# Opposite cross symmetry



## Zarxrax (Feb 19, 2011)

Ever since I became opposite-color neutral, I've noticed some strange things about my crosses.
If I end up with 1 piece already solved on white, it seems quite common that I will also have 1 piece already solved on yellow.
2 solved on white? It seems like there's a pretty good chance that I also have 2 solved on yellow...
A bunch of pieces 1 move away from solved? Seems like it works the same on both sides.

Of course, sometimes I have drastically different crosses on both sides, but at other times, the crosses seem oddly familiar to each other.

Am I just singling out coincidences and trying to find meaning where none exists?
Or is there a real reason why my opposite colored crosses often work out to be very similar?


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## qqwref (Feb 19, 2011)

I don't think there's any mathematical reason that this should happen often. However, you actually ARE more likely to have an easy yellow cross when more white cross pieces are solved (and vice versa). The reason is simple: more white edges on the white layer means fewer yellow pieces on the white layer.


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## Chiv (Apr 12, 2011)

Sounds weird - as qqwref says, you are _very slightly _more likely to have more pieces solved on the yellow cross if more of the white edge pieces are in the right place, but you shouldn't really be able to notice the similarity. Probably just a coincidence to be honest.


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## Zbox95 (Apr 12, 2011)

I don't think there is any meaning with it, just coinscidence.


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## Athefre (Apr 12, 2011)

I've noticed this with Roux inspection. Very often I'll see two pieces together (whether correctly or not), then look on the opposite side and the "opposite" of those pieces are together.  And some of the "opposite" corners are on opposite sides and oriented the same way.


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## Lucas Garron (Apr 12, 2011)

Chiv said:


> Sounds weird - as qqwref says, you are _very slightly _more likely to have more pieces solved on the yellow cross if more of the white edge pieces are in the right place, but you shouldn't really be able to notice the similarity. Probably just a coincidence to be honest.


 


Zbox95 said:


> I don't think there is any meaning with it, just coinscidence.


 
False. You call 50% more "coincidence?


```
Average number of yellow stickers on the yellow cross:

Assuming 0 yellow edges guaranteed to be on white cross: 0.666
Assuming 1 yellow edge  guaranteed to be on white cross: 0.727
Assuming 2 yellow edges guaranteed to be on white cross: 0.800
Assuming 3 yellow edges guaranteed to be on white cross: 0.888
Assuming 4 yellow edges guaranteed to be on white cross: 1.000
```

The numbers are even more skewed if you want to know the probabilities given some exact number of yellow stickers on the yellow cross.



Athefre said:


> I've noticed this with Roux inspection. Very often I'll see two pieces together (whether correctly or not), then look on the opposite side and the "opposite" of those pieces are together. And some of the "opposite" corners are on opposite sides and oriented the same way.


Interesting. The orientation is still random, but the pieces are certainly a bit more likely to be together, and hence noticeable for whatever desired bias.


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## Athefre (Apr 12, 2011)

Most of the time I notice it because I didn't like what I saw for, example, the yellow block choices. So I look at the situation with the white side and it's almost exactly the same. Things like a corner and it's edge on opposite sides of the other edge for the 1x2x2 and the third edge bundled in with them. So I just have to quickly pick a side. It happens too often and with too many pieces at once to be meaningless coincidence.


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## Chiv (Apr 12, 2011)

Sounds like I was wrong here..sorry...


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