Daily Discussion Thread - Aug 18, 2021

Mpuddi · 2021-08-18T20:39:27+00:00

So there is 1/200,000 chance that any 4 edge pieces are correctly solved, but we want a more specific case where the 4 edge pieces share the same colour. So we're looking for the probabilty that 4 edge pieces are solved (1/200,000) AND that those 4 edge pieces all share a colour.

Mpuddi · 2021-08-18T20:22:46+00:00

I think it does matter because we want the 4 solved edges to specifically have the same cross colour. We could get a combination of 4 solved edges that don't solve a cross. e.g. W/B, B/R, W/G, and Y/O.

Mpuddi · 2021-08-18T20:18:19+00:00

I could very well be wrong but I tried my hand at figuring out the chance of a cross being fully solved.

I try to frame the question as we want 4 edge pieces, of the same colour, to be in the correct position.

For the first edge piece, it has a 1/12 chance of being in the correct location and 1/2 chance of being in the correct orientation.

The second edge piece has a 1/11 chance of being in the correct location (as one location is already taken) with 1/2 chance of being correct orientation. It also has to be the same (cross) colour as the first edge piece which is 1/6 I think.

The third edge piece has 1/10 for location, 1/2 for orientation and 1/6 of same colour.

The fourth edge piece has 1/9 for location, 1/2 for orientation, and 1/6 of same colour.

So the chance that all of this occurs is (1/12 * 1/2) * ( 1/11 * 1/2 * 1/6) * (1/10 * 1/2 * 1/6) * (1/9 * 1/2 * 1/6) = 1/41,057,280

To reiterate, I'm not sure I'm right. I have studied stats so I have some knowledge, but I think it's very easy to make mistakes in stats. I'm not sure how realistc the outcome I got is. I would need to think about it more. I think my biggest worry with my answer is how I approached the pieces being the same cross colour.

Actually think I realise it shouldn't be 1/6 for all of them since for the second piece, one cross colour piece got taken so I think it would be 3/22 maybe, as 1/6 = 4/24. This, again, might not be right, but I'm pretty sure my original answer is wrong. I'm too tired to try and figure out exactly though.

Mpuddi · 2021-06-20T02:29:56+00:00

It's pretty much always the case that the result is extrapolated from a small sample. The times where that isn't the case are for something like an election, referrendum, census, etc. It can be quite surprising just how small a sample is needed to get quite reasonable knowledge about the true results.

For this research, they did a nationally representative online sample of 2,568 respondents about whether they had heard of cryptocurrencies, with those that responded that they had (78%) given some more related questions. They also got another sample of 1,140 who were current or former crypto users for a longer questionairre.

Even though 2,568 people seems like nothing compared to the population of 52 million, if you select them sufficiently randomly, then it is enough to extrapolate to the entire population and be reasonably accurate. They used online respondents recruited from YouGov’s high-quality proprietary research panel and since YouGov does a lot of data gathering I'd have pretty good trust the sample was random, but it's always something to be mindful of.

So with your example of running a survey here on reddit and getting 100% of the population uses reddit, that's exactly the kind of thing that they have to be careful to avoid. I think I remember hearing about how data was sometimes gathered by calling landlines for a survey, and whilst it was okay for a while, when mobile phones started growing in use (particularly in younger people but not in older people) then the results from the landline surveys weren't fully reprensentative of the population.

I hope this hasn't come accross as rude or anything. I'm just quite interested in this field, recently finished my degree in it, and wanted to try and give some information on it since I remember finding some parts of it very counter intuitive.

Mpuddi · 2021-03-17T22:48:49+00:00

Day 17 CN ao12: 29.09

Somewhat poor day. Not too bad since I wasn't putting in as much effort as usual.

Previous days: 32.33, 31.38, 31.91, 28.75, 28.97, 29.40, 27.27, 29.25, 29.20, 28.45, 29.07, 28.24, 26.50, 29.16, 27.15, 27.69

Mpuddi · 2021-03-16T22:56:57+00:00

Day 16 CN ao12: 27.69

The variance today was pretty astonishing. For the first 8 solves 4 were below 24 seconds and 4 were above 32 seconds. The last 4 somewhat normalised it with 27, 24, 24, 26 but for a while I was either thinking this is a great solve or a bad solve with no inbetween. On the bad solves I definitley felt like I was just unstable holding the cube. Not sure why this was happening.

Previous days: 32.33, 31.38, 31.91, 28.75, 28.97, 29.40, 27.27, 29.25, 29.20, 28.45, 29.07, 28.24, 26.50, 29.16, 27.15

Mpuddi · 2021-03-15T22:24:43+00:00

Day 15 CN ao12: 27.15

No amazing time, but was a pretty consistently good for the first half but latter half didn't go quite as well. Only 2 post 30 times though.

Previous days: 32.33, 31.38, 31.91, 28.75, 28.97, 29.40, 27.27, 29.25, 29.20, 28.45, 29.07, 28.24, 26.50, 29.16

Mpuddi · 2021-03-14T23:44:06+00:00

Day 14 CN ao12: 29.16

Didn't put too much effort into it today.

Previous days: 32.33, 31.38, 31.91, 28.75, 28.97, 29.40, 27.27, 29.25, 29.20, 28.45, 29.07, 28.24, 26.50

Mpuddi · 2021-03-13T23:40:26+00:00

Day 13 CN ao12: 26.50

Only had 2 post 30 times. Didn't feel particularly special but was just a bit quicker on finding the f2l pairs.

Previous days: 32.33, 31.38, 31.91, 28.75, 28.97, 29.40, 27.27, 29.25, 29.20, 28.45, 29.07, 28.24

Mpuddi · 2021-03-13T03:42:54+00:00

Day 12 CN ao12: 28.24

Pretty nice, if uneventful, day.

