I am currently studying the Tarrasch Defense `1.d4 d5 2.c4 e6 3.Nc3 c5`, and naturally I've stumbled upon many Kasparov games as he frequentloy and quite successfully employed this opening throughout his career. In particular, in the game [Yasser Seirawan vs Garry Kasparov (1983)](https://www.chessgames.com/perl/chessgame?gid=1070068), a remarkable endgame position transpires:

```
 [title "Seirawan-Kasparov 1983, position of interest after move 47.f5"]
 [fen "8/8/5p2/p1k2P1p/Pp2P2P/3K4/8/8 b - - 0 1"]
 [startflipped "0"]

 1...Kc6 2.Kc4 Kc7 3.Kd3 Kd7 4.Ke3 Kc6 5.Kd3 Kc5 6.Ke3 b3 7.Kd3 Kb4 8.e5 Ka3 0-1

```

Kasparov wins this game, but his technique goes very quickly beyond me and I'm struggling to understand the maneuvers that followed, particularly, black starts retreating towards the 7th rank and then returns to `c5`, and only then advances the `b` pawn after white has to make a move away from the its current `d3` square. My questions:

* Did white miss any drawing chances in this position?
* What was the plan underlying black's retreating king march?
* Given this starting position, is one already able to recognize a winning pattern for black?

*My attempt with this question is to learn more about how to reason about such endgame and to understand how Kasparov composed this (to me counterintuitive) plan.*