Random Dice
GoldToken has been in operation for more than 11 years now and we would be lying to you all if we were saying that we never had a complaint about the dice on GoldToken.
We can regroup those comments in 5 categories.
What is random anyway? Let start with a simple example; you are playing head or tail with a coin. You toss the coin 6 times and get 6 heads in a row. So this coin is not random, right? Wrong, statistically the odd of getting a head on a toss is 50% thus we could expect to get 3 heads and 3 tails. However every time you toss the coin you start the game over. Even if you toss 6 heads in a row, the chance of getting a tail on the next toss is 50%. The coin does not remember what where the previous toss and cannot adapt itself. If it was able to do so, then it would not be random.
The same applies to a roll of dice. There are 36 possible rolls and every time you roll the dice you have 1 chance on 36 to roll the same dice as the previous roll.
On 36 possible rolls there are 6 doubles, making the odds of getting a double 1 on 6. Since doubles enable you to play the roll twice, they are very noticeable. Even more if the double is hurting you. We often will get email saying there were 25 doubles in a match. If you look at the match and count 155 rolls in all, you can see that the statistic was respected. There is no law in backgammon saying that the number of doubles should be the same for both payers. Further more, some matches may have more or less doubles than the statistics would expect. If the statistics were always as expected, only then you could say that the dice were not random.
Assuming this means that our dice games, for whatever reason, would be favoring a player against its opponent. There are a few questions to ask ourselves about this assumption:
Ever wonder why your opponent seems to get better dice? Maybe, just because, he plays better than you. The art of backgammon is playing our pips in such a way that you will have the best dice possible on the next roll and/or give less chance to your opponent of getting a good roll.
This is another misconception that comes form the fact that the dice are generated by a machine. In fact some players tend to believe that if they would roll the dice themselves they would get better dice. If they where able to do so, they would most likely be cheating.
Also, we are quite sure that most of the players play more backgammon online than they play in real life. How can they come to the conclusion that real life dice are better? If they would play as much in real life, they would also see strange odds.
Backgammon is an easy game to learn and very difficult to master. If backgammon were only a dumb luck game, not many books would have been written on it. After all, how many books where written on Snakes and Ladders?
As one player said "I have been playing backgammon for about 25 years now and have an ELO of about 1625. The reason is that I never really studied the game strategy and never really tried to improve my game. I play for fun and this is my choice. You will never hear me say that I have a 25 years experience in backgammon, I consider myself having 25 X 1 year experience."
In conclusion:
http://www.gnubg.org/index.php?itemid=21
When looking at an analysis please check out all the moves one by one and try to understand your good moves and your errors. This is the only way to learn. Too many players will go directly to the game and/or match summary and make their opinion from that information alone. That would be like saying that by reading the index of a book, you read the whole book.
Added 2.15.10
Let's do the math as an example where we're rolling five dice. Intuitively, you may expect that the five rolls should come up different a lot of the time (at least this is what people often mention when discussing how random the dice are or aren't). So what's the chance of all the five rolls being different? The first die is trivial. Any of the six possible values is fine (none will result in duplicates), giving a probability of 6⁄6 = 1. After you've rolled the first die, the chance of the second coming up different from the first is 5⁄6, because there is now one less value you haven't seen before. The third is 4⁄6, and so on. Hence the total probability of all your five rolls turning out different is:
Hence, if you roll five dice repeatedly, you should expect over 90% of the rolls to contain duplicates (Now I don't mean the exact same duplicates, but it very well could be to be truly random). If you roll six dice, you can multiply the value above by a further 1⁄6 and you'll get approximately 1.54%. Hence, if you roll six dice repeatedly, you can expect to get six different values only about once in every 65 rolls. The following table shows the probabilities:
For a great little introduction to calculating probabilities, check out this page titled Introduction to Probability and Statistics at http://www.fourmilab.ch/rpkp/experiments/statistics.html
We can regroup those comments in 5 categories.
- Dice are not random
What is random anyway? Let start with a simple example; you are playing head or tail with a coin. You toss the coin 6 times and get 6 heads in a row. So this coin is not random, right? Wrong, statistically the odd of getting a head on a toss is 50% thus we could expect to get 3 heads and 3 tails. However every time you toss the coin you start the game over. Even if you toss 6 heads in a row, the chance of getting a tail on the next toss is 50%. The coin does not remember what where the previous toss and cannot adapt itself. If it was able to do so, then it would not be random.
The same applies to a roll of dice. There are 36 possible rolls and every time you roll the dice you have 1 chance on 36 to roll the same dice as the previous roll.
- There are way too many doubles.
On 36 possible rolls there are 6 doubles, making the odds of getting a double 1 on 6. Since doubles enable you to play the roll twice, they are very noticeable. Even more if the double is hurting you. We often will get email saying there were 25 doubles in a match. If you look at the match and count 155 rolls in all, you can see that the statistic was respected. There is no law in backgammon saying that the number of doubles should be the same for both payers. Further more, some matches may have more or less doubles than the statistics would expect. If the statistics were always as expected, only then you could say that the dice were not random.
- My opponent always gets better dice
Assuming this means that our dice games, for whatever reason, would be favoring a player against its opponent. There are a few questions to ask ourselves about this assumption:
- What could a gamesite/server gain doing such thing?
- How would the server proceed to decide what player to favor?
- Why would the server target players to let help them win or loose?
Ever wonder why your opponent seems to get better dice? Maybe, just because, he plays better than you. The art of backgammon is playing our pips in such a way that you will have the best dice possible on the next roll and/or give less chance to your opponent of getting a good roll.
- I never get such odd dice when I play for real
This is another misconception that comes form the fact that the dice are generated by a machine. In fact some players tend to believe that if they would roll the dice themselves they would get better dice. If they where able to do so, they would most likely be cheating.
Also, we are quite sure that most of the players play more backgammon online than they play in real life. How can they come to the conclusion that real life dice are better? If they would play as much in real life, they would also see strange odds.
- I have been playing for 30 years and I am a good player
Backgammon is an easy game to learn and very difficult to master. If backgammon were only a dumb luck game, not many books would have been written on it. After all, how many books where written on Snakes and Ladders?
As one player said "I have been playing backgammon for about 25 years now and have an ELO of about 1625. The reason is that I never really studied the game strategy and never really tried to improve my game. I play for fun and this is my choice. You will never hear me say that I have a 25 years experience in backgammon, I consider myself having 25 X 1 year experience."
In conclusion:
- If you play on a lot of sites, check the competition. We can tell you that complaints about dice are not exclusive to GoldToken.com.
- The dice are one thing in backgammon, as well as our other dice games, how you play them is a completely different story.
- A good practice to improve your game is to perform analysis of your matches. There is a lot of good software available to do so and I would recommend GNU backgammon. It is considered to be the closest thing to Snowie, and best of all, free.
http://www.gnubg.org/index.php?itemid=21
When looking at an analysis please check out all the moves one by one and try to understand your good moves and your errors. This is the only way to learn. Too many players will go directly to the game and/or match summary and make their opinion from that information alone. That would be like saying that by reading the index of a book, you read the whole book.
Added 2.15.10
Let's do the math as an example where we're rolling five dice. Intuitively, you may expect that the five rolls should come up different a lot of the time (at least this is what people often mention when discussing how random the dice are or aren't). So what's the chance of all the five rolls being different? The first die is trivial. Any of the six possible values is fine (none will result in duplicates), giving a probability of 6⁄6 = 1. After you've rolled the first die, the chance of the second coming up different from the first is 5⁄6, because there is now one less value you haven't seen before. The third is 4⁄6, and so on. Hence the total probability of all your five rolls turning out different is:
| 6⁄6 | 5⁄6 | 4⁄6 | 3⁄6 | 2⁄6 | 9.26% |
Hence, if you roll five dice repeatedly, you should expect over 90% of the rolls to contain duplicates (Now I don't mean the exact same duplicates, but it very well could be to be truly random). If you roll six dice, you can multiply the value above by a further 1⁄6 and you'll get approximately 1.54%. Hence, if you roll six dice repeatedly, you can expect to get six different values only about once in every 65 rolls. The following table shows the probabilities:
| Number of Dice Rolled Chance of Duplicates: |
| 1 0% |
| 2 ~16.7% |
| 3 ~44.4% |
| 4 ~72.2% |
| 5 ~90.7% |
| 6 ~98.5% |
For a great little introduction to calculating probabilities, check out this page titled Introduction to Probability and Statistics at http://www.fourmilab.ch/rpkp/experiments/statistics.html