
<UL>
<LI>
VN(A,x,y): inputs a matrix A , m by n say, where player Row has
m different strategies and player Column has n different strategies
and the payoffs are A[m][n] and -A[m][n], respectively. Outputs the expected
gain for Row (alias minus expected gain for Column) if they play a mixed strategy x and y
<P>
<LI>
VN2(A,x,y): the payoffs for 2 by 2 matrix and strategies [x,1-x], [y,1-y]
<P>
<LI>
RP(n): a  random point in [0,1]^n
<P>
<LI>
RD(n): a random distance between 2 points in the n-dim unit cube
<P>
<LI>
RD(n): a radom distance in n-dimensions
<P>
<LI>
RD(n): the average of the distances between two random points in [0,1]^n done N times
  MC:=proc(n,N) local i:
  add(RD(n),i=1..N)/N:
  end:
 
 #RC3(): the exact value of the 3-dim Robbins constant
 RC3:=proc() local x,y,z:

 int(int(int( sqrt(x^2+y^2+z^2)*(1-x)*(1-y)*(1-z)*8,x=0..1),y=0..1),z=0..1);
end:

  #RC3e(): The excact value of the Robbins constant (due to David Robbins)
 RC3e:=proc()
 1/105*(4+17*sqrt(2)-6*sqrt(3)+21*log(1+sqrt(2))+42*log(2+sqrt(3))-7*Pi)
 end:

 #RC2(): the exact value of the 2-dim Robbins constant
 RC2:=proc() local x,y:

int(int( sqrt(x^2+y^2)*(1-x)*(1-y)*4,x=0..1),y=0..1);
end:

 #RC44(): the exact value of the 4-dim Robbins constant
 RC4:=proc() local x,y,z,w:

 int(int(int(int( sqrt(x^2+y^2+z^2+w^2)*(1-x)*(1-y)*(1-z)*(1-w)*16,x=0..1),y=0..1),z=0..1),w=0..1);
end: