Game classified as counting and wythoffs nim

Wythoffs Nim

This is another variation of Nimbetween 2 players invented by W.A.  Wythoff in the early 20s.

There are 2 piles of chips and the 2 players play alternately picking up chips from  2 unequal piles.

The rules for a player are that at each turn he can pick up any number from 1 pile or an equal quantity from both piles

The player who picks last is the winner

.

Here the  two piles A and B have

12 and 23 chips at start.

1st player picks 4 from A and 10 from B

Leaving  8 and 19

2nd player picks 0 from A and 6 from B

Leaving 8 and 13 

In the paper and pencil version of the game graph paper is used for both piles A and B with round circles for the chips. When they are once played they are crossed off to get the new totals.