On Thu, 2008-06-12 at 09:28 -0600, Jason Hall wrote: > On Thu, Jun 12, 2008 at 9:24 AM, Andrew Jorgensen > <[EMAIL PROTECTED]> wrote: > > What's the process on the binary grab bag? It's been a while. > > Everybody counts off 1-$MAX > Flip a coin, Heads sets the bit, tails is a blank bit. > Flip until you have the bits necessary to represent $MAX > Congrats, you have a number for the winner of the first item.
Something about that method just didn't sit right with me. Seemed like
some numbers would come out more often than others. So I sat down and
coded up a simulator to see if I was right. According to my results,
this particular distribution method unfairly favors some numbers
whenever the sample size ($MAX) is not an even multiple of 2 (2, 4, 8,
etc.).
I've attached my simulator. Here are a couple of simple examples which I
think will illustrate the point:
[EMAIL PROTECTED] binary-grab-bag]$ ./simulate.pl 7 1000 |sort
-n
0 = 115
1 = 122
2 = 135
3 = 244
4 = 123
5 = 114
6 = 147
[EMAIL PROTECTED] binary-grab-bag]$ ./simulate.pl 8 1000 |sort
-n
0 = 132
1 = 152
2 = 131
3 = 138
4 = 114
5 = 114
6 = 115
7 = 104
When there are only 7 people, being person #3 seems to pay off. But when
there are 8, the prize is pretty evenly distributed, give or take a few.
Different numbers of contestants have their own consistent patterns
which could, with a little pre-calculation and some head counting, be
used by a Fugal to cheat the system. The simplest method would be to
stay close to the center.
So, while the binary grab bag system is high on geek points, I recommend
we find a new strategy.
Corey
simulate.pl
Description: Perl program
signature.asc
Description: This is a digitally signed message part
/* PLUG: http://plug.org, #utah on irc.freenode.net Unsubscribe: http://plug.org/mailman/options/plug Don't fear the penguin. */
