Backgammon on the Microsoft Network Gaming Zone

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“Friends, Romans, and backgammon players. Lend me your ears.  I come to bury the Zone, not to praise it.”This page includes some topics specific to backgammon on the Microsoft Network Gaming Zone. In contrast to the rest of this site, on this page I've included some of my own opinions. I'd love to hear yours too. You can post them on the message board, or you can email me.

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An analysis of the randomness of the dice on the Internet Gaming Zone.
 
A more detailed discussion - Can the dice be hacked?
 
A discussion of the rating system used on the Internet Gaming Zone.
 
You can also go to my separate page on cheating at backgammon on the Zone.

If you played on the Backgammon Zone, you know what it was.  If you didn’t, there’s no point talking about it. It’s gone.

Maybe I’ll find something clever to say about it in time.  For now, I’ll just say that an awful lot of people gave an awful lot of time to create a great community.

Nevertheless, I leave you with this vast information I have acquired throughout my years of playing on the Backgammon zone, some of you might find it useful when playing backgammon online for free or for money on other major sites.

The topics covered here include:

Randomness of the Dice on the MSN Gaming Zone 

I must admit that I was growing suspicious as to whether the dice on the MSN Gaming Zone were really random. It did seem to me that the doubles come in sequences and flurries. I decided it was worth analyzing.

Before you start reading this, let me say two things:

  1. If you have already made up your mind that the dice are somehow non-random and are not willing to listen to facts, then don’t read any further. No matter what, I’m not going to be able to convince you. But do remember - I started with the same skepticism about the dice. It’s not like I’ve been hired by the Zone to prove something for them. Either you’re going to read this with an open mind, or you’re not.
  2. Even seemingly odd events do happen sometimes. Four doubles in a row will come up one time in 1296. If every game of backgammon had 23 rolls, that would mean there were 20 sequences of 4 rolls. If you play 65 games of backgammon, you would expect this to happen one time. Human nature is that you’ll remember the one time it happens more than the 1295 times it doesn’t. The same is true for someone rolling, say, 4 doubles in their first six rolls. It’s very frustrating, but it happens.

Sometimes I hear really odd things. Like the person who said “My opponent rolled 17 doubles in a row.” The odds of rolling 17 doubles in a row are 1 in 17 trillion. Someone who could really believe that their opponent rolled 17 doubles in a row - well, let’s just say that they’re obviously more focused on the frustration of playing a game where when the dice don’t go your way, you’re going to lose. And backgammon is a very frustrating game!

What really happens is more like this, I think. I was watching a friend play a match last week, and I got there a few rolls after the game started. His opponent said "He started with three doubles." Well, I looked at the dice record. He had actually had three doubles in the first four rolls. Now, yes, of course he was lucky to get three out of four. But three out of four is still 3 1/2 times as likely as 3 in a row. Players just have this perception that certain things happen more often than they really do. Perceptions, though, can be deceiving, but the computer record of the dice doesn't lie.

Now for the results. I am a qualified statistician, but I am going to try to present my methods and findings in somewhat non-technical terms. Those of you who are more technically inclined, please don’t take me to task for this.

The Zone makes it easy to record dice rolls. You can look at the dice for any match, even if you’re not playing in it, and you can save it to disk. So far I have saved over 180 matches, containing over 700 games and 27,000 dice rolls. Some of these I played in, some I just watched to save the dice rolls.

If you toss a coin 100 times, you expect 50 heads and 50 tails, but you wouldn’t be surprised if you got 52, or 55, or even 60 heads. On average, you will get 60 heads or more about 2.5% of the time. If you had 10,000 people tossing a coin 100 times each and one of them got, say, 70 heads, you wouldn’t be surprised, or claim that the coin is biased. You have to take it all in context.

What I did was to look at two things:

  1. Sequences. I took every sequence of two rolls for the same player, and saw how many of them contained two doubles. This should be 1/36 of the time. I did the same for three and four in a row, which should come up 1/216 and 1/1296 of the time. If the actual occurrence of these sequences is more than that, and the difference is larger than could be explained by chance, then we’d say the dice are biased.

