Temptations

I haven't exactly kept a diary, but from my memory this is what happened when I started with M1-h:

• day 1: Improvement from 1 to 4 mates/minute (doing several hundreds exercises)
• day 2-10: Plateauing at 4 mates per minute (doing several hundreds exercises per day)
• day 11-14: Switch to FAC. Improvement from 12 to 15 mates per minute at FAC.
• day 15: Switch to M1-h again. Improvement  to 7 mates per minute.

If we look at day 1 as adaptation to the exercise and the board, we might decide to ignore the improvement made that day. In that case we might say that the improvement at M1-h is solely due to doing FAC. It is too premature to draw any definite conclusions already of course, but the facts are intriguing.

This is a comment made by Anon this day:

I started with M1-h first (because back then M1-e was not available). It was pretty difficult, and not much fun, either.
Then (when it became available) I did M1-e for a while. I could improve ~20% in speed here. Then I tried M1-h - and I scored much better here then, too. Without having trained M1-h. So there was an obvious transfer from M1-e to M1-h.
The speed improvement in M1-h was about twice as fast (~100%!), but this is mainly because the numbers are so low.
Initially I solved about 3-4 M1-h per minute, and when I came back after the M1-e training, then I managed about 5-9 M1-h per minute.

Aox is right - if we cant improve at M1... it might not be worth to do any tactics other at all. Though my impression is, that a 20% speed gain in M1-e can cause a much better result in M1-h. So the impression that a 20% gain is not so much is maybe underestimating the transfer to more difficult tasks.

The story of Anon has some striking similarities with my own story. Although he did M1-e while I did FAC. So what has happened? Have a look at the following position:

White to M1-h

This is typical M1-h position with a lot of temptations. These are the checks in this position:

• Ndc2+
• Nb3+
• Nb5+
• Nf3+
• Nc6+
• Nxe6+
• Ndf5+ 
• Ne2+
• Nd1+
• Nec2+
• Nc4+
• Nd5+
• Nef5+
• Nxg4+
• Ng2+
• Nf1+
• Rd5+
• Rxe6+

All checks but one are refuted by either:

• Black king walking away
• Check giving piece can be captured
• Check can be blocked by a black piece

So one would be inclined to say, that doing FAC should speed up M1-h. Yet it is not that straightforward. I improved FAC from 12 to 15 checks per minute. Meaning that a check cost me 1 second less. Here are 18 checks, so my advantage is 18 x 1 second = 18 seconds. But that would mean that the checks themselves cost me 18 x 4 seconds = 72 seconds. And that is way beyond the time I need to solve these kind of positions.

The conclusion of this all is:
Training the subtask FAC improves my speed of the main task M1-h, but not necessarily by seeing the checks faster. Apparently I don't check all checks when doing M1-h, since the time to check all checks is greater than the time to solve the M1-h as a whole by a few times. That leads to the question: what subtask do M1-h and FAC have in common, but is trained better by doing FAC?
If I add the story of Anon:
What subtask do M1-h, M1-e and FAC have in common, but is trained better by doing FAC or M1-e?