I am learning the hard way that complex changes ARE difficult. Why am I trying it anyway ?
1. I am a stubborn extremist. If you optimize, why not go all the way?
2. I never learned to touchtype properly, I hunt&pecked. So, I am new to touchtyping. A clean slate..... so why not learn the complex layout?

This being said - man, it is hard. I am learning 2 things at the same time: touchtype and a radically different layout.....So if you are wiser and less stubborn than me, you better learn Colemak !

OTOH, people are able to learn the Dvorak layout, my layout is not harder....

You should never count bidirectionally. Backwards typing is satanic. ;)

@ lalop, I understand your distance metric, but maybe an easy solution is good enough? (yes, I dropped even the Damerau-Levenshtein metric :-) Say, a text has 10,000 letters and you want a perfect 1x1 alternation  (LRLRLRLRLR). You could fit the digram LR maximum 5,000 times in that text (actually, 4,999 times. Let's just call that 5,000  OK?) And by the way, i only count from left to right :-)   

So, simply count the number of LR digrams in the text. Let's say, there are only 3,000 instances of LR in the text. In that case, the test for "is this a 1x1 layout?" is: 
- calculate predicted # of LR digrams: 5,000
- count actual # LR digrams: 3,000
- divide actual/predicted =  3,000/5,000 = 0.6 = 60%.  In other words: the layout has a 60% fit. That is, not a very good fit. In other words: it is not a good alternating 1x1 layout. 
(note: in reality, 100% scores are unlikely. Actually, I do not know what are acceptable percentages. in other words, I don't know what would be a good cutoff point)

Now for LLRR (2x2) layouts. The same thing. In a 10,000 letter text, you can expect maximum 2,500 instances of this 4-gram. The test is:
- calculate predicted # of LR digrams: 2,500
- count actual # LR digrams, let's say we find 1,000
- divide actual/predicted =  1,000/2,500 = 0.4 = 40%.  In other words: this layout has a 40% fit. Not a good alternating 2x2 layout. 

Something along this line, lalop? Is this going anywhere?

Update on alternations.  i had an interesting e-mail conversation with martin Krzywinski from Carpalx, who wrote this specific Dutch language layout for online magazine De Correspondent:

QFKLMWVUJY[]\
SDTNRIAEOG'
;ZBHXPC,./

I constrasted it with my own Juli16 layout:
. u o p y x c l b v
a i e n h m d r t s
: , ? k q f g w j z

Martin showed me good statistics that indicated that mine is indeed rather left hand sided, plus can have long slurs of letters, specifically on the left hand. The main reason is that ENA are the most used letters in Dutch, and EN is by far the most used digraph. In is also on that hand, IE is a much used digraph and AN as well. So, there are more strings of 3, or 4 letters on the left hand; than there are on the right hand. This leads to an unbalanced feel  (very good nevertheless in terms of distance)   

This got me thinking again, and I played with MTGAP's settings and got this:

. u o f y q p l m w
a i e s h c d n t r
: , ? k x b g v z j

This one is much better balanced (52/48, versus 57/43) and has shorter strings. Better alternation. But, at the cost of some 'breakage of nice rolls'  such as EN, DR and ST, which have disappeared here. According to Patorjk's stat "consequetive hand use" as good as Dvorak. I will try this one out and also that Carpalx one, as an aside, I see some less nice features in that one - carpalx assumes that all positions on a row are equally good. Which they are not. So some letters are in too good positions and some in too bad spot, like the W that he puts in the dreaded qwerty Y spot. I also don't like that R and I are not under the fingers on the home row - they deserve that!  

TL;DR

1. carpalx has nice, very nice, detailed stats on alternation. Look at his program
2. patorjk also has some stats (i dont know how he calucates it though)
3. with mtgap you can play with the settings and find very alternating layouts
4. alternation goes at at cost of other things.  aiesh has more alternation and better balance than aienh (a.k.a. Juli16), but at the cost of rolls.
5. you (lalop) were looking for corpus text,right? krzywinski has published freqs, digraphs and trigraphs on the Dutch language, based on a very large corpus, much larger than mine. see the carpalx site, under ' correspondent'

I actually find the ring to pinky roll easier to do than the pinky to ring roll on the right hand, with adapting to the ion trigram. I don't really like it when it roles the other way, like in going. I tend to pause a little after the I key trying not to accidentally hit the E key as well, But I don't really have that pause problem with other words that have the "ing" trigram in them without the letter before that trigram being a "O".

@davkol -  great idea. Some people on the Google ADNW-group mentioned though that a repeat key might be complicated to learn. Should try it out, actually. I had also been thinking about mapping the most used digrams to keys. That would solve a part of the problem (of too high same hand strings) as well.

Comning back to the original poster's question: what are the best layouts for hand alternation? Recently I have worked with ADNW and the ADNW optimising software, which is great. The support is in the ADNW Google Groups. One possible disadvantage for some: it is mostly in German, so you have to make translations if you cannot read that. 

