Subject: Re: Netgammon's Dice

From: Gary Wong 
Date: 1998/10/02
Newsgroup: rec.games.backgammon 


Casual_Observer  writes:
> If you really want a solid dose of dice
> frustration - go play on the MS Zone for a
> few days. I was fortunate enough this evening
> to be the recipient of 5 rolls in a row that
> were 51. And if you are a fan of multiple
> doublets in a row, this is the place. I have
> had as many as 4 or 5 in a row both in my
> favor and against me. I have even seen, much
> to my wondering eyes, 12 and 14 sets of doublets
> appear in a single game. I grant you, the server
> does have its good moments, but overall, I have
> had games come my way and taken away by
> inordinately ill distributed dice.

I was going to post the probabilities of each of those events happening,
but I guess a bunch of numbers is roughly as interesting to read as the
phone book.  Instead, here's what someone who played a few games every
night with fair dice might typically observe (for themselves or for their
opponent):

  2 identical rolls in a row: a couple of times a game
  3 identical rolls in a row: once a night
  4 identical rolls in a row: a couple of times a month
  5 identical rolls in a row: once a year
  6 identical rolls in a row: a few times in your life
  7 identical rolls in a row: most of us will never see it

(Rolling 51 then 15 counts as 2 identical rolls in a row.)

  2 doubles in a row: a couple of times a game
  3 doubles in a row: a couple of times a night
  4 doubles in a row: a couple of times a week
  5 doubles in a row: once or twice a month
  6 doubles in a row: a few times a year
  7 doubles in a row: once every couple of years
  8 doubles in a row: a few times in your life
  9 doubles in a row: once in your life
 10 doubles in a row: most of us will never see it

(Rolling 44 then 22 counts as 2 doubles as a row.)

The number of doubles rolled in a game depends so strongly on the
distribution of lengths of game that they can't really be estimated
by a simple model (it depends on the players, anyway -- two very pure
and positional players would expect to roll many more doubles per game
than two "run and play safe"rs).


FIBS generates roughly a million dice rolls a week.  This is probably
as many dice rolls as a casual player would make in ten years!  They're
being generated so fast that we would expect several FIBS players a
week to see 5 identical rolls in a row (just like the 5 51's you got
on the Game Zone).  Every couple of weeks, expect somebody to be given 6
identical rolls in a row.  4 doubles in a row happens several times an
hour, and 5 doubles in a row many times a day.

If EVERYBODY who rolled something 5 times in a row (like you did)
posted about it on r.g.b., then by the time you add all the FIBS and
Yahoo and Game Zone and Games Grid and Netgammon players out there
(not to mention those playing against their own computer, and those
playing real games with real dice), then we would be FLOODED with
several posts per day complaining about "inordinately ill distributed
dice"!  Yes, your experience was uncommon (most players would only see
that happen to them about once a year); but there are so many people
out there that I am sure it happens to several people every day.
Since your sample was self-selected, I don't regard it as any evidence
that the Game Zone dice are unfair.

Cheers,
Gary.
-- 
        Gary Wong, Department of Computer Science, University of Arizona
            gary@cs.arizona.edu     http://www.cs.arizona.edu/~gary/