The Three Doors of Serendip Applet 1
start new game clears your current winnings and all playing history, while play again starts a new trial within a game, without clearing any winnings.
Playing
1) First choose a door by clicking on the numbered button (#1, #2, or #3) on any of the three doors. Your selection will be highlighted with two arrows.
2) Serendip will then open a different door to show you that the money is not there. You are then given the choice to stay with your current door, or switch to the other remaining, unopened door. Click on either the stay or switch button.
3) Serendip then opens the door you've chosen and you either win or lose $5.
4) To continue playing, click play again.
- When you think you understand how the game works click on "I've got it!", but keep playing some more, Serendip will remember when you press the button.
- Your total money is displayed in the current winnings monitor and is also plotted on the winnings plot below.
- After you're finished playing, click summary.
Posted by Laura Cyckowski and Paul Grobstein on 24 July 2008. Applet created using NetLogo, the availability of which is gratefully acknowledged.
If you think about it, always
If you think about it, always picking "switch" makes a lot of sense. When you choose one of the 3 doors, you have a 33.33% chance that it holds the $5 and there's a 66.67% chance that one of the other 2 doors holds the $5. When the computer eliminated one of the 2 remaining doors, that made the likelihood that the last remaining door held the money 66% chance. Therefore, you have a 66% chance of getting the $5 if you always pick switch.
?
I just got to $40 and I still don't understand how this works...
when my partner and I met
we had an interesting discussion about how seriously we took the direction not to think about it, just play. Our different prior experiences/histories with games, and computer games in particular, led to different attitudes towards the need to follow the directions, different strategies. Also, it was fascinating to me how different our experiences of the game were. My partner eventually stopped because she felt bored after the fun of winning a lot of money wore off; I stopped because I felt defeated and perplexed/mystified . . . and didn't win more than $40 (and was happy to do that!)
Probability
Playing around with the game, looking for an edge, as I would if approaching the market, it became apparent that the "switch" button pays out significantly more often that the "stay" button. A statistical edge in a money game is a license to print money, after 273 rounds, I am up $205 dollars, including the intitial exploratory losses.
So, do the same boring thing, click door #3, click "switch", and collect your pay.
Perhaps there is a more ingenious way to beat the game, but if I get paid for my method, I'll stick with it.
Happy trading.
It's not that difficult. All
It's not that difficult. All you have to do is think that there's a little child behind the doors that places the $5. You can easily trick the child in most of times because the child doesn't have the AI to always trick you (it's just java code after all). Just always pick the last winning door and remember which doors where "X" in the 2-3 previous times. Normally, you'll find the 5$ in the most "X" marked door of the 2-3 previous games. Once in a while you may really not know which door is because the chances are 50% even with that method, so it's plain luck. My english isn't my native language, therefore it's not easy to make you understand how to understand what I've understood for understanding this game. :p
By the way my score was 23/27, which under circumstances it gets better.
Seeking scaffolding but not the answer
Ok, so this is my fourth try at the first door game, and I am feeling like a loser! I can't figure it out. And it makes me sad. Also, it makes me worry: that I'm stupid, entering a memory-loss cave (it's hard for my brain to hold onto any story of the play I've already engaged in), doomed! I also feel like I should keep trying, alone, to get to the bottom of this -- it is NOT FUN.
So I've decided to ask for help, which itself is a kind of experiment, because I don't know who I'm asking or if folks who answer (if any do) will be able to help me without doing it for me.
Is this why I've never liked board or card games?
scaffolding for three doors
Actually, there is a "less wrong" way that will work, not on any given trial but on the average. And yes, your frustration probably is related to your distaste for board or card games ... and your tendency to worry that you are "stupid." You have to stop worrying about being wrong, stop thinking about the game, and just play it over and over again. Your unconscious will learn how to do it, if you let it. Feel the force.
Technically, there is no
Technically, there is no "right way" to beat it; it's mathematically proven. I'd suggest always trying to switch guesses and experiment.
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