What is the fair value of dice?

When you roll a fair die you have an equal chance of getting each of the six numbers 1 to 6. The expected value of your die roll, however, is 3.5.

How fair are standard dice?

A standard six-sided die, for example, can be considered "fair" if each of the faces has a probability of 1/6. But there are a number of factors that come into play here, and things get more complicated when you start considering shapes for dice other than a cube.

What are the values of dice?

These are six-sided dice with sides numbered 2, 3, 3, 4, 4, 5 , which have the same arithmetic mean as a standard die (3.5 for a single die, 7 for a pair of dice), but have a narrower range of possible values (2 through 5 for one, 4 through 10 for a pair).

What is the expected payoff of one roll?

Let's suppose we have only 1 roll. What is the expected payoff? Each roll is equally likely, so it will show 1,2,3,4,5,6 with equal probability. Thus their average of 3.5 is the expected payoff.

Is the dice game fair?

There are many dice games - some are more fair than others. The most popular dice game is craps, which is not a fair game. The house has an edge on all the bets. Unlike many games, however, the amount of house edge varies, and there is even a bet with ZERO house edge - though there is a catch.

Fair Dice (Part 1) - Numberphile

Is the 120 sided dice fair?

The shape is a fully-symmetrical polyhedron (an isohedron) known as the disdyakis triacontahedron. This shape is the ultimate fair die allowed by mathematical symmetry. The numbers are distributed perfectly uniformly, so that the sums of the number groups of each type are uniform.

Is rolling two dice fair?

If the die is fair (and we will assume that all of them are), then each of these outcomes is equally likely. Since there are six possible outcomes, the probability of obtaining any side of the die is 1/6. The probability of rolling a 1 is 1/6, the probability of rolling a 2 is 1/6, and so on.

What is the expected value of dice games?

To calculate the expected value we multiply the value of each event by its probability and then add the results. So, for the event of getting a sum of 2, 4 or 10, we multiply -3 times 7/36, which equals -21/36. And for the event of getting a sum of 7, we multiply -2 times 6/36, which equals -12/36.

Which game has the highest expected value?

In technical terms, this means the Die Game has a higher expected value. In the long run, you'd expect to win about per play in the Die Game, as opposed to for the Coin Game. So the Die Game is the more advantageous one, on this analysis. On average, people tend to win more playing that game.

What are all the fair dice?

The full geometric set of "uniform fair dice" (with all congruent sides) are: Platonic solids: 5 regular polyhedra: (4, 6, 8, 12, 20 sides) Catalan solids: 13 Archimedean duals: (12, 24, 30, 48, 60, 120 sides) Bipyramids: infinite set of prism duals, triangle faces: (6, 8, 10, 12, ... sides)

What are the most fair dice?

Dice Fairness

Mathematicians suggest that there are really only five polyhedrons (three-dimensional objects) which are actually “fair” for dice rolls by the rule set above. These five are a cube, tetrahedron, octahedron, dodecahedron and the icosahedron.

Why dice always equal to 7?

The value of the roll is indicated by the number of "spots" showing on the top. For the six-sided die, opposite faces are arranged to always sum to seven. This gives two possible mirror image arrangements in which the numbers 1, 2, and 3 may be arranged in a clockwise or counterclockwise order about a corner.

Is a 30 sided dice fair?

Sorry to break the hearts of all the RPGers out there, but by Diaconis' reckoning, the aforementioned 30-sided die (otherwise known as a rhombic triacontahedron) isn't actually “fair.” Even if its 30 faces are of the same surface area, they aren't sharing the same number of vertices (angular points).

How do you test for fair dice?

Place the die in the water, note which side of the die faces upwards, and then give it a flick. For reasonably balanced dice, you should see a good variety of numbers facing upwards. For badly balanced dice, you'll probably see the same one or two faces regularly. Throw those bad dice out.

Are dice perfectly balanced?

It could be that Tymora is messing with you, but more than likely it's a matter of dice balance. Most dice are inherently unbalanced, at least to some degree. Many have small manufacturing errors like air bubbles or uneven sides. Others have aesthetic inclusions.

What is the 3 4 5 rule in craps?

Most casinos allow what is known as "3- 4-5X Odds." This means the player may bet up to three times his Pass bet on the odds after a point of a 4 or 10, four times after a 5 or 9, and five times after a 6 or 8.

What number statistically comes up most in craps?

As you can see, the most likely dice roll is a seven, which will occur on six of the 36 possible combinations from the two dice. The next two most likely are six and eight followed by five and nine and so on, reducing in probability as you move further away from seven lower and higher respectively.

What number is statistically most likely to be rolled in craps?

As you can see, 7 is the most common roll with two six-sided dice. You are six times more likely to roll a 7 than a 2 or a 12, which is a huge difference. You are twice as likely to roll a 7 as you are to roll a 4 or a 10. However, it's only 1.2 times more likely that you'll roll a 7 than a 6 or an 8.

What is the true probability of dice?

The probability of one dice being a particular number is 1/6. The probability of two dice being the same particular number is 1/6 x 1/6 = 1/36. This is not the same as saying that both dice are the same number. There are six different possible numbers, so that would be 6/36 or 1/6.

What is the expected value of roll dice 100 times?

If we roll a dice 100 times then the expected value of the sum of the rolls is 100E(X) = 350.

What are the odds of dice results?

The probability of rolling any given number with a single die on a single roll is equal to one divided by the number of die faces. For example, with a 20-sided die, the odds of rolling 20 is 1/20 or a 5% chance. With a classic six-sided die the probability of seeing any particular face is 16.667% or chance odds of 1/6.

How to find the expected value?

To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products. The formula is given as E ( X ) = μ = ∑ x P ( x ) .