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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.

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.







Mastermind's picture

Idk if its right or

Idk if its right or wrong...but a good way to get money is to always push switch no matter what. when you get the right answer choose that same door first next time. then push switch. if you get it right again..choose that door that had the money and push switch again...and continue. if you get it wrong choose the door that had the money in it last (or the only door not chosen) first again. and keep repeating. I got $110 in thirty presses

Serendip Visitor's picture


the strategy is goog because you theorically get to touch every door, and have 2/3 of chance of getting money if you switch. Because if you are wrong you are already wrong, but switching may make you right. you have 33%, then 50% and if you switch another 50%... So basically you use all you possibilities and get more chance.

maths.'s picture

yeah, so I was already

yeah, so I was already acquainted with the monty hall problem before coming here. the correct answer is to always switch.

the correct answer is not to complain that you are 'bad at maths' or this 'isnt your kind of thing'. there is a correct answer, and if you would prefer to give up when you are met with a challenge, then that attitude carries over into the rest of your life.

moral of the story- stop complaining and do some homework, you might be surprised by the results.

Too Hard!'s picture


I don't get it!

Tracey Datsi Pennell's picture

Don't know

I don't know the math but I really want to understand this. I'm an artist not a mathmetician.

Tracey Datsi Pennell's picture

Wanting to know

I want to know more!
This is all new to me but what is the technical theory behind this thing? I am so glad I stumbled on this website! ;)
I kept picking the same door in hopes of finding a pattern. When I thought I did and then tried to test it in some way I was then wrong.
what is going on? Really? This is sooo cool.

Tracey Datsi Pennell's picture

When I think I understand

When I think I understand a pattern and try to test it to see if it is right I always come out finding that what I thought was the answer is not necessarily so. I have gotten 150 in winnings and played 180 times and I still don't know the pattern.

Roderick Dhu's picture

I got better results when I

I got better results when I stopped trying to figure it out and responded as quickly (randomly) as possible

Julie Hastings's picture

I believe I "Got It"..

I believe I "Got It".. Serendip will state okay you picked door number 3 (for example) and than will open one of the other doors, such as 2 and asked you do you wish to stay? You are not asked to chose to Stay or Switch only one or the other each time you play. Therefore, if asked do you wish to Stay, than you stay. When asked do you wish to switch, you switch.

Jason Johnson's picture

I GOT IT! You loose a couple, You win lots!!!!

The first time around I noticed when I tried to predict what door the $5 was behind I was just loosing Money. So then I stopped trying
And noticed I was quickly winning all my money back. So my brain figured out a pattern that I was not
conscious of. Then I made a conscious effort to figure out what my subconscious new that my conscious
did not, And. . . . . . I figured out that The $5 will never appear in the same place it has just been.
But if the computer knows you know this, it will change the rule and keep giving you Frowns where
ever you pick. How does the computer know that you know the pattern? By how fast you are moving your mouse
to the right answers. So what you have to do is go quite slowly.

[How to get to $40 in 10 plays]
after your first loss or win the $5 will never be in the same place
twice. So remember where the $5 was on the last turn, and you choose that door to cancel it out and
then the computer will give you an X door. And the $5 will be behind the last door standing (remembering the
$5 will never be in the same place twice) so you switch doors on the last move and collect your money. (Remember move slowly)
Now this only works FIVE times, then the computer will attempt to trick you and make you think
you did not figure it out. So it will give you a blue frown if you keep trying to use that strategy after the FIFTH
win. So what you do is after the FIFTH win, you will get the Blue-Meany! Remember the blue face won't be behind the same door twice
only after a winning streak. So you will pick the same door the X was last (making the computer think you don't know the pattern)
then you pick the door the blue face was last, and collect your money.

NOW THIS IS THE COOL PART......... The computer can tell what you know by how fast you move the cursor to click the buttons.
So pace your self, (try counting to "five-one thousand" between each move and move the cursor slowly) and
this strategy will work like Gangbusters. That is how I got to $40 in 10 plays.

Serendip Visitor's picture

not giving it away..

The quizmaster would never open the door with the money behind it, now would he?
and he would never open the door you picked.. so each has a 1/3 chance when you start..
when one choice is eliminated you chance doesn't move to 50/50.

Serendip Visitor's picture

yeah, the door you picked

yeah, the door you picked still has a 33% chanve of winning, while the one remaining door has a 66% chance

Allen Ng's picture

After trying to find a pattern.

I chose to stick with 1 door through my trip from $-20 to $60 . I chose the middle door to separate the two outer doors. After reading everyones inquires, and my philosophy book, I believe that the doors represent the choices, Yes, Maybe, and No. When you choose maybe (green door) you eliminate the opposing choice of either Yes or No. But in making the final decision you must switch doors, because everyone wants a definite answer, Maybe just won't cut it.

Thomas Bayes's picture

it is *simple* probability thoery

Candi 10/04/2009 - 8:31pm is exactly right and I couldn't have explained it better myself.

Anonymous's picture

Okay, I'm so glad I'm not in

Okay, I'm so glad I'm not in Vegas. I'm getting really tired of constantly finding the little blue frowny faced dude. I know, stick with it. My cat, wanting milk, is attempting to train me... perhaps he will be better at this than I have been! Oh, Kurt!! Here, Kitty... ;D

Anonymous's picture

maybe, sure, I dunno

maybe the door that had the money in it on the previous turn would be less likely than the other two to get the money again. so i picked that one to go with the odds. one of the two doors opened and odds were better for the money to be behind the other door, so i switched. worked pretty well. wasn't this in the movie "21"? maybe i ought to take up blackjack now.

Jonathan's picture

well there is no "truth" in

well there is no "truth" in this game but life has truth...
but it was fun to "understand" that the point of this game is to prove that people make "understanding" of a way of beating it like "oh the money is never on the same spot in a row" or "oh its BS it just lets me win when it wants me to, just to keep me interested, i cant really win". I believe I understand. in conclusion this game told me that life is a bunch of BS. PEACE

Candi's picture

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.

Anonymous's picture

your math was a bit off but i

your math was a bit off but i get what your going at

Liz's picture


I just got to $40 and I still don't understand how this works...

alesnick's picture

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!)





Daytrader's picture


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.

dimitris's picture

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.

alesnick's picture

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? 

Paul Grobstein's picture

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.

Brie Stark's picture

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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