3 years ago
Colour neutrality - the ability to begin solving a puzzle on any colour.
I’ve always thought that being colour neutral (CN) gave me and others a very slight edge over those speedcubers who solve on just one or two cross colours. Simply put, if you are truly colour neutral, your potential cross solution is always equal to or better than someone who solves one cross. However, looking at all six crosses does come at a cost - as you have to spend time making a decision about your starting colour, where single colour solvers can spend this extra time planning the start of their solve. Additionally, picking a cross colour can sometimes be a bit more stressful than it should be, and it’s easy to spend way too much time deciding on your starting colour.
Lars Vandenbergh ran a frequently cited cross study over on his website. He found that on average, the move-optimal colour neutral cross solution is 4.81 moves, compared to 5.81 moves for a single cross colour. People sometimes quote this statistic and say that the benefit is marginal compared to the cost. Looking at these numbers alone, it may appear so.
However, I don’t think that’s the most important number to be looking at in this study. If we take a look at the probability of a cross solution being 4 moves or less, there is a big difference. For single colour cross solvers, the probability of a cross which is 4 moves or fewer is 5.99%, as compared to 29.17% for colour neutral solvers. That is, when you are colour neutral, you are almost five times more likely to get a really easy cross, when compared to a single colour solver, assuming you can correctly identify these optimal solutions. (Which shouldn’t be too hard if it’s less than or equal to 4 moves).
The main takeaway from this is not that you only get easier crosses on average, but that there is a significantly larger proportion of time when colour neutral solvers get a very easy cross. For advanced solvers, it becomes much easier to look ahead into the F2L stage with a shorter cross, and even 1-2 moves can make a big difference with regard to tracking pieces during inspection time. This greatly improves Cross-F2L transition because you get a <5 move cross in 1 in 3 solves, as compared to 1 in 17 solves. The advantage is more significant for top speedcubers, and probably not as pronounced for beginners. Max Park, Bill Wang, Seung-Hyuk Nahm, and myself are all examples of colour neutral solvers. Although in the long run the difference in optimal move count is only 1 turn, there is the potential for a set of scrambles to provide an even greater advantage than that because an official 3x3 round is only 5 solves, quite a small sample.
So then, how does someone become colour neutral? This is quite a difficult question for me to answer because I actually don’t have experience switching from a single cross colour to all six, I started out colour neutral. So without the experience of switching myself, I’ll just try to give intuitive advice that makes sense and advice that has worked for others.
The first tip is to try it out as soon as possible. If you’re a newer cuber and only solve on one cross, the habit won’t be too ingrained in your mind and it will be relatively easier to learn how to solve on all 6 colours. If you’ve been cubing for years then it may be really hard to change your cross-solving habit and any attempts to try colour neutrality may prove very difficult or completely useless.
This brings me to my second point, which is that you don’t NEED to switch. As much as I like talking about the benefits of neutrality, it’s not the thing that’s going to make you improve incredibly quickly or make any magical difference to your times. It just provides a marginal advantage over single cross solving. For many people, the months that may be required to completely switch could be far better spent practicing other parts of your solves. If you’ve put in serious effort to try and get used to more colours but it’s just not clicking, then my advice (as strange as it may sound) is to give up and move your focus elsewhere. After hearing experiences from many different people over the years, it seems to be an individual thing - some people are able to get used to solving with new colours, whereas others struggle a lot. There’s no reason you can’t break world records using just one cross colour.
My third piece of advice is that opposite colour cross solving is a really great compromise. It brings you approximately 50% of the benefits of full neutrality (well, it's hard to quantify) for only a fraction of the work. For example, if you solve on the white cross, it’s probably easier to get used to solving with the yellow cross as compared to the blue cross. This is because the colours of the F2L pieces are the same and the only major difference is the relative position of the center pieces around the F2L - which can certainly be confusing at first.
So, if you’ve decided to try switching to CN, then what sort of approach should you take? Personally, I think that if you’ve just started out cubing, then it’s fine to jump in and try solving on all 6 colours, because you haven’t formed too many habits yet and it should be relatively easy to get used to it. If that doesn’t work for you then perhaps try one of the more structured approaches that I’m going to outline below.
Because solving on different crosses can be very difficult, I think that it makes sense to get used to solving on each colour one at a time. For example, if you solve the white cross at the moment, spend time practicing just solving on yellow until you’re used to it and it becomes automatic. After that, try switching between white and yellow on alternate solves until that becomes subconscious. Following this, it’s time to add in the more difficult colours - try solving on blue cross and see how long it takes you to get used to the pair colours and the positions of the centers around the F2L. If you can get comfortable with solving F2L starting on blue, then try and do averages where you solve on white, yellow, and blue. You can repeat this process until you’re confident with solving on all 6 colours. It may take a while and be quite challenging, but I think this is one decent way of incorporating more cross colours into your solves.
An alternative is to do individual (separate) colour practice and then combine it all at once at a later stage. Seung-Hyuk Nahm (who switched to CN when he was sub-10 seconds) told me that he simply did 100 solves each day on every single cross colour (so 600 total) until he was comfortable with them, and then eventually began to do full colour neutral cubing sessions. 600 solves a day is probably not realistic for most people, this can certainly be scaled down. Essentially the point is that you practice only one colour at a time whilst you’re getting used to it, and only once you’re ready, do full CN solves. It might also be handy to practice opposite colours at the same time because the F2L colours are the same - eg: do practice sessions with both the orange and the red cross at the same time.
The hardest part about switching to colour neutrality after doing one cross for a long time is becoming familiar with seeing *patterns* as opposed to *colours*. For example, if you ask any full colour neutral solver what colour cross they did right at the end of a solve, in most cases they won’t be able to remember. This might seem strange, but it’s because after doing colour neutral solves for so long, it becomes so subconscious that they’re actually not even thinking about individual colours, only the patterns that come up during the solve. This is your end goal, but obviously when you start learning CN you’ll need to intentionally decide and think about which colour cross to do.
Personally, I have never actually deliberately memorised the order of centers around the cube for each cross colour, probably because that requires too much thinking and it can be easy to make a mistake or mis-remember the order of the colours. Instead what I do is figure it out during inspection. If I need to solve the green cross for example, I'll simply look for the green cross edges and then plan out how to insert them into the bottom layer by holding the green face on the bottom and take note of relative positions of the center pieces around the middle layer. This is a subconscious process by now, and it definitely takes practice to get used to it - easy for me to say when I’ve been doing it for 9 years.
Lastly, people often ask me about big cubes and whether I am colour neutral on those. On the 4x4 I only solve with the white and yellow cross, I haven’t yet spent effort to try and solve on the other colours - I’m not sure that the advantage is big enough to justify spending a lot of time to get confident with Green/Blue/Red/Orange crosses - perhaps I should have taken my own advice and started out colour neutral using the Yau method, it’s a bit late now! For other big cubes I am completely colour neutral and solve centers starting on any colour. I don’t see any reason why this isn’t achievable for everyone, because it’s not like F2L whereby you have to get familiar with a whole new set of colours - you’re literally only solving pieces which have a single colour on them. For 2x2 it’s essential and for megaminx I think it’s ridiculously hard, but there are a few brave souls that are actually colour neutral on megaminx - I’m pretty amazed by that.
TLDR; Colour neutrality is fun, challenging, but certainly not essential. As always, keen to hear your opinions - have you tried either successfully or unsuccessfully to switch to colour neutral solving? Do you disagree and perhaps think that the costs don’t outweigh the benefits for 3x3 solving? What are your thoughts on colour neutrality and its usefulness for big cubes and other puzzles? Other questions or thoughts about things not covered in this blog?
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