Disclaimer: This is nothing new. Just some numbers trying to convince you to do what the thread title says.
After doing your OLL parity alg which pops up half the time, assuming you're not stupid, your chances of getting an LL with all edges oriented is 5/16 on a 4x4x4, as opposed to 1/8 on a 3x3x3. In other words, you're 2.5 times as likely to get an LL with all edges oriented on a 4x4x4 than on a 3x3x3. Another way to put it (probably sounds more convincing to laymen) is COLL is 250% as useful on a 4x4x4 as it is on a 3x3x3.
After COLL, the probability of getting a PLL skip is 1/24, as opposed to 1/288 if you just did your usual alg. So you're 12 times as likely to get a PLL skip with COLL as you are without, that's 1200% (not 120%, it's 1200%).
After COLL, the probability of getting a 1-look PLL is 17/24 (I consider PLL skip a 0-look PLL although there's a 3/4 chance of a required AUF), as opposed to slightly more than 1/2 (I didn't bother counting) if you just did your usual alg. That's almost 1.5 times as likely (it's a little less than 1.5). Edit: I found a better way to put this. Without COLL, approximately half the time, you need to do 2-look PLL; with COLL, exactly 1/4 of the time, you need to do a 2-look PLL, AND the second PLL is always a U perm, read on to find out how to achieve this.
And finally, with COLL:
Oh, and COLL is really easy to learn - more than half of them are intuitive. "Intuitive" here does not mean the exact same thing as it does in "intuitive F2L". "Intuitive" here is like: I know that Niklas is a commutator, and all commutators are intuitive, but when I execute Niklas, I'm not really thinking commutators; heck I'm not even thinking, I'm just executing it like any other alg. But learning/memorizing the alg is easy because it's just a commutator.
Edit: I don't have proof or stats for this, but I guess it's pretty obvious that the (execution time on 4x4x4) : (execution time on 3x3x3) ratio for a <R,U> 2-gen alg is lower than that for a non <R,U> 2-gen alg.
Edit: This thread's probably not gonna get any replies, is it?
After doing your OLL parity alg which pops up half the time, assuming you're not stupid, your chances of getting an LL with all edges oriented is 5/16 on a 4x4x4, as opposed to 1/8 on a 3x3x3. In other words, you're 2.5 times as likely to get an LL with all edges oriented on a 4x4x4 than on a 3x3x3. Another way to put it (probably sounds more convincing to laymen) is COLL is 250% as useful on a 4x4x4 as it is on a 3x3x3.
After COLL, the probability of getting a PLL skip is 1/24, as opposed to 1/288 if you just did your usual alg. So you're 12 times as likely to get a PLL skip with COLL as you are without, that's 1200% (not 120%, it's 1200%).
After COLL, the probability of getting a 1-look PLL is 17/24 (I consider PLL skip a 0-look PLL although there's a 3/4 chance of a required AUF), as opposed to slightly more than 1/2 (I didn't bother counting) if you just did your usual alg. That's almost 1.5 times as likely (it's a little less than 1.5). Edit: I found a better way to put this. Without COLL, approximately half the time, you need to do 2-look PLL; with COLL, exactly 1/4 of the time, you need to do a 2-look PLL, AND the second PLL is always a U perm, read on to find out how to achieve this.
And finally, with COLL:
- 3/4 of the time you're gonna get a 0-look or 1-look PLL
- 1/6 of the time you can do PLL parity alg from any direction and get a U perm anyway (which means you save time and moves not doing unnecessary AUFs)
- 1/12 of the time you have to do "the other PLL parity alg" (the one that swaps 2 adjacent edges) to get a U perm, otherwise you get an annoying Z perm, and fortunately enough for you, there are only 2 such cases and they're easy to recognize - opposite colors are opposite each other (try your best to understand this, it's really easy to recognize but not easy to describe )
Oh, and COLL is really easy to learn - more than half of them are intuitive. "Intuitive" here does not mean the exact same thing as it does in "intuitive F2L". "Intuitive" here is like: I know that Niklas is a commutator, and all commutators are intuitive, but when I execute Niklas, I'm not really thinking commutators; heck I'm not even thinking, I'm just executing it like any other alg. But learning/memorizing the alg is easy because it's just a commutator.
Edit: I don't have proof or stats for this, but I guess it's pretty obvious that the (execution time on 4x4x4) : (execution time on 3x3x3) ratio for a <R,U> 2-gen alg is lower than that for a non <R,U> 2-gen alg.
Edit: This thread's probably not gonna get any replies, is it?
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As I've mentioned, it was 3 in the morning when I did this 
