  Let gcd(a,b)=1. J. Olsson and D. Stanton proved that the maximum number of
boxes in a simultaneous (a,b)-core is (a^2-1)(b^2-1)/24, and that this maximum
was achieved by a unique core. P. Johnson combined Ehrhart theory with the
polynomial method to prove D. Armstrong's conjecture that the expected number
of boxes in a simultaneous (a,b)-core is (a-1)(b-1)(a+b+1)/24. We extend P.
Johnson's method to compute the variance to be ab(a-1)(b-1)(a+b)(a+b+1)/1440.
By extending the definitions of "simultaneous cores" and "number of boxes" to
affine Weyl groups, we give uniform generalizations of all three formulae above
to simply-laced affine types. We further explain the appearance of the number
24 using the "strange formula" of H. Freudenthal and H. de Vries.
