de Groot Exercise

As part of some recent analysis of my analysis, I decided to do the last two exercises at Chess Tempo using a de Groot exercise. Most of what I just learned comes from NM Dan Heisman's Novice Nook #29. In the late 1930s, Dr. Adriaan de Groot published research on the thinking processes used by players of all grades from world champions down to class players on a small series of positions. Mr. Heisman has an excellent discussion of both Dr. de Groot's conclusions and his own from administering the de Groot exercise to hundreds of his students. One set of Dr. de Groot's conclusions was quite interesting:

Strong players have four phases of thought process:
1.Orientation to Possibilities.
2.Phase of Exploration.
3.Phase of Investigation.
4.Striving for Proof.

Without reading more on de Groot, I'm a little fuzzy on the difference between steps 2 and 3, but 1 and 4 seem clear.

The proper de Groot exercise utilizes positions that are rich in possibilities, not tactical move and win positions like at Chess Tempo. Nevertheless, I am trying not to miss things that are there, so I'm curious what things are slipping through my dragnet. My de Groot exercises involve two successes, so in that sense, perhaps I will not learn much, but perhaps eventually I'll meet more failures and then be able to produce refinements.

Chess Tempo #41477

Material is even. My black queen is attacked by white's last move g4. Wild checks go nowhere. I have a threat of Bd4 pinning White's queen to his king. The Nc3 is a little insecure from a removal of the guard on d2 either from Rxd2 or from a queen trade offer and takeback. My Nb4 is loose.

Candidates:
-Qa5 to hold my knight in the middle of the melee?
-Bxg4 fxg4 Qxg4 doesn't look so good, but the threat of Bd4 increases the possibilities of crazy moves working. My evaluation says that I'm simply losing material.
-Nc2 threatens White's queen and if gxh5 Nxe3 forks rooks, but Bxe3 Bxc3 is just equal.

So back to main line Qa5 Qf4 Rd4 or better yet Qa5 Qf4 Qc5+ to hit c3 twice.
But what about simply Qa5 Kh1 then Nc2 Qg5 (Qf4 Bxc3 Ah, the Qa5 was also hitting c3.)

After Qa5 Kh1 Nc2 Qg5 what about Bxc3? Qxa5 Bxa5 Bxa5 Rxd1 Rxd1+=

What about Qxg5 Bxg5 Bxc3 but doesn't Rc1 get one minor back? Bd2! holds the extra minor. Then Bxe7 Bxc1 Bxd8 Be3 Bf6.

After Qa5 Kh1 Nc2 Qg5 Qxg5 Bxg5 Bxc3 Rxd8+ Rxd8 Rc1 Bd2 Bxe7 Bxc1 Bxd8 is still a minor up.

My line was correct. The problem had a rating of 2103 when I did it. I could have been #6)overconfident, not seeing my own hanging knight at b4. I also could have #3)overlooked the defensive resource Kh1. I almost #4)pruned too early after Bxc3 and before Bd2!

Chess Tempo #50698

Material is even. White has doubled b pawns, Black has two bishops.
White is fully developed, Black is behind on QB and QR development and has vulnerable dark squares around his king.
Crazy checks: Nf6+ seem to dead end, but there is a discovery from Re1 if I get the bishop out first.
Forcing moves: Bc5 hits queen, Rxh4 distracts queen. Preparing Nf6+

Line: Bc5 (One fantasy is Qd8? Rxh4 Qxh4 Nf6+ Qxf6 Rxe8+ Kg7 Bf8+ Kg8 Bh6#) gxh5 Bxe7 Rxe7. White comes out with the Q vs R+B advantage of +1 nominal material. Black's kingside pawns are messy.

Other line Rxh4 Qxh4 Bg5 {intending Nf6+ and Rxe8} Qxg5 Nxg5 Rxe1+ Kh2 seems worse -1 disadvantage of Q vs 2R.

Bc5 was right! Rxh4 suckered a lot of the commentators. This problem had a 2125 rating when I did it. I probably still #4)pruned too early because I didn't think about what to do about my pinned Ne4 to my loose Re1 at the end of the Bc5 variation. I have to go back to my mini-study to figure out why I missed some #7)bishop complexities, like the key move here. I almost missed #3)defensive resource and #1)queen complexities on the Qxg5 ending to the Rxh4 line.

I'll try to Google some more resources on de Groot to try to understand the difference between Phase 2 Exploring and Phase 3 Investigating.