The ancient Welsh game of Nim

In the ancient Welsh game of Nim, the objective is to remove the last object, each play consisting of the removal from any pile of as many objects as desired, from one to the entire pile.

It was my go in the Welsh final - the piles had dwindled and I was left with 3 piles:

1 penny; five 5p pieces and ten 10p pieces. 

I had sixteen choices: remove the penny; remove 1, 2, ... up to all five 5p pieces; or remove 1, 2 up to all ten 10p pieces.

Only one choice guarantees victory, can you make the right call?

taking away 6 10p pieces would do the trick.  Figured it out with two bits of knowlodge, 1-2-3 is a win, and two even stacks are a lose for the person to play.

as a proof, try out 6-6. 6-5 5-5, 5-3 3-3, 1-3 1-1 and the second player wins

1-2-3 is also a loss for the player to move, no matter what the first player does, the second player will be able to make 1-1 or 2-2 in response every time.

Now look at this, 1-4-5 is a win because removing the penny allows 0-4-4.

removing ten pence leads to 1-3-5/1-3-2, 1-2-5/1-2-3, 1-1-5/1-1-0, 1-0-5/1-0-1.

Removing the 5 pence leads to 1-4-4/0-4-4, 1-4-3/1-2-3, 1-4-2/1-3-2, 1-4-1/1-0-1, 1-4-0/1-1

Thus, it's a win.

 Respect to your Afghani intellect, maybe one day there will be a Wales versus Afghanistan nim tournament.

Now the famous chess player Lasker developed a version of nim where not only can you take any number from any pile you can also split any pile into 2 (not necessarily equal) piles. 

With the same start 10,5,1 there are now 23 possible first moves but again only one guaranteed win.

Anyone nimtastic enough to figure it out?

split the penny in half!