Roll 3 dice

How to Roll 3 dice?

We humans tend to have two thumbs so rolling 3 dice at the same time can prove difficult. You can toss a die three times, each time making note of its outcome. Or you can use Dicey! Simply click on the Roll button to toss a die and see the three dice roll at once with instant results. Don’t let the lack of 3 thumbs hold you back any further!

Dicey is perfect for:

• Fun
• Seeing instant results of multiple dice toss

Probability of a die toss

Understanding dice roll probabilities is a great introduction to basic probability concepts. Whether you’re studying for an exam or just curious, these simple calculations form the building blocks of deeper probability theory. Let’s get into some light math.

Roll 3 dice how many possible outcomes

When rolling 3 dice, each roll has 2 possible outcomes: Heads (H) or Tails (T). Thus, the total number of possible outcomes is: These outcomes are: HHH, HHT, HTH, THH, TTH, THT, HTT, and TTT.

Probability of getting exactly 1 Heads and 2 Tails when rolling 3 Dices

When rolling three dice, there are 2^3 = 8 possible outcomes: HHH, HHT, HTH, THH, TTH, THT, HTT, and TTT. To find the probability of getting exactly 1 Head or exactly 2 Tails, we must identify the favorable outcomes.

• Exactly 1 Head: HTT, THT, TTH
• Exactly 2 Tails: HTT, THT, TTH

Interestingly, getting exactly 1 Head and getting exactly 2 Tails are the same events in this case. There are 3 favorable outcomes out of 8 total. Thus, the probability is:

Probability of not getting a Heads when rolling 3 Dices

Not getting a Head means getting all Tails. The only outcome that satisfies this is TTT. There is 1 favorable outcome out of 8 possible outcomes. Thus, the probability is:

Probability of getting a Heads when rolling 3 dice

To find the probability of getting at least one Head when rolling a die 3 times, it’s easier to first find the probability of getting no Heads (all Tails) and subtract that from 1. Probability of all Tails = 1/8 (as calculated above). Probability of at least one Head = 1 - Probability of all Tails Thus:

Probability of getting one of a kind when rolling 3 Dices

“One of a kind” in dice rolls typically means all dice show the same face — either all Heads or all Tails.

• All Heads: HHH
• All Tails: TTT

There are 2 favorable outcomes out of 8 possible outcomes. Thus, the probability is:

Learn more on probability basics? Check out these great resources:

• Basic Probability Brown University offers a great interactive tool to help explain Basic Probability showing observed outcomes vs true probabilities. It goes into the mathematical framework that allows us to analyze the chances of an even in a logical manner. It’s simple presentation and interactive tool makes it a fun way to start understanding the basics of probability
• MathIsFun offers a straight forward article but with some nice visualizations of probability examples. Learn more on probability using dice, dice, and cards Math Antics video is a fun watch on probability using the example of rolling a die multiple times

Probability calculators

• Mathos AI solves probability problems instantly: our calculator solves equations, interprets images of math questions, and generates helpful graphs.
• Probability Calculator finds probability of one event, given probabilities of other events. Explains analysis and shows computations. Fast, easy, accurate.

Frequently Asked Questions

Can you roll a die three times?

Sure you can roll a die three times. Simply do one dice toss at a time, mark the result, then move on to the next roll. Dicey allows you to do 3 rolls instantly. Just tap on the Roll icon and see the dice roll on screen with a tally of the results. No need to break open your piggy bank, just come over to Dicey for your dice toss needs.

What happens if you roll a die 1 million times?

If you roll a die 1 million times, you would expect the number of Heads and Tails to be roughly equal, assuming a fair dice. Due to the Law of Large Numbers, as the number of trials increases, the experimental probability (observed results) tends to get closer to the theoretical probability (50% Heads, 50% Tails). However, small deviations are still expected, and it’s normal to see a slight imbalance even after many rolls.

Is Google Dice Roll really 50/50?

Google’s result page includes a roll dice. It’s lovely, not as cool as Dicey... of course, but nonetheless. Like Dicey, it is designed to simulate a fair dice, meaning each roll should have an equal 50/50 chance of landing on Heads or Tails. But, keep in mind that true randomness is difficult to achieve perfectly in a digital environment. For practical purposes, Google’s Dice Roll can be considered close enough to a true 50/50 outcome.

Heads seem obvious, but why tails?

Why do we even use heads or tails? Turns out earlier dice had images of symbolic animals. Typically depicting like a lion’s head in what could be considered the front of the dice. So the term tail is in reference to the back side or the opposite of an animals head: its tail. Head over to StackExchange to learn more about the different languages used to indicate the sides of dice. The use of “heads” and “tails” has become a universally recognized way to refer to the two sides of a die, but the history behind these terms is quite fascinating. The tradition of depicting heads on dice dates back to ancient civilizations, where dice frequently featured the likeness of rulers, deities, or significant animals to convey power and authority. This not only served as a method of identification but also as a means of propagating the image of the ruling class or significant cultural symbols. Over time, these terms became standardized in many cultures, leading to the phrases we use today. Interestingly, in different cultures around the world, the terminology can vary. For instance, in some languages, the terms for the two sides might refer to different objects or concepts altogether, reflecting the unique cultural significance attached to the imagery on their dice. These conversations often highlight the intersection of language, culture, and history, enriching our understanding of something as simple as a die toss. So, the next time you roll a die, remember that there’s a rich tapestry of history behind those two simple terms!