# Rubik's Revolution: Code Cracker



## cmhardw (Dec 26, 2007)

Hi everyone,

I noticed something fishy going on with Code Cracker on Rubik's Revolution and wanted to post some findings I made.

I systematized the way I approach finding the codes to always checking the colors in the following order: yellow-green-orange-blue-red-white. In doing this I noticed some common patterns. There are 720 possible codes, and each one has an equal opportunity of appearing given a fair code-writer, which the revolution is not.

I played 50 games and wrote down the final code for each one, and I found that in 50 games I only saw 15 different codes. Below I list the code, and the number of times I saw it.

YOBGWR: 7
YROWBG: 5
YROGBW: 3
GBYORW: 5
GBWROY: 1
GWYROB: 2
OGRWBY: 2
OBRGWY: 3
BGRYSO: 5
BRYGWO: 2
RYGOWB: 3
ROWBYG: 3
RWYBGO: 3
WYBROG: 2
WOYRGB: 4

The probability of getting only 15 codes in 50 tries assuming a fair game is (15/720)^50 = (1/48)^50 = 8.7 x 10^(-85)

So clearly the game is a cheap shortcut of the fair game that could be made with the same rules. Also notice that codes starting with yellow are far more common than codes starting with orange. Another interesting thing I saw was that at one point I got the code YOBGWR 4 times in a row. Not counting that group of 4 I got the same code twice in a row 3 times. I just thought it was interesting that the Rubik's Revolution people didn't put a random number generator in place for this game. Is it that much harder to do than to just program in a small number of codes and set those codes on a random loop?

One last thing, I took an average of how many moves it took me to figure out the code when I stuck to my system and I got 21.76 moves on average sticking to my system, below the expected 23.5 average if you look at the fair game. Then just for fun I used my observed probabilities for each code and tried again. I did 25 attempts and averaged 9.4 moves to figure out the code. Not only that but since I always start by guessing the most probable code, one of my 25 tries was that code, so I guessed it in 6 moves ;-) Using these cases the worst case scenario requires 13 guesses to find the correct code. I just thought it was funny, that is well below the predicted average based on the fair game ;-) Now if only at the WC 2009 they have a code cracker competition for 1,000 Euro ;-)

Chris


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## badmephisto (Dec 26, 2007)

well technically random number generator in any computer is just a list of numbers as well, and the initial point you start at changes. However on a computer it is so huge that it takes a significant time to get a sequence that you know and can predict. I guess their list of numbers must be really tiny if you can run into patterns like that


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## Stefan (Dec 26, 2007)

cmhardw said:


> The probability of getting only 15 codes in 50 tries assuming a fair game is (15/720)^50


No it's not. That's the probability of getting a specific set of 15 codes. And there are 720C15 of those so you better multiply with that number in order to get what you're looking for.


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## cmhardw (Dec 26, 2007)

(720 C 15) * (1/48)^50 = 4 x 10^(-54) so I still claim the game is horribly unfair from the mathematical standpoint.

Chris


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## Stefan (Dec 26, 2007)

Of course, this also includes all the sets with less than 15 elements, but you got exactly 15, so that's a difference. But this won't change much. Anyway, it's rather obvious that this is very poor quality, even without the calculations.

Excellent finding. Btw, I also checked your 23.5 average and the 13-strategy, and agree.


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## slncuber21 (Dec 29, 2007)

Chris... you have WAY too much time on your hands bud, lol.

my least #of moves is like 12 or something, did it this morning.


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## Lt-UnReaL (Dec 29, 2007)

I got under 2 seconds twice about a month ago, and could get under 9 seconds usually(no real method)


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## Mike Hughey (Dec 29, 2007)

I seem to be confined to the same set of 15 codes. I have yet to get a sequence not on your list. And I was averaging about 10 moves per attempt (looking at your list).

Pretty funny.


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## cmhardw (Dec 29, 2007)

I'm interested in these sorts of mathematical games. When I play Code Cracker I don't really care much about the time, but the number of moves it takes to solve. I was curious if this was really the mathematical game that it could be, with 720 possible codes each with equal probability of occuring. I was a bit disappointed when I found out it's not, but at least the number of codes, and the rough probability of each, is manageable to be memorized by a human. I doubt the company that makes the Revolution will hold a Code Cracker competition in the same manner that they did the light speed competition at Worlds 2007. However, it would be funny if they did since a person could average probably close to 10 moves on average to guess the code when that average should be 23.5 moves if the game was as I mentioned above.

haha and yes slncuber21 I guess I do have too much time on my hands ;-)

Chris


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