Crosswalk Efficiency
Python - 489

Uses all pairs shortest paths.

import re
R=re.sub
exec R("I"," in ",R("F","for ","""s,m,i=sum,map,int
r=2**.5/2
n=1e309
g=[0,1,1,n,r],[1,0,n,1,r],[1,n,0,1,r],[n,1,1,0,r],[r]*4+[0]
f="01021323"
o=lambda v:[list(v[x:x+2])FxIrange(0,len(v),2)]
v=o(f+"04142434")
q=m(sorted,R("12|21","14 24",R("03|30","04 34",raw_input())).split())
r=range(5)
u=[m(i,x)FxIv if x notIq]
l=s(g[i(y)][i(x)]Fy,xIq)
Fy,xIu:g[y][x]=n
FaIr:
 FbIr:
    FcIr:g[b][c]=min(g[b][a]+g[a][c],g[b][c])
w=s(g[i(y)][i(x)]Fy,xIo(f+"0312"))/6.
print 1/(w*l)"""))