How Can You Draw a Endgame When You are Down More Than 5 Pawns

It's a pretty well known fact that the following position is a dead draw:

However, can you even image that you can also draw the following positions?

You are definitely surprised, but you can! (NOTE: Engines give a huge advantage to all these endgames, but as you will see, engines are wrong!)

First of all, note that I can as well add a pawn on the 2nd rank to the above positions, so that White is down six pawns, but it doesn't change the result and I will just analyze the positions given above.

Analyzing these endgames is a nice demonstration of a key endgame concept: Flowchart. It's a concept I have just learned in IM Silman's great endgame book: Silman's Complete Endgame Course. This concept also inspired me to construct the above endgames.

Flowchart

So what exactly is a flowchart? It may seem to be a rather complicated concept but it's actually easy to understand. It simply means that to solve a seeming complicated endgame, you have to start from some basic building blocks. That is, you have to start from some much simpler endgames and gradually add more material to it to construct a much more complex one!

So let's start with this very simple building block:

Building Block One

You might have immediately recognize this endgame and the fact that it's a dead draw. Why? Because you simply have to shuffle your king on h2 and g2 and check Black's king once it touches that Black pawn.
Here is what you have to do:

Okay, that was easy. But what if you add another pawn to this position?

Building Block Two

This is also a basic draw. You don't have to change your strategy. Here is what you do:

How about a Black pawn on the h-file. It's easy to see it's also a dead draw:

Building Block Three

That's nice, isn't it?

However, you have to be careful. A pawn on any other file except a-file is a dead lost for White. Here is one such example where that extra pawn is on the f-file:

Building Block Four

Building Block Five

This building block is also the key to understanding why the position I showed in the beginning is a dead draw, it's easy to prove that it's a dead draw yourself!

Now that you have 5 basic building blocks at hands, we can return to our starting position and see why White can draw that despite being down 5 pawns.

First, you should note that adding another pawn on the same file doesn't change the result:

Wow! You suddenly realize that no matter how many pawns you add to that file, it's still a dead draw! This proves the claim that the following endgame is a dead draw:

Final Position

Pretty amazing, isn't it?

Thanks for your reading!
Hope you enjoy it!