note
Dominus
Yes, and that 5XP a day from voting looks even smaller when you
consider that the same person is also getting a free 2XP
every day just for logging in.<p>
On a related metter, a couple of days ago I got to wondering
how big the voting bonus really was. An Acolyte gets
8 votes per day, so it's easy to see that the Acolyte can
expect to acquire an extra 2 XP from casting votes.
(Not counting an additional bonus of 2 XP for using them all up.)
But the 2XP is really a 25% chance of 1 XP for each vote, so
the Acolyte might be lucky and get more XP, or unlucky and get
none at all.
<code>
my $n = shift || 8;
my $p = shift || .25;
for ($i=0; $i<=$n; ++$i) {
my $prob = choose($n,$i) * ($p**$i) * ((1-$p)**($n-$i));
$x += $i * $prob;
$tp += $prob;
printf "%2d %.4f\t(%.4f)\n", $i, $prob, 1-$tp;
}
print "Expected: $x\n";
sub choose {
my ($n, $r) = @_;
return 0 if $n < 0 || $r < 0 || $r > $n;
return 1 if $r == 0 || $r == $n;
return choose($n-1,$r-1) * $n / $r;
}
</code>
(THe program will run
When you run this, you can give it an argument which is the
number of votes you get per day; it defaults to 8.
Then it prints out a table showing the probability of getting
each possible number of XP:<p>
<code>
0 0.1001 (0.8999)
1 0.2670 (0.6329)
2 0.3115 (0.3215)
3 0.2076 (0.1138)
4 0.0865 (0.0273)
5 0.0231 (0.0042)
6 0.0038 (0.0004)
7 0.0004 (0.0000)
8 0.0000 (0.0000)
Expected: 2
</code>
The '3' line here says that there is a 20.76% chance of
receiving exactly 3 XP, and a 11.38% chance of receiving
more than 3 XP. The '0' line says there's a 10.01% chance
of receving nothing at all. <p>
<p>The chances fall off pretty quickly as the number of points
increase, but still about one Acolyte in 11 can expect to
get 4 XP from casting votes instead of only 2 XP on a
given day.<p>
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