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Houdini's analysis didn't really interest me, as it can't give me a plan to win. Long lines of computer analysis can't beat a simple human plan.
Maybe you could recognize there are some winning ideas here and try to exploit them instead of accepting a draw-your opponent may also make mistakes after all. But i doubt you could found out that 1.Kd1 is the only winning move(as Houdini said after 30s)
The last part of your statement is why I take a draw most likely.
You wouldnt know the last part of my statment if position appeared before you during the game. What you might know is that you cant loose here(unless you play very bad or you loose on time) and that you have reasonable winning chances. If you realise that you shoudnt take draw unless you have less than 1 min time left. But even to get this it takes some time, depending on your strength.
Computer cant give you a plan, but it can help you to construct your plan a lot. At least it shows you which plan is right and which is wrong.
After 3. Kf1 Kd7, both 4. Ke1 (zugzwang) and 4. Kg2! preserve the win.
After 4. Kg2:
I'm still very confident that white wins after 1. Kd1. If someone wants to propose a move that saves black after 1. Kd1, I'll try to refute it (without looking at Houdini) to see if my method holds up.
3. Kf1 Kd7 4. Ke1 returns us to our original position which we then repeat 4. ... Ke7 5. Kf1 Kd7 etc.. so, yes white has zug. advantage but still stuck on rank one with this line.
as for 3. Kf1 Kd7 4. Kg2 .. on closer look, white does have zug. advantage, and black can not seem to break it.
So both 3. Kd1 Kd7 4. Kd2 and 3. Kd1 Kd7 4. Kg2 both appear to win for white.
I'm kind of proud to have come up with Kd1-e1-f1 right away, obviously trying to break the opposition. But like Pfren said it's just schematic thinking, this time turns out to give a win.
Seems others came up with the same idea... I guess there's not much else to try in this situation :)
EIther way, I still take a draw. If you realized that I tend to get a bit confused when I start having to calculate a bunch of what ifs, maybe then you'd understand. If you considered that the line of best moves, that has many possible variations is 30 moves to win, you'll understand why I am not going to risk losing, unless you are better rated and/or in a tourney against me.
If you are lower rated, I won't waste my time. The problem I find with postions like this is,if you just start winging it, though things seem ok and you may have widdled down the final list of moves to 15, thinking your worst outcome is a draw, you very well might have missed something and it could be a sure loss, that you can't see.
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