The algorithm can be tweaked in many ways, both by modifying the source code (it is in C++) and at runtime, by giving flags or modifying settings (which are in .txt files). ADNW is aimed at maximizing alternation and minimizing rolls of neigbouring fingers. The highest "penalties" are for outward rolls and for ring/pinky. So (qwerty) sa l; are worst. (qwerty) sf lj are the best rolls. The program can analyse digrams and trigrams, in trigram setting "too much" alternation is penalised as well, so (qwerty) SLAIDLE would be considered as worse then (qwerty) SDKJDF.  (disclaimer: as far as I understand it !!)

And here it is for English. Calculated only the  English corpus (so optimized for the English language). Since ADNW is sort of " Dvorak on steroids" I called this one DvorMax.

For comparison, I calculated how other keyboard layouts score with this same English corpus. I have grouped them into
-  a "Dvorak-like" category (DvorMax, Dvorak, MTGAP, Aus der Neo Welt (=ADNW, actually the same as DvorMax, but developed for 50% English and 50% German)  and Klausler),
- a "Colemak-like" category (Colemak, Capewell, Workman),
-  the "Mixed approach group"  (MTGAP).   
- and then there is Qwerty of course, for giggles. 

As always, the scores depend heavily on the algorithm used, in this case the ADNW layout.  Also, put you favorite characters (/;"?!and so on) on the spots äßöü.  The black box below contains many layouts, just scroll down in it! 

Scores of layouts. Lower is better.  ranked from best to worst 


CONTENDERS IN THE DVORAK-LIKE GROUP

DvorMax          291.491 Gesamtaufwand  179.388 Lageaufwand        links rechts
                   0.882 Kollisionen      7.423 Shift-Kollisionen  ob  6.1 13.1
  kyu.ö zlmdpv    65.718 Handwechsel     28.070 Shift-Handwechsel  mi 39.5 31.4
  rieao hnstcw     1.016 Ein-/Auswärts    6.177 IndirKollision     un  3.3  6.5
  xßü,ä jqfgb      8.665 benachbart       9.226 Shift-benachbart  sum 49.0 51.0
                  8.8  8.7 14.2 17.3 --.- --.- 15.8 11.0 14.3  9.9 Sh  2.0  0.8

Aus der Neo-Welt 337.581 Gesamtaufwand  189.071 Lageaufwand        links rechts
                   2.052 Kollisionen     17.995 Shift-Kollisionen  ob  4.5 12.0
  kuü.ä vgcljf    70.173 Handwechsel     25.534 Shift-Handwechsel  mi 38.3 31.8
  hieao dtrnsx     2.043 Ein-/Auswärts    7.458 IndirKollision     un  6.1  7.3
  yö,qb pwmzß      7.827 benachbart      16.064 Shift-benachbart  sum 48.9 51.1
                  8.9  9.6 12.9 17.6 --.- --.- 18.9 11.4 10.8 10.0 Sh  1.7  1.0

Dvorak           348.893 Gesamtaufwand  186.358 Lageaufwand        links rechts
                   2.662 Kollisionen     13.058 Shift-Kollisionen  ob  6.0 16.8
  ß,.py fgcrlö    70.517 Handwechsel     33.563 Shift-Handwechsel  mi 36.1 30.5
  aoeiu dhtnsü     1.617 Ein-/Auswärts    6.624 IndirKollision     un  3.0  7.6
  äqjkx bmwvz     11.139 benachbart      20.861 Shift-benachbart  sum 45.1 54.9
                  9.7  8.3 13.0 14.1 --.- --.- 16.5 13.3 13.7 11.4 Sh  1.8  0.9

Klausler         366.072 Gesamtaufwand  184.919 Lageaufwand        links rechts
                   2.506 Kollisionen     14.113 Shift-Kollisionen  ob  8.1 13.2
  k,uyp wlmfcß    68.668 Handwechsel     34.314 Shift-Handwechsel  mi 37.3 32.6
  oaeid rnthsü     0.678 Ein-/Auswärts    8.528 IndirKollision     un  3.2  5.6
  q.öäz xvgbj     14.512 benachbart      14.371 Shift-benachbart  sum 48.6 51.4
                  9.6 10.2 14.2 14.5 --.- --.- 19.5 13.0  8.3 10.6 Sh  1.8  1.0


CONTENDERS IN THE COLEMAK-LIKE GROUP

Colemak          355.884 Gesamtaufwand  185.391 Lageaufwand        links rechts
                   1.348 Kollisionen     14.374 Shift-Kollisionen  ob  7.8  8.2
  qwfpg jluyäö    58.143 Handwechsel     39.607 Shift-Handwechsel  mi 32.7 37.3
  arstd hneioü     1.041 Ein-/Auswärts    8.772 IndirKollision     un  6.8  7.3
  zxcvb km,.ß     17.492 benachbart       9.009 Shift-benachbart  sum 47.2 52.8
                  9.1  7.8 11.6 18.7 --.- --.- 18.8 15.4  9.8  8.7 Sh  1.1  1.7

