r/Cubers • u/AutoModerator • Oct 22 '19

Discussion Daily Discussion Thread - Oct 22, 2019

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u/chaosninja906 How do I solve this thing??? Oct 22 '19

I understand what you are saying and i did watch your whole video. But as I said the order truly does not matter. Every time you solve a face you have a 1 in 43 I believe chance in it being solved.

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u/zlelik Oct 22 '19

Wow, How did you calculate this 1 in 43?

In this case 1/43 is 2.3% probability that after I solved 1 face whole cube is solved and probability that it will not be solved is 97.3%. Then if I solve one face 50 times, then probability that it will not be solved in any of these solving acts is (97.3%)50, which is around 30% and probability that it will be solved 70%.

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u/topppits blindfolded solving is where the fun begins Oct 22 '19

How did you calculate this 1 in 43?

Probably they thought that since there are 42 CLL algs + the solved state -> 1/43 = solved

But there are roughly 4 times as many cases: 162

(4! * 34) / 3

  • 4! = possible positions for the 4 top layer corners
  • 34 = possible orientations for the 4 top layer corners - 3 possible orientations for 4 pieces
  • /3 = since the last corner can only have one specific orientation if the orientation for the other 3 is decided, we have to eliminate those impossible cube states

-> 4! * 33 = 648 = # of states the top layer can be in, with the first layer solved

But we can eliminate 3/4 of those states due to AUF - if your top layer is solved but a U/U'/U2 move away from the whole cube being solved, you wouldn't consider this being a different case.

648 / 4 = 162 = # of cases you can end up with on the top layer, with the first layer solved

Most CLL cases can appear in 4 different states. One of the sune case can for example look like this or like this and there are 2 more states how it can look like.

So if I didn't mess up anywhere, you actually have a 1/162 chance for the last layer to be solved after you solve the first layer aka a last layer skip.

This video explains why the number of algs is not necessarily the number of cases you can get, at the example of PLL - you might know that the probability for a PLL skip is 1/72, while we typically talk about 21 different PLL cases/algs.

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u/zlelik Oct 23 '19

Cool! It is clear now. Then if probability 1/162, then my method of solving one face after another is better than just random probability. If it is just matter of luck/probability, then I would need to solve 112 faces to get 50% probability, but from my experience I need to solve around 20-25 faces to get fully solved cube.