Do you think that triangulation is useful?

I like triangulation and find it fascinating as concept, but I have the impression that I will never use it in an actual game, especially if all I play is blitz and rapid. The only usefulness that I can see, is that it trains your calculation skills.

All the examples I have seen, seem like they require heavy calculation, in order to be solved properly (without intuition or guess work). First, you need to figure out that if it was your opponent’s turn you would had won. For doing that, you need to calculate about 3 variations (usually involving all you opponent’s King moves). Then, after you prove that, you need to prove that all replies from your opponent while you are performing the triangle would again result in him/her losing. You also need to prove that he/she can’t triangulate as well, in order to neutralize you moves. We are talking about another 4 variations at least.

I am not sure that a position like that can be spotted, proof read and simulated by an average player in anything less than a classical game, except if the position is very similar or the same, with a previously played and learned position (for ppl with good chess memories).

Has anyone used triangulation in his own games and if yes, what was the time control? Do you have any tips in recognizing and/or solving them? For example, it usually (or always?) applies to positions that the opponent can only move his King.

This example does not seem to me to be too demanding.

https://www.chess.com/forum/view/endgames/triangulation-troubles

I have never used the idea in one of my own games.

Have seen it and it is still of no use to me to be honest. Will probably solve it as an endgame tactic, but in a game, not even close. It's not part of my arsenal of tools that I can use during a game.

It feels like I stay floating on the surface with triangulation and I am not sure there is anything deeper, but you never know. Someone might have dived deeper and found something that will help me grok this concept.

For the moment, I also do not have the feeling that I am likely to use triangulation in a game. I do have the feeling that I understand that example and that, if I have enough time and I am not overcome with exhaustion, I think that I might be able to correctly play a similar position over the board. Silman discusses triangulation in the 1600-1799 section of his endgame book, and that gives me the impression that I may have been a bit premature in paying attention to the concept. In view of your rating, I would think that you could match my level of understanding without much trouble. Thinking such things through might continue to be difficult in a blitz or rapid game.

Take this drill for example (looks similar to yours, but needs more): 

You actually need to do a square (or double triangulation) and not just a triangle, if the opponent resists hard, by performing a triangle too in response to yours. Haven’t seen this mentioned anywhere (I mean the square or double triangulation and not the actual drill). I find it quit hard and came up with these terms by myself. Still far from perfectly clear to me.

I have no doubt that there are hard triangulation problems, but it seems to me that the existence of relatively easy triangulation problems suggests that it is plausible to introduce oneself to the concept when one's rating is around 1600-1799. By the way, I am not sure that I understand your thinking for the position that you give. Back in 1895, Lasker gave a lecture on the endgame to "an audience of London chess players" and he discussed a position equivalent to yours. Converting to your position, his comments went:

"... Black has two chances of winning, one based on his passed pawn, the other on the weakness of the a3-pawn. The white king occupies at present a position of advantage in regard to both. This is changed by the following manoeuvre:

Now the move is changed, and Black wins easily, or

And mates in a few more moves."

I think that I get it okay. If some of these moves seem hard to you, maybe ask about the first hard one. After 1...Ke4 2 Kf1 in your position, it seems to me to be equivalent to the position at

https://www.chess.com/forum/view/endgames/triangulation-troubles .

The Dvoretsky line seems to me to be essentially the same as the second Lasker line.

Triangulation is useful and we have to learn it.

Yea that is how I do it too, but with different order (it results in same shape). It isn't a square actually, neither a triangle, but I call it square, because the King uses all 4 squares of a square. In triangulation uses only 3 squares. It is still triangulation (is it? the very least you are threatening with it), but the shape required is different and requires more moves (5 insetad of 3, still an odd number which key). See the shape in the image. In 7th and 8th rank you can see a normal triangulation that uses only 3 squares.

As I see it, triangulation is just a name for part of the process: e4 -> f5 -> e5 -> e4. (e4 -> e5 -> f5 -> e4 would be just as good.) In the above position, 1...Ke4 is just a preliminary in order to compel White to move out of contact with the f3 pawn and enable Black to go a-wandering (triangulating). After the trangulation,

White is toast. It is the same position as it was after 1...Ke4 2 Kf1, except that it is now White's move. White has no helpful move. After 5 Kf2, there is 5...Kf4, and, after 5 Ke1, there is 5...Ke3.

I like how you see it. Will check what you say with other triangulation examples too.

edit: Yea, it confused me a bit, because at start if it was the opponent's move you win and thought, I should perform triangulation to reach the same position with my opponent playing. That is not possible, if the opponent replies correctly. But, in second move, again if it was the opponent's turn you win and this time triangulation is possible. That is why was thinking of double triangulation, but only one triangulation is actually performed. 

I don't know what it is and I don't care

Something like Ali's footwork. Very useful.

I've had games where I've used triangulation to gain The Opposition on my opponent and Queen a Pawn.

Triangulation does NOT work in all situations. It only works for sure when the three moves you make results in your King being back where he started but your opponent's King can not make three moves that puts him in the same or equally strong position.

I've had games where my opponent apparently didn't know the importance of the opposition and made a mistake and allowed me to achieve it by triangulating my King.

Here's a game where I had The Opposition on my 40th move and he had one Pawn move left, at which point I could have triangulated to regain The Opposition because he had limited places he could move his King.  Stockfish and Lucas Chess rated my move 40 as a "!" because that position, plus trangulation if needed, guaranteed I was going to Queen a Pawn.

Three words: Triangulation is useful.

There are many 1900s that get to their level without using triangulation.

Or even how to checkmate with two queens. It's quite embarrassing to lose to some of these fools.

It's so much a part of zugzwang and opposition I probably don't even notice I'm doing it to be honest

Triangulation is just a fancy word meaning your king can lose a tempo and theirs can't, so you can put them in zugzwang and (usually) infiltrate with your king.

Zugzwang, by the way, is found everywhere in endgames.

He's 1200 so...