Capewell         384.614 Gesamtaufwand  184.724 Lageaufwand        links rechts
                   1.779 Kollisionen     16.490 Shift-Kollisionen  ob 10.4  8.7
  .ywdf jpluqß    49.080 Handwechsel     51.941 Shift-Handwechsel  mi 33.8 30.9
  aersg btnioü     0.914 Ein-/Auswärts    6.664 IndirKollision     un  5.8 10.4
  xzcvä kmh,ö     21.958 benachbart      13.577 Shift-benachbart  sum 50.1 49.9
                 10.8 13.4 10.7 15.2 --.- --.- 15.3 15.5 10.8  8.4 Sh  1.6  1.2

Workman          392.782 Gesamtaufwand  191.440 Lageaufwand        links rechts
                   3.005 Kollisionen      8.626 Shift-Kollisionen  ob 13.0  6.8
  qdrwb jfupßö    55.794 Handwechsel     51.567 Shift-Handwechsel  mi 29.6 34.1
  ashtg yneoiä     1.088 Ein-/Auswärts    8.415 IndirKollision     un  7.6  8.8
  zxmcv kl,.ü     18.394 benachbart      12.531 Shift-benachbart  sum 50.3 49.7
                  9.0 10.5 13.2 17.6 --.- --.- 15.3 15.4 10.2  8.9 Sh  0.9  1.8


CONTENDER IN THE MIXED APPROACH GROUP

MTGAP            345.128 Gesamtaufwand  180.198 Lageaufwand        links rechts
                   1.270 Kollisionen      9.038 Shift-Kollisionen  ob 13.4 13.1
  ypouj kdlcwü    66.034 Handwechsel     40.419 Shift-Handwechsel  mi 34.5 28.4
  inea, mhtsrq     1.643 Ein-/Auswärts    6.551 IndirKollision     un  3.1  7.6
  zöä.ß bfgvx     18.561 benachbart       2.359 Shift-benachbart  sum 50.9 49.1
                 10.5  8.8 18.7 12.9 --.- --.- 15.3 14.4 10.5  8.9 Sh  1.8  1.0



AND THEN WE HAVE.... QWERTY

Qwerty           640.636 Gesamtaufwand  346.732 Lageaufwand        links rechts
                   6.804 Kollisionen      6.299 Shift-Kollisionen  ob 28.0 20.2
  qwert yuiopü    52.755 Handwechsel     41.474 Shift-Handwechsel  mi 22.1  9.5
  asdfg hjkläö     1.080 Ein-/Auswärts   11.226 IndirKollision     un  6.8 13.3
  zxcvb nm,.ß     21.628 benachbart      12.586 Shift-benachbart  sum 56.9 43.1
                  9.1  8.4 18.5 20.9 --.- --.- 18.4  8.9 12.1  3.6 Sh  1.1  1.7

Of course (by definition) the layout that the algorithm has calculated scores best, according to that same algorithm ;-)   But still, let's look at some figures.

DVORAK-GROUP
DvorMax beats Dvorak on nearly everything: much lower same finger (=Kollisionen), more alternation, less neighbouring fingers, smaller distance, better hand balance (49/51 versus 45/55), less load on pinkies. Hence, the overall score is much better. Dvorak has more inwards movements though. Klausler is nothing special. If you are after a Dvorak like layout, chose Dvorak for ubiquity, calculated your own

Standard ADNW (Aus der Neo Welt, made for 50% English, 50% German) scores worse than Dvormak (made for 100% English) on a 100% English corpus. Duh. If you use various langauges, like the Dvorak approach and don't want to calculate your own, ADNW is a very good choice. Also, it is in standard Linux distributions. 

COLEMAK GROUP
Colemak scores about the same as Dvorak (a little bit worse, actually), but the score is made up differently. Same finger is much better in Colemak than in Dvorak. I was surprised to see that it has less inward movement than Dvorak has. Inward rolls are one of the goals of Colemak, isn't it? Next there are some factors that ADNW sees differently than Colemak does. These are Handwechsel (=alternation) and Benachbart (=neigbouring fingers = rolls). ADNW gives penalties for the low alternation and high rate of rolls that Colemak has.  Capewell and Workman are nothing to write home about.  If you want it Colemaky, use Colemak :-) 

MIXED APPROACH GROUP
The MTGAP layout aims for both rolls and alternation. And it shows in the figures! In a sense it's in between Dvorak and Colemak. A very nice layout, really.

QWERTY
Qwerty is, as expected, bad.

That's all for now folks!