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Probabilities of Outcomes of Throwing Weighted Dice

probabilities of outcomes of throwing weighted dice

Six-sided dice pose no mystery, and most of you have already played hundreds of games using them. Classically, dice throwing odds are calculated by estimating the chance of landing a certain sum on the faces of six-sided dice. The chances of rolling a particular number are approximately one in six 16.667 percent when you roll a perfect six-sided dice. However, adjusting the dice slightly increases your chances of landing the dice the way you want. 

Additionally, you can increase the chances of a certain number landing on any given roll. Throughout this article, we will cover what probabilities of outcomes are possible when throwing dice.

Probabilities of Outcomes of Throwing Weighted Dice

Probabilities of Outcomes of Throwing Dice: Weighted Dice Probability

probabilities or rolling regular dice
Probabilties of Rolling Regular Dice

Probabilities measure the likelihood of different outcomes occurring. A six-sided dice, for example, will have the same probability for all numbers since there are six possibilities for every number. However, the odds of each outcome are not equal for every scenario. When you roll a dice, you have a one in six chance of landing on one of the sides. 

That’s what casinos want for every roll. That’s why you can’t buy dice off the shelf at land-based casinos. They are called “precision” dice because their dimensions are exactly proportional, so whoever rolls them gets a fair chance of landing any of their six faces. 

The precision of each of them is so exact that each one is made within a tolerance. The standard tolerance is less than 0.005 inches or within the total tolerance within the dice. A spot that is drilled into to create the markings on each side must be filled with the same amount of material, whether paint or something similar. The sides of casino dice should be arranged in the same way.

What are Weighted Dice?


Weighted dice are also referred to as loaded dice or crooked dice. Loaded dice are being altered in such a way that the loaded side faces upwards more often than normal. You can use weighted dice to win, amaze, or confuse. Using a loaded dice is fun, no matter what improbable magic tricks you want to perform or how you want to dominate the craps table. 

Probabilities of Outcomes of Throwing Weighted Dice

You can increase your chances of any particular number facing up with loaded dice. It’s not surprising that people are willing to try anything to turn the dice in their favor at many of the world’s top casinos, considering the amount of money at stake. Throwing weighted dice has different results depending on how they are loaded.

When you drill out a small area behind the dots and fill it with metal, you get loaded dice, meaning that the unaltered side will land up more often. If you remove a little material from dice and don’t add any extra weight, you’ll create a floater. This works similarly to an upside-down dice since the lighter side will most likely end up facing up. By adding a little space to the sides of the dice, cheaters can get what are called flats. In this case, there is a higher likelihood of the dice landing on one of these larger sides.

Probabilities of Outcomes of Throwing Two Dice

Estimate how many possible outcomes can be obtained for the scenario. Rolling two dice, for instance, gives you 36 possible outcomes since there are six outcomes per dice, so multiply six times six. Find the number of feasible outcomes. When playing a board game and winning depends on rolling an eight, it is necessary to determine the five ways an eight can be rolled (for example, (2,6), (3,5), (4,4), (5,3), and (6,2).

The weighted probability is calculated by dividing the number of possible outcomes by the number of ways to achieve the desired outcome. You can finish the example by dividing five by 36, which gives you 13.89 percent of the probability.

A Short History of Dice

In modern times, dice are used for social interaction and games. However, in the past, dice were also used for divination. As early as 2000 BC, evidence of dice was found in Egyptian tombs, which indicates they used these units. Among the first civilizations in the Americas, dice were made of animal bones and were used for divination. The Greeks and Romans used various kinds of dice in the early days, mostly composed of stone or ivory. There are traces of the cubical shape of dice only dating back to 600 BC in China. According to some theories, dice from Asia may have been brought to Europe during Marco Polo’s expeditions in the 14th century. 

The 1920s saw the introduction of handcrafted dice made with cellulose nitrate, which was used to create dice in the early 20th century. The 1950s brought cellulose acetate into use as a more durable material in the industry. The use of plastics as raw materials for dice manufacturing arose with the invention of plastic technology. 

Throughout history, dice have evolved, but casinos have retained the cubical nature of the unit. When you look at precision dice used in casinos, you’ll notice that they are not cut corners. Despite reducing the roll’s randomness, cut corners or rounded corners are popular in many board games because they meet child safety standards. Usually, casino dice are 3/4 inches in size, but they can also be as large as 5/8 or 11/16 inches.

Weighted Dice Probability: Frequently Asked Questions

What is Precision Dice?

Precision dice are all-purpose dice used in casinos. This is because they are made according to exact dimensions and with perfect precision. Most of them come in the color red, but some can also come in the colors blue, green, and purple. The outcome of dice, when rolled, can be dramatically altered by adjusting it little by little. Hence, each dice undergoes complex processes that must be calculated precisely. This is how they can ensure that each dice is unique and random.

What is the best way to load a dice?

The process of converting a normal dice into a loaded one involves a variety of steps. A simple way to a gimmick or load a dice is by drilling into the plastic and weighting one end to ensure that it lands down more often. Therefore, you must decide what side you want to appear on most often and weigh the opposite side. There’s no need to gimmick your dice at all, but if you plan to play craps, weigh your dice so that the six comes up most often or weigh them so that other rollers won’t crap out. You can make the decision.

How loaded dice work?

When a dice is loaded, a weight distribution determines its outcome. As long as you roll the same dice, both “predictable” outcomes will be the same. Nevertheless, if you load several sides, you will rely on luck again, which might be the fairest option.

Could loaded dice be legal?

Tampering with dice is illegal, and you will face stiff penalties if you’re caught with loaded dice. Craps should be played fairly, however, to keep it fun for all casino patrons. You can win a small amount of money by cheating, but the fines and jail time you can face if caught are much greater.

Do you know which dice can be loaded?

Adding weights to one side of each dice is possible if the dice are not transparent. The lead is inserted on one side of the dice if it is not transparent. Whenever you add more weight to the dice, its center of gravity moves away from the center, and the heavier side always faces downward.



Most casinos do everything they can to prevent players from using loaded/ weighted dice. The dice at a casino are initially inspected carefully to make sure they have not been tampered with. Additionally, casinos take additional security measures to prevent dice tampering. For this reason, the odds of outcomes of tossing dice at casinos are fair and the weighted dice probabilities are far less likely to pass among players and becomes harder to calculate.

Mike Horton (head of Weighted Living)

by Mike Horton

Mike is one of the lead editors at Weighted Living and the author of this article. He's become fascinated with weighted products (a bit too much we think) and loves to see all the different ways they can improve our loves. He's written quite a few weighted product guides as well.

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