     

  2. Flurries. In a game with, say, 24 rolls, you’d expect 4 doubles. By a straightforward math formula, you can determine that the odds on a specific number of doubles, or less, out of 24 rolls are:
    0 1.3%
    1 7.3%
    2 21.2%
    3 41.6%
    4 62.9%
    5 80.0%
    6 90.9%
    7 96.5%
    8 98.8%
    9 99.7%

    So the odds of 5 or fewer doubles are 90.9%, which just happens to be 10/11, and the odds of 6 or more doubles are 9.1%, or 1/11.

    What I did was this. For each number of rolls in a game, I took the lowest number of doubles that would come up just one time in 10. For 24, that number is 6. Then, for every game in my database, I assigned points when the number of doubles was high enough. For example, if a game of 24 rolls had 5 or fewer doubles, I assigned 0 points. If it had 6 or more, I assigned 11 points. So if you had a large number of games with exactly 24 rolls, on average 1 in 11 would have 6 doubles or more, and that game would get 11 points, while the other 10 games would get zero. So the idea is that the total points for doubles should equal the total number of games. I know this is a little complicated, but the problem was that I don’t HAVE 1000 or more games with exactly 24 doubles. I ignored all games that had less than 10 rolls. I did this analysis separately for each player, not for the two players combined.
    Points Closed Tries Expected Misses Actual Misses
    1 654 18 19
    2 1043 116 120
    3 1272 318 303
    4 1445 642 631
    5 1152 800 797

    At least based on this analysis, players on the Zone actually fail to enter LESS often than chance would dictate. But the difference is pretty small - 1870 misses compared to an expected 1894. There is certainly nothing here that suggests that there's any problem with the dice.

Let me also add that in every case, I ignored the first roll of the game. Obviously, since this roll can never be doubles, it would have been inappropriate to include it.

I’m also going to present the T-statistic. Most readers will be familiar with the normal distribution, the so-called “bell curve.” The T-statistic is just the position on the bell curve. 95% of the bell curve falls within plus or minus 1.96 standard deviations of the mean. The accepted statistical test is that if a result falls within plus or minus 1.96 standard deviations of the mean, it is considered that the results are random.

Now I’m going to present the results. I may update these periodically, if I collect more data and analyze them.

Total number of rolls: 58,830
Total number of doubles: 9,749
Expected number of doubles: 9,805
T-statistic: -0.62

Total number of sequences of 2 rolls for the same player: 54,111
Total number of sequences containing 2 doubles: 1,382
Expected number of sequences containing two doubles: 1,503
T-statistic: -3.17

Total number of sequences of 3 rolls for the same player: 51,015
Total number of sequences containing 3 doubles: 208
Expected number of sequences containing 3 doubles: 236
T-statistic: -1.84

Total number of sequences of 4 rolls for the same player: 47,978
Total number of sequences containing 4 doubles: 29
Expected number of sequences containing 4 doubles: 37
T-statistic: -1.32

Total number of games analyzed: 2382
Expected score for games with concentration of doubles: 2,382
Actual score for games with concentrations of doubles: 2,372
T-Statistic: Very close to zero.

I have tested for a few other things. I will post the precise results when I have time to format them properly. But here is what I tested:

  1. The same number repeats many times in a row. I had about 20,000 rolls that were not doubles. I found that a number that comes up has a 1/20 chance of coming up on the next roll. I would have expected it to be 1/18. This is actually statistically significant, but it’s sufficiently odd that I wonder if I didn’t make a mistake in my programs. Once a number comes up twice in a row, it came up on the next roll 1/18 of the time, as expected. I had only 54 occurrences of a number coming up 3 times in a row, so the sample was too small to draw any conclusions about a number coming up 4 times in a row.
  2. The same single number doesn’t come up for a long time. People complain that when they’re on the bar, they need a particular number to enter, and that number doesn’t come up for 4, 5, 6, 7, or more rolls. I tested this for all sequences of 8 rolls, and found that in no case was the likelihood of having to wait a certain length of time for a certain number more than 2% different than the theorectical length of the wait.
  3. Entering from the bar. One of the most frustrating things in backgammon is getting stuck on the bar, and the worst is wasting a roll of 6-6, especially when your opponent has only a one-point board. In fact, there is even a backgammon book called "Double Sixes From The Bar." (I haven't read it and don't know what it's about.) I did an analysis of the likelihood of entering from the bar. I may revise these results later, because there might be a bug in my program, but I wanted to post them because it's such a controversial issue. What I will show is the number of rolls where one or more checkers was on the bar against a board with 1, 2, 3, 4, and 5 points made, the expected number of times you would fail to enter a checker, and the actual number of times the player failed to enter:

If you're still skeptical and would like to do your own test, you can download my dice data and work with them yourself. I have about 340 matches saved of various lengths. About 60% of these are matches I played in, the remainder are matches that I either watched or that were sent to me by people. I only solicited matches for this test from one person, who was instructed to be very careful not to screen matches and only send those which were somehow odd with respect to the dice. If you do anything interesting with these data, please send me the results!

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Can Zone Dice be Hacked?

Yes they can.

For many years I said they could not be, but now I know that they can.  I have seen it.

This does not mean that every time your opponent gets lucky, they are manipulating the dice.  There is one person who has developed a dice hack, and I generally trust that he has not distributed it.  His goal was to demonstrate to the Zone that it could be done.  As I write this (June, 2004) he is trying to get the Zone to let him fix the dice hack and other problems with backgammon.  I hope he succeeds.

So rather than pronouncing that the dice cannot be hacked, I will make a more modest statement.  If your opponent is very lucky, and you think it's because he is manipulating the dice, the odds are overwhelming that he is not.  You're just unlucky, and that's backgammon.  But I'm not going to say that it is impossible anymore.

If you're unlucky, don't accuse your opponent.  Just get over it.  If you can't handle it, play on another site or take up chess.

The Rating System on Microsoft Gaming Zone

Most of this section is not really relevant to the MSN Gaming Zone anymore.

Why?

Because the reality of the rating system on the Zone is that it is hopelessly broken.  The ratings are now the exclusive province of cheaters and ratings manipulators.  You can still go in there and play for fun.  You can even try to get a high rating.  But it doesn't mean you're a good player.  If you want to get a high rating, you can work at it, just like you can build a model airplane for fun.  Both show dedication and hard work, but neither has anything to do with backgammon skill.

I will leave this material here though, because it is good information about rating systems in general.  Also, there are two tournament groups on the Zone with honest rating systems that use these principles.  You can read about them elsewhere on this site.

Now, for the information on the rating system.

There is an excellent article on the rating system on the Zone. The article is actually written about another server, FIBS, but the formula is the same on the Zone.

I also have a program that will calculate rating changes. This was also written for FIBS, but works fine for the Zone. I think there may be some minor inaccuracies if your experience is less than 400. I didn't write this program, but it's freeware.

If you don't want to wade through that, though, here is an FAQ (Frequently Asked Questions) on the rating system:

Microsoft Gaming Zone Backgammon Ratings FAQ

  1. How do the ratings work, generally?

    You start with a rating of 1500. Every time you win a match your rating goes up, every time you lose a match it goes down. How much it goes up or down depends on the rating formula.

  2. How generally does the formula work?

    If you play someone rated higher than you, you stand to win more points if you win and lose fewer points it you lose, and vice versa. If you’re a new player, your rating will go up or down somewhat faster. Longer matches move your rating more, but it’s not linear – a 10-point match doesn’t move 10 times as much as a one-point match. And in a longer match, the formula recognizes that the skill of the better player will play a greater role.

  3. What factors specifically go into the rating formula?

    The following are the ONLY factors:

    The length the match was set for
    Your rating
    Your opponent’s rating
    Who wins
    Your experience, if experience is under 400

  4. What factors don’t matter?

      

    How much you win or lose by
    Scoring gammons or backgammons, except insofar as they determine who wins
    How many games were actually played
     

  5. Are you absolutely sure that it doesn’t matter if I win a 3-point match by 5-0 instead of 3-0? I don’t have to play for a gammon when I’ve already won the match?

    I’m absolutely positively 100% sure. I’m as sure as I am that Bill Gates is the ultimate nerd and that Bill Clinton cheats on Hillary. I’m as sure as I am that the IRS is not going to send you a letter that says “You were so good last year that you don’t have to pay any taxes this year.”

  6. Does it matter if I play higher or lower ranked players?

    Yes, of course, but you don’t have to play higher-ranked players to advance, and it also doesn’t help to beat up on lower-ranked players. In theory, the formula accounts for all this.

  7. Can you give an example?

    Sure.

    Let’s say you play a 3-point match. The “basic” value for a 3-point match is 6.9 rating points. That is the square root of 3, multiplied by 4. This means that if you win the match, your rating will be 6.9 points higher than if you lose.

    Let’s say you play someone rated 300 points lower than you. The rating formula assumes you have a 65% chance to win the match. So if you win the match, you’ll go up 35% of 6.9 points, or 2.5 points (everything is rounded). If you lose, you’ll go down 65% of 6.9 points, or 4.5 points. In the long run, if you actually win 65% and lose 35%, you’ll break even.

    Now, suppose you play someone rated 200 points higher than you. Your chances of winning the match are about 40%. If you win, you’ll win 60% of 6.9, or 4.1 points; if you lose you’ll lose 2.8 points. Again, you break even.

    Let’s change it so that you’re playing a 9-point match rather than 3. The basic rating value is 12 points (square root of 9 multiplied by 4). If you play someone rated 300 points higher, your chance of winning is only 26%, because of the greater impact of skill vs. luck in a longer match. So you will either win 8.9 points or lose 3.1. If you play someone 200 points below you, your match-winning chances are 33%, so you’ll win 4.0 points or lose 8.0.

    (All the actual point changes are rounded to the nearest whole number.)

  8. How can you possibly know the chances of winning a match?

    Well, it’s just an assumption the formula makes. It seems to work reasonably well in practice. Basically, if you consistently play weaker players, you will have to win more than 50% of your matches to rise in rating; if you play stronger players you can stay steady or rise with less than 50% wins.

  9. What is this “Experience” thing? Is experience good

    Experience is the total length of all completed matches. If you have played 7 3-point matches and 5 5-point matches, your experience is 46.

    Experience has only one thing to do with the rating formula. When you first start playing, your rating will move 5 times as fast as it will later. Every experience point moves that down by .01, so that if your experience is 50, your rating change (up or down) will be multiplied by 4.5. When experience reaches 400, the multiplier goes to 1 and stays there.

    So if you’re a good player and think your rating will increase, experience is actually bad, because you’d rather get the higher multiplier. But there’s nothing you can do about it. You have to play, right?

    Having 5000 experience points by itself just means you’ve played a lot. It doesn’t have anything to do with your rating. There’s nothing inherently admirable about high experience.

  10. What about these matches where people say “One game, automatically double to 64?”

    Those are very good for the lower-rated player and very had for the higher-rated player.

    The basic rating value for matches like that is 32 points (square root of 64, times 4). Suppose you play one against a player 200 points below you. Well, you have one game to beat them. Your chances of winning that one game are maybe 55%. But the rating formula assumes that your skill advantage is working over a very long match, and that you are actually about an 86% favorite to win. So you will win only 4 points when you win, and lose 28 points when you lose. Not really a good bet, I’d say.

  11. So what’s the best way to increase my rating?

    Play matches and win.

    The only real advice I’d give is, when you’re first starting to play, don’t play very weak players. You want to take advantage of the “introductory” multiplier, and when you’re playing weak players, you won’t get as many points when you win, even though you’ll win a lot of the time.

If you have opinions on the rating system you'd like to share, feel free to post them on the message board.

 

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