[Sylver's coinage][1] is an example of an unbounded finite (if slightly modified) combinatorial impartial game. Quoth wikipedia:

> The two players take turns naming positive integers that are not the
> sum of nonnegative multiples of previously named integers. After 1 is
> named, all positive integers can be expressed in this way: 1 = 1, 2 =
> 1 + 1, 3 = 1 + 1 + 1, etc., ending the game. The player who named 1
> loses.\*

This can be made to have the normal play convention if we make $1$ an illegal move.

In Conway's ONAG, it is shown that Grundy's number can be generalized to ordinal numbers for unbounded impartial games.

**Is anything known about Grundy's ordinal for Sylver's Coinage and its various positions?**

<sub>*Wikipedia contributors. "Sylver coinage." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 21 Oct. 2014. Web. 27 Mar. 2015.</sub>
  [1]: http://en.wikipedia.org/wiki/Sylver_coinage