test that claim that you find out if it’s true or not. Frankly, trusting instructions implicitly and assuming that the game mechanics are as claimed is irrational to me. I’d rather test it and form my own conclusions. In this case, experimentation showed that there was no logical reason not to switch if I felt like it.
So, again, their test doesn’t measure what it claims to measure, and their conclusions are based on flawed logic.
I switched 3 times in the first round and zero in the second. I found the description of what would happen to the doors very confusing and felt I needed to “play around” with the doors a few times to see what was meant.
I soon realized that switching doors only slowed me down in either scenario because the click to open a door wasted a click that garnered me zero points. After that, I just picked a door at random, the middle one, and clicked on it at full speed.
(1) They didn’t say what the optimal strategy is.
(2) Your complaints about optimal strategy are complete irrelevant, because they are the same whether the doors shrink or not.
(3) “They make an assertion that switching hurts you…” I don’t think they did, cite please?
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