What is the Rarest Roll in Dice?

The rarest rolls in a standard pair of six-sided dice are 2 and 12. Each of these totals has a probability of only 1/36, or approximately 2.78%, making them the least likely outcomes when rolling two dice. This scarcity is due to the fact that there is only one specific combination of dice faces that will produce each of these totals: a 1 on both dice for a total of 2, and a 6 on both dice for a total of 12.

Why Are 2 and 12 the Rarest?

The probability of rolling a specific total on two dice is determined by the number of unique combinations that produce that total, divided by the total number of possible outcomes. When rolling two six-sided dice, there are 36 possible combinations (6 outcomes for the first die multiplied by 6 outcomes for the second die).

• Rolling a 2 (Snake Eyes): The only way to achieve a total of 2 is by rolling a 1 on both dice. There is only one combination that achieves this outcome: (1,1). Thus, the probability is 1/36.
• Rolling a 12 (Boxcars): Similarly, a total of 12 can only be achieved by rolling a 6 on both dice. This has only one combination: (6,6). Again, the probability is 1/36.

In contrast, a total of 7, which is the most common outcome when rolling two dice, can be made by six different combinations: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). This illustrates why the probability of rolling a 7 is significantly higher than that of rolling either 2 or 12.

The Probability Distribution of Dice Rolls

Understanding the distribution of dice roll probabilities is key to grasping why some numbers are more common than others. The following is a breakdown of the probabilities for rolling different totals on two six-sided dice:

• 2: 1/36
• 3: 2/36
• 4: 3/36
• 5: 4/36
• 6: 5/36
• 7: 6/36
• 8: 5/36
• 9: 4/36
• 10: 3/36
• 11: 2/36
• 12: 1/36

As you can see, the probabilities create a bell curve shape, with 7 being the peak and 2 and 12 being the two tails with equal probabilities, highlighting how much less likely they are compared to the other outcomes. This variance in probabilities makes some rolls significantly less common than others.

Why This Matters

Understanding the probability distribution of dice rolls is not just a matter of curiosity; it is essential in various applications, such as:

• Board Games: Many board games utilize dice rolls, and understanding the probability of different results can inform strategic gameplay.
• Gambling: Knowledge of dice probabilities is crucial in games like craps, where players bet on the outcomes of dice rolls.
• Probability Theory: Dice rolls serve as a practical and tangible example of probability distributions in mathematics.

Common Misconceptions

One common misconception is that all numbers have an equal chance of appearing on a dice roll. However, when rolling multiple dice, the combinations and their respective probabilities are not equal. The central tendency towards the middle numbers like 7 makes the extremes, 2 and 12, much rarer.

Frequently Asked Questions (FAQs)

Here are 15 frequently asked questions related to dice rolls, probabilities, and more to enhance your understanding of this topic:

What is the most common roll on two dice?

The most common roll on two standard six-sided dice is 7. This outcome has a probability of 6/36 or 1/6.

How many different combinations are there when rolling two dice?

There are 36 different combinations when rolling two six-sided dice (6 possibilities for the first die multiplied by 6 possibilities for the second die).

What are the odds of rolling a specific number on a single die?

When rolling one six-sided die, each number (1-6) has an equal probability of 1/6, or approximately 16.67%.

What is the probability of rolling double sixes on two dice?

The probability of rolling double sixes (a 12) on two dice is 1/36, or roughly 2.78%. This is the same as rolling double ones (a 2).

How often should you expect to roll a 7 with two dice?

You should expect to roll a 7 approximately one in every six rolls, on average.

What are the terms ‘snake eyes’ and ‘boxcars’ in dice?

‘Snake eyes‘ refers to rolling two ones (total of 2), while ‘boxcars‘ refers to rolling two sixes (total of 12).

Are there dice with more or fewer sides than six?

Yes, there are dice with various numbers of sides including 4, 8, 10, 12, 20, and even 100. These are often used in role-playing games and other activities.

How do casino dice differ from normal dice?

Casino dice, often referred to as precision dice, are made to very high standards of accuracy to ensure fairness. They have perfectly sharp edges and square corners, and often feature serial numbers to track their history.

Do different colors of dice affect their probabilities?

No, the color of dice does not affect the probability of a particular outcome, as long as the dice are otherwise uniform and unbiased.

What is the Zocchihedron?

The Zocchihedron is a 100-sided die, invented by Lou Zocchi. It is shaped like a ball with 100 flattened spots and is sometimes called “Zocchi’s Golfball”.

What is the oldest dice ever found?

Some of the oldest known dice were excavated at the Burnt City in Iran, dating back to between 2800 and 2500 BCE.

Why are some dice illegal in casinos?

Dice that are not perfect cubes or have been tampered with are illegal in casinos because they can be used to cheat, affecting the fairness of the game.

What is the most expensive die ever sold?

The most expensive die ever sold was a Roman glass d20 (20-sided die) which sold for $17,925 in 2003.

How do 10-sided dice commonly work?

10-sided dice are often sold in pairs, one numbered 0-9 and the other numbered 00-90, used for percentile rolls to generate numbers from 1 to 100.

What is the game that uses the most dice?

The board game PoshFrosh utilizes a pool of 39 dice, including d4, d8, d10, d12, d14, d16, d18, and a greater number of d6 and d20 dice.

By understanding the probabilities and various aspects of dice rolls, one can gain a deeper appreciation for not only games involving dice, but also the underlying principles of mathematics, chance and fairness in games. The rarity of the combined 2 or 12 serves as a practical example of how even seemingly simple systems can yield intriguing patterns.