How thin can I use sand and cement?

[theflyingpig]

I've just had a composite door and frame fitted and need to create a small slope to keep rain from bottom of door. The stone underneath has worn such that water collects in the middle. I'm thinking a strong mix of sand and cement should do the job, but wondered if anyone a better idea?
Thanks in advance

 

[cdbe]

Cement likely to crack and look rough. Personally I would re-lay the blocks, I think you can still buy that style.

 

[Mottie]

As above or perhaps even treat yourself to a new step to compliment the door?

 

[DiyNutJob]

Clean up then hybrid polymer seal the bottom.

 

[theflyingpig]

Clean up then hybrid polymer seal the bottom.

What is that?

 

[DiyNutJob]

It's like silicone but better. They come in different colours. May be grey will work for you.

 

[williamglossop]

CT1

 

[JohnD]

Cement likely to crack and look rough. Personally I would re-lay the blocks, I think you can still buy that style.

They look to me like stable blocks. Not commonly sold in the last hundred years.

But practically indestructible so you can find old ones.

 

[cdbe]

Obviously reproduction but still available: