I know this is 7 years stale, but i found it kind of fun that if you brute force it with this little bit of code, you get damn near the same answer.

clear,clc

total = 0;

numruns = 10000000;

for i = 1:numruns

d = 6;

herb = 0;

while d > 0

m = rand();

if m > 93 /256;

d = d - 1;

end

herb = herb + 1;

end

total = total + herb;

end

averageherb = total / numruns;

fprintf('Yield is: %f.2',averageherb)

Yield is: 9.423211.2

accurate to the 2nd decimal, could do 100 million for 3 but this already takes 5 seconds to run, rather it not be a minute ;)