1) I am using sage 3.2.3, which was current when I installed it in
January. It was convenient for me to compile it from scratch, but it
then takes a long time to install.
2) Here is my sage code. The program estimates the probability of
ever getting a 6-way tie if you repeatedly roll a die and count the
number of times that you get each result.
n = 100
s = 0.
for k in xrange(1,n+1):
t = float(factorial(6*k)/factorial(k)^6/6^(6*k))
s += t
print k,s,float(t),t*float(k)^(2.5)
c = sqrt(6.)*float(2*pi)^(-2.5)
print "Limit by Stirling's approx:",c
tu = 2*c/3.*float(n)^(-1.5)
print "Tail upper bound:",tu
s += tu
print "Total upper bound:",s
print "Estimate for chance ever:",s/(1.+s)
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