Heuristics and the 3x3 F2L learning process

[TheDreamMaster]

I am in the process of writing a guide to speed solving the 3x3 cube, which is something I am very often asked about. I am approaching this guide from the perspective of training and the psychological aspects required for best learning to speed solve, since it is these two areas which I feel have been under-explored by the available literature. With a proper training method and mental techniques, speed solving learning can become much more efficient.

Solving a cube quickly requires certain cognitive processes to be "automatized" by our brain through practice, mainly pattern recognition and algorithm execution.

Algorithm execution has been the main focus of those teaching how to speed-solve and those learning how to do it; even when it is commonly recognized that most speed gains come from quick pattern recognition such as "looking ahead", to create a non-paused execution.

Perhaps this is the case because it is both easier to teach and learn algorithms and finger tricks, than it is to give advice to aid the pattern recognition tasks.

I am not saying there is a void of information in this regard, there are several very useful guides with tips for different steps in the solve. But most of what we often hear as advice is "...practice looking ahead", which is useful but gives the learner little information about how to undertake the process.

Let me focus on solving the F2L intuitively, which is the most promising stage for an intermediate puzzler to gain time, and the most difficult to master.

After enough hours of practice have been logged, recognizing the patterns for the corner-edge pairings becomes automatic, but before that happens, we can aid the recognition by using heuristics.

If you boil down the F2L to its essence, you have 3 cases for solving the corner-edge pairs (assuming standard cube color distribution and a white cross):

1- Opposite colors on top
2- Same color on top
3- White on top

Recognizing these patterns is simple enough, and with their associated algorithms we are now equipped with 3 nice heuristics.

(One can argue that all patterns with their associated algorithms are heuristics, therefore, learning all the algorithms for the F2L provides a solution. But the algorithm list is long enough to reduce its practical value for an intermediate learner. For the purposes of this discussion, heuristics are more general "tricks" that will aid in pattern recognition.)

I remember when I was learning F2L and while it seemed straight forward to me, it was a slow process at first because I was visualizing the movement of the pieces. The problem is that visualization is slow. What I needed was fast recognition "tricks" while my brain was getting trained to recognize the patterns automatically. The 3 heuristics above are a good starting point, but once we try to look ahead we need more.

For example when we have a corner on the top layer with the white sticker on the side, and its edge pair is still on the second layer, we need a way to quickly figure out how to bring that edge to the top such that we end up with the proper positioning of case #1, which is the easiest to solve.

One possible heuristic method is:

1- Get the corner to the upper-front edge such that the white sticker is on the left or on the right.
2- Rotate the two bottom layers such that the desired edge is on the back layer and the sticker on its side is the same color as the sticker facing front on the associated corner.
3- Rotate the back layer to bring the edge to the top layer (... and rotate the top layer once more to move it out of the way and bring the back layer down again).
4- Rotate the top layer to bring the corner above its proper position (between its two proper colors)

At this point the corner-edge pair is positioned such that a simple 3-move will join and insert the pair (L'U'L or RUR'). With little practice, steps 1 and 4 can be merged.

This is not the heuristic I used when learning F2L, and now my brain seems to visualize the patterns automatically without having a heuristic or rule of thumb. But these kinds of tricks/patterns/rules helped me a lot during the learning process, and I am sure they will help others currently learning to speed solve the cube.

Now to open the discussion... what heuristics did you use when learning F2L or which do you still use?

 

[Mike Hughey]

A full set of heuristics like this could be VERY useful in teaching a child to solve with F2L corner-edge pairs. I've already started trying to develop some such heuristics in teaching my daughters, with some success. (Although I wasn't really realizing that was what I was doing - I was just trying to give them some easy ways to see how to insert certain pairs that they hit. But effectively, that's what I was doing.) The problem is that my set of heuristics is very incomplete, so they still can't do it in every case.

 

[Lucas Garron]

How about making a decision tree? That works well for 2-sided PLL recognition.

 

[miniGOINGS]

How about making a decision tree? That works well for 2-sided PLL recognition.

That's how I recognise my LSE orientation. Quite fun and easy!

 

[TheDreamMaster]

A decision tree is good for outlining the whole method, which is possibly what Mike is looking for.

Now I am talking about specific heuristics, which could possibly be the nodes of such a decision tree

When an intermediate puzzler solves the cube, most of his time is spent not in deciding but in recognizing. Once the pattern is recognized, decision is almost instantaneous. And what the heuristics attempt to do is aid with the recognition part.

In other words, the question we are asking is how do we recognize the pattern fast? (before the brain has been hardwired through practice)

 

[Dene]

Firstly, I will point out that I do not like the cross on white bias. But going with it just for the sake of consistency...

I guess the easiest way to do this is for anyone who can be bothered to just write one up. So I'll pitch in.
Here's another that anyone can feel free to enhance or change or whatever.

Case: opposite colours on the top layer:
1. Put the corner in the FRU position.
2. Put an empty slot in the in the position opposite the corner on the same face as the white sticker.
3. Using one face turn, put the corner in the bottom layer, while bringing the empty slot into the top layer.
4. Turn the top layer until the edge is in the position opposite to the opposite colours of the corner.
5. Return the corner to its original position.
6. Rotate the top layer to bring the corner above its proper position.