How to spot the win in this kind of pawn endgame position?

(Updated with correction!)

There's one (Correction: two!) correct move(s) here. How obvious do you think it should be?:



I suppose there are two thought-obstacles I failed to pass.

First, I would have needed to *rule out the wrong plan*, the one I took. After 47.Kxc4, the white king is 'inside the box' to prevent my f pawn's promotion. Clearly I should actually learn to recognize that sort of thing as a fact that will dictate the outcome of the position.

But how to clear the second hurdle: recognizing that the alternate move 43...f4+ is worth looking at (Correction: you don't need to, as Ke5 also wins; see below.)? I lose the f pawn, the white king is still inside the box of the c pawn, and bringing up the king to defend its promotion looks scary because white's a pawn can start running.

But in the end the c pawn will queen with check, just in time.

That's nontrivial for someone like myself to calculate with 1:21 on the clock. Is there something conveniently visible in the position that should have told me to put in the effort?

(Correction: 43...Ke5 also wins, and doesn't lose the f pawn, and just doesn't seem to have anything scary to it. But it was also hard for me to see for whatever reason. I thought I had checked the alternatives with the engine, but apparently I had not done so to a proper depth.

Update to correction: Turns out the engine gives inconsistent evaluations for the Ke5 option in 3-line multi-PV at depth 18! On some runs it says it's winning and on some runs it's not sure. Looks like it might depend on whether you've already evaluated some later position first, before evaluating the position at move 43 for black.)

@tpsinnem Well, I must admit that 43 ...f4 is not obvious for me, I would play 43 ...Kc5 if I had no time to think. But after looking at the position a couple of minutes without further reading, I strongly thought ...f4 is a move you're talking about.

So, you're right that first of all you need to determine that Kc5 is not winning. Just looking at the position, you can already suspect this, because 1) you need many tempi to capture the passer and return 2) a king can capture both passers if they are separated by two files and given enough tempi [note that the king cannot capture both passers if they are separated by any other number of files: they can defend each other remotely, threatening to pass when the king tries to capture another one]. Of course, some basic calculation of a line like was played in the game is needed though, as these are only euristics, and pawn endgames are very concrete.

Second, if the plan "capture enemy passer and promote own queen" fails, the plan "promote own queen with the help of the king as soon as possible" comes to mind. This leads to the move ...c3: you need to push a pawn, right? But after looking at c3 Kd3 f4 Kxc3 f3 Kd3 you can notice that the plan fails: the king is inside the square. But then this counterintuitive f4 move from the failed plan comes for me to the mind. The typical idea in chess: try to transpose the move order. Although it seems to drop the pawn, you already know that the white king aim at the position is to capture c3 pawn if it moves there, so f4 Kxf4 clearly deflects the white king and MAY help, but the calculation is needed to ensure this.

The final part: this calculation. Actually, there are two moves looking at in this position after ...f4 Kxf4: these are shouldering with Kd4 and pushing c3. [In fact both win if we look closely, but that's a priori unknown] c3 is my first option as I looked at this move earlier (the transposition with that move actually lead me to f4). Also it excludes the possibility of the "scary a-pawn" to promote first. The rest is the pure brute-force: both sides have only 2 sensible moves at each move: pushing the pawn and drawing the king, so generally it's not hard to calculate like 2-3 moves deep, after which the position becomes quite clear. The main line should be Ke3 Kf4 and then a5 cause white wants to force c3-c2 push to be able to get to d2, so Ke3 Kf4 a5 c2 Kd2 Kb3 Kc1 oops, this fails, so Ke3 Kf4 a5 Kb3 a6 c2 a7 c1=Q+ oh thank goodness this is a check! We likely win! In time trouble no more calculation needed, but of course we could have blundered something, so double-checking all this is useful if you have more time.

After that ideally you should also ensure ...f4 doesn't fail somehow else if white doesn't take the pawn, but if you have no time, you can risk and not calculate this unlikely event, of course.

King+Pawn endgames: deceptive simplicity

There‘s no estimation or „hope-chess“. It‘s often bad-ass brute-force calculation like here.

@Wolfram_EP

Turns out I spoke carelessly, in saying there's just one correct move! As it happens, 43...Ke5 also works.

And somehow in hindsight that seems more intuitive than f4, in that you're still safe with respect to the a-pawn, but you're also not immediately losing any material, and you're leaving white with the question of how to proceed. 44.a5 is still fairly natural for white, but so is the response 44...f4+, which, in this variation, is protected from immediate capture, and after the a-pawn is chased down, black has no risk, and white is left with the task of dealing with black's c and f pawns, which turns out to be impossible (and rather clearly so, for an advanced player, I presume).

But funnily enough Ke5 did not even occur to me until now after some moments of having taken a step back.

This one is not that hard , f4 kxf4 is easy to calculate (only two options are a-pawn running or K goes to take c pawn) and f4 king doesnt take, you can put king on a8 and and two pawns win on their own (placed on c4 and f4) as described in almost every book on basic endgame theory
Therefore f4 wins.
Hope it helps. Regards

@tpsinnem, Ke5 is one of the three moves that came to my mind at glance (Kc5, Ke5 and c3), as it seems to take the opposition and just somehow feels helping to promote the f-pawn ("promote own queen with the help of the king as soon as possible" as I wrote). However, it seemed that after Ke5 a5 f4+ Ke2 c3 a6 c2 Kd2 black doesn't achieve much. Now I see that Ke5 a5 f4+ Ke2 Kd5! lol (not c3 which draws), and the black pawns are so advanced that white king can't capture them anymore. Well, this manoevre is also not entirely trivial, but of course the position just looks so winning it is no wonder there are several ways.

Also, in the shouldering line 43... f4+ 44. Kxf4 Kd4 there is a beautiful idea that if the white king tries to escape the check from c1 with the move 45. Kf3 (which also helps to get closer to c-pawn), black can still lose a tempo with shouldering further 45... Kd3! and then [46. Kf2 c3 47. Ke1 c2 is a dead end] the pawn race results in black promoting first, finishing white by the skewer Qc1-h1+ and Qxa8. So @Sarg0n is right about the deceptive simplicity, and that's why many players avoid attempts of converting in the tricky pawn endgames and sometimes prefer to keep a pair of pieces so that the position is in a sense "more stable".

I just want to point out that 40... Kxc4 would've probably been an easier win. :P

@BongcloudMasterKe2 Yeah move 40 wasn't an obvious choice at all. Kxc4 would've certainly given me an easier *first promotion to queen*, but I figured the queen would have been likely to have to chase down a team of a king and a very advanced pawn or two. I've found such scenarios easy to blunder.

With bxc4 the two threats of separate passers looked like it might just turn out to be simple. Well, didn't quite happen to be that way, although from now on I suspect that if I run into a possibility similar to 43...Ke5, I might actually see it fairly easily.

40...Kxc4 wins easily. It takes 7 moves for Black to queen, while White needs 9 moves to queen. Plus, the queen can easily block the pawns if you calculate it.