Grundy Numbers Concept in Game Theory (C++)

By UDDESHYA PANKAJ

Grundy Number is a number used in Game theory which defines the state of the game. Through this concept we can define a impartial game like the (Game of Nims) in terms of Grundy.

So, before coming to Grundy Numbers , we will know about MEX which means Minimum Excludent Set.

MEX is defined as the smallest non-negative value not present in set.

So, here we are creating a set and recursively inserting in it the value n/2 , n/3 , n/6 where n is the number for which we have to find the equivalent Grundy Number.

Grundy(0)=0;

 

for example:

MEX{1,2,3}=0

MEX{0,1}=2

 

So, basically what's the use of Grundy Numbers in Game theory when (Game of Nims) already exits for calculations , its beacuse it solves the impartials concepts of Game of Nims.

So, that's why  we use the concept of  Grundy Numbers and its quite easy to implement .

The Sprague-Grundy Theorem is an advanced concept ahead of Grundy Numbers.