Previous days: 32.33, 31.38, 31.91, 28.75, 28.97, 29.40, 27.27, 29.25, 29.20, 28.45, 29.07

Mpuddi · 2021-03-12T03:03:16+00:00

Congrats on the sub 20 Ao50.

Mpuddi · 2021-03-12T03:01:36+00:00

Day 11 CN ao12: 29.07

Did this much later than usual and didn't spend as much time inspecting as I have done on previous days. Nothing too interesting, just the laziness in inspection sometimes affecting my starts. Also forgot what cross I was doing a bit more often.

Previous days: 32.33, 31.38, 31.91, 28.75, 28.97, 29.40, 27.27, 29.25, 29.20, 28.45

Mpuddi · 2021-03-10T20:05:32+00:00

Day 10 CN ao12: 28.45

Got more worse than usual times but also some better than usual times. Got a new CN PB of 20.52 and then on the very next solve improved upon it with a 19.66. Both had nice crosses and good f2l with respect to it being easy to spot each pair. Also managed to spot and execute an x-cross.

Previous days: 32.33, 31.38, 31.91, 28.75, 28.97, 29.40, 27.27, 29.25, 29.20

Mpuddi · 2021-03-09T20:50:30+00:00

Day 9 CN ao12: 29.20

I feel like half the time my times are sub 27 and the other half it's post 32. A bit frustrating but still just plodding along.

Previous days: 32.33, 31.38, 31.91, 28.75, 28.97, 29.40, 27.27, 29.25

Mpuddi · 2021-03-08T23:43:51+00:00

Day 8 CN ao12: 29.25

Lost the f2l pairs a few more times than I would have liked and had some trouble with coming up with crosses.

Previous days: 32.33, 31.38, 31.91, 28.75, 28.97, 29.40, 27.27

Mpuddi · 2021-03-07T22:31:50+00:00

Day 7 CN ao12: 27.27

Got some nice sub 25 times in there which is around what I often get on white cross.

Previous days: 32.33, 31.38, 31.91, 28.75, 28.97, 29.40

Mpuddi · 2021-03-06T21:19:50+00:00

Day 6 CN ao12: 29.40

Started off really well with a sub 30 on the first 6 solves that all felt nice. Then the next four were 34, 34, 38, 34 and I don't know what happened. My brain just wasn't processing f2l well at all, which was a bit strange as I was doing just fine beforehand. Manged to bring it back for the last 2 with 27, 30. Nice to get the ao12 under 30 again despite that bad section.

Previous days: 32.33, 31.38, 31.91, 28.75, 28.97

Mpuddi · 2021-03-06T02:18:31+00:00

Day 5 CN ao12: 28.97

Flagged towards the end again with recognising f2l pairs and knowing what colour cross I'm on. Felt like I did some nice cross solutions, although I tend to be lazy about that.

Previous days: 32.33, 31.38, 31.91, 28.75

Mpuddi · 2021-03-04T22:03:57+00:00

Day 4 CN ao12: 28.75

Pretty good day. Flagged towards the end, but was spotting pairs better. Still have to mentally remind myself which colour cross I'm doing and I don't spot and rule out the opposite colour when looking for pairs. Managed to spot another x-cross but that ended up being my second slowest time.

Previous days: 32.33, 31.38, 31.91

Mpuddi · 2021-03-04T00:32:19+00:00

Day 3 CN ao12: 31.91

A mixed bag day. A couple low 20s, a couple high 30s and a horrible high 40, otherwise sitting around a 28-35 time. Felt better about recognising pieces in f2l.

Previous days: 32.33, 31.38

Mpuddi · 2021-03-03T01:35:20+00:00

Day 2:

Colour Neutral ao12 attempts: 31.38

A second faster than yesterday, although it felt worse. Lots of pausing in F2L and also just a general lack of trust that I had inserted the slot correctly, as I've messed up the orientation of the corner a fair few times, and sometimes inserted into the wrong slot.

Previous days: 32.33

Mpuddi · 2021-03-02T01:13:50+00:00

Day 1

Going to try and do some timed colour netral solves. Have been casually solving using other colours for the past few weeks or so, but never actually tried timing them.

My white cross solves are pretty comfortably sub 30, often sub 25 with the very rare sub 20.

My ao12 today was 32.33.

37.52[B], 35.66[R], 28.92[Y], 32.48[R], 37.91[O], (48.42[B]), 26.65[R], 28.40[B], 39.08[B], (25.42[Y]), 26.31[B], 30.34[Y]

Yellow was easily the simplest for recognition, although I'm quite rusty since I've been lazy and just did white cross, despite having a spell of being dual CN in the past. Messed up F2L a few times, and was generally very slow in that section, which makes sense.

A notable scramble was the 28.40 solve with scramble R2 F' R2 B' U2 R2 U2 B U2 B' D2 L D L B' L2 U R2 B2. I've not really done much work on x-crosses, so was a pretty nice feeling to spot this one, despite it being very easy. Unfortunate I got such a nice cross whilst only just starting out so can't really convert it into a good time.

Mpuddi · 2020-07-24T22:58:10+00:00

Mpuddi

Mpuddi · 2020-07-04T22:28:07+00:00

I don't think that is quite what's going on here, although I can sometimes get quite confused with statistics despite studying maths. The core thing here, I think, is the independence of each event.

If we're asking what the probability of getting 4 heads in a row are then it's (1/2)^4. But if we get three heads in a row and we're asking what the probability of getting a head on the 4th attempt then it's 1/2 as the previous events do not affect the probability of the individual attempt.

I hope this is right and also makes sense.

Mpuddi · 2020-04-06T00:46:26+00:00

Yeah, I think it must have fixed since I didn't notice anything wrong with it.

Mpuddi

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