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RE: X-treme P-ondering

by Dominus (Parson)
on Nov 13, 2000 at 21:32 UTC ( #41356=note: print w/replies, xml ) Need Help??

in reply to RE: X-treme P-ondering
in thread X-treme P-ondering

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.

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.

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; }
(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:

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
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.

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.

Replies are listed 'Best First'.
RE: RE: X-treme P-ondering
by Blue (Hermit) on Nov 13, 2000 at 21:42 UTC
    All very true, but perhaps not as significant as it seems. While any given day you may get up to 1 XP per vote while others you get 0, in order to get enough votes to go up a level, you need more then one days worth of voting. As such, over a large number of votes, it will most likely average about 1/4 XP per vote. Because of the randomness factor there will always be local variation and noise, but over a large number of votes, it will average out.

    BTW, nice program, and thanks for bringing Perl into our discussion.

    =Blue might be eaten by a grue...

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