How random are dice really?

Lukas Wagner

Lukas Wagner

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Enthusiastic ludo players know the thrill: you have three tries and one of them has to be a 6 to bring your pawn into the game. And often it is like this: you roll the dice three times, no 6. Next round: you roll the dice three times, again no 6. That’s just too bad. At some point it has to work.

The appeal of dice games is the randomness, because you never know what number will come next, so it always remains exciting. But is there a system behind the roll of the dice? Is it really purely random, or can it be influenced?
These are the questions we explore in this article.

Dice – the oldest random number generator known to man

The precise origin of dice is still surrounded by mystery. We know that they were already widespread in the Orient in 3000 BC and the individual areas were marked with dots. Later in antiquity, variants with letters, symbols and numbers were added. They were used not only to play, but also to predict the future.
Roman soldiers eventually brought the game of dice to Europe. The first mention of gambling houses, where people played for money by throwing dice, dates back to the 13th century. The game of dice was frowned upon, especially in the Middle Ages, because it distracted people from their daily work and was therefore considered the work of the devil.

It was already known at that time that the surfaces of dice had to be even and the weight had to be distributed equally to all lying positions, so that there were no irregularities during the game.

Cheating players had their methods of inconspicuously tinting dice by polishing edges or manipulating the weight distribution inside the dice. Some cheaters were even so skilled that they could roll dice (without prior manipulation) in such a way that they often rolled the desired number. The countermeasure invented at that time, which we still use today: the dice cup. Serious thought about how random a dice roll is, however, was not given until the Renaissance (from 1450), when the principle of chance was approached from the scientific and mathematical perspective.

All numbers are equally likely

The basic principle of a fair, i.e. non-rigged, dice is that all numbers appear with the same probability. This is called the law of large numbers, which states that if you roll the dice long enough, the frequency of the numbers on the dice becomes similar. Rolling a 6 is, therefore, exactly as likely as rolling a 1 or any other number – even if our subjective sense often doesn’t see it that way when we’re hoping for a particular outcome.
If you ever get very bored, you can try it out for yourself: Roll the dice for an hour with an ideal dice and note the occurrence of each number. At the end, you will see that the frequencies are roughly the same. In the case of the aforementioned game of ludo, this means that on average you can send your pawn into the race in the second round, as statistically every sixth roll is a 6. But that doesn’t mean that it has to happen that way: the probability calculation also says that one out of three players will not roll a 6 after six rolls – and two out of ten players even need at least ten attempts to roll the desired number.

Image: Dice in all shapes and colors are part of the basic set of many games. Image source: carufrannco via pixabay.com

Modern dice

Today, dice are manufactured by machines in industrial processes and are, therefore, close to ideal.
“Close to” because, purely theoretically, there is no ideal dice. For example, applying the color to each pip, number, or symbol is strictly speaking a cog, as the weight varies depending on the design. However, this effect is negligible in practice for an otherwise very precisely manufactured dice that have flat faces and burr-free edges.
Dice are not only used in pure dice games, but also as a random generator in board games. Especially in pen & paper role-playing games they are part of the inventory and come in quite different forms, not only as the traditional D6 with 6 faces, but also as D12, D20 or dice with even more faces. In PC or smartphone games where dice are used, a random number generator algorithm does the rolling and then shows the relevant number on the display.
unidice shows that you can combine both worlds: the first physical game cube with 6 touchscreen displays on which players can load and display their own symbols depending on the game. This takes traditional dice rolling to a new level, as the analog and digital worlds converge here, creating entirely new opportunities for players to customize their game. Rather than being obsolete, the traditional dice has been given a makeover.

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