Newsgroups: rec.games.backgammon Path: netcom.com!pattib From: pattib@netcom.com (Patti Beadles) Subject: Analysis of over 5 million FIBS rolls Message-ID: Organization: NETCOM On-line Communication Services (408 261-4700 guest) Date: Tue, 27 Jun 1995 22:05:30 GMT Lines: 247 Sender: pattib@netcom4.netcom.com About six months ago, after yet another round of screaming about FIBS dice in rec.games.backgammon, I decided to collect the output of the "dicetest" command to see if I could find anything out of the ordinary. The most common complaint is that doubles occur more often than they should, so that is what I pursued. I've included my original article/hypothesis at the end of this article. In it I made some wild guesses, and predicted that I would find that doubles were rolled 16.83% of all rolls. I actually found that 16.71% of the rolls were doubles, which is more than the expected number (16.67%) but far less than my prediction. Doubles also occurred far more often than any other six-roll-set that I counted. Methodology: I grabbed random samples of the output of "dicetest" and stored them in a file, then post-processed that file. I ensured that no roll was counted twice by also saving the first line of the "stat" command. Since FIBS clears its dice counters on reboot, if I collected a sample with the same date as a previous one, the previous sample was overwritten. The total number of samples collected was 49, starting Monday Jan 16, and ending Monday, June 26. ====== Raw data ====== Total rolls: 5530616 Total/6: 921769 Doubles: 924319 [The following section counts the number of times each roll occurred. Since 2-1 is a different roll than 1-2, it is counted separately.] 1-x 2-x... x-1 x-2... ---------- 920854 922142 923248 921092 922372 920908 923016 921869 921677 920859 920870 922325 [The following section counts the number of times that each individual number showed up on the dice. i.e. a 1-2 roll would be counted as a 1 and a 2. 5-5 would be counted as two separate fives.] Number totals expect 33.333 ------ ------ 1 1843870 33.339 2 1844011 33.342 3 1844925 33.358 4 1841951 33.305 5 1843242 33.328 6 1843233 33.328 [The following section takes the totals for 1-x, 2-x, etc., x-1, x-2, etc., and the total number of doubles, sorts them, and reports the difference from the expected value, and the total percentage.] ====== Sorted data ====== Total Diff Percentage ----- ---- ---------- 920854 -915 16.650 920859 -910 16.650 920870 -899 16.650 920908 -861 16.651 921092 -677 16.654 921677 -92 16.665 921869 99 16.668 922142 372 16.673 922325 555 16.677 922372 602 16.678 923016 1246 16.689 923248 1478 16.693 924319 2549 16.713 <== doubles I won't draw any conclusions; you can form your own opinions. If there is sufficient demand, I will put this information, the raw data file, and the PERL script used to generate the report on my web page. -Patti -- Patti Beadles | http://www.gammon.com/ pattib@gammon.com | IMPORTANT! After June 30, pattib@netcom.com | pattib@ichips.intel.com will no longer or just yell, "Hey, Patti!" | be a valid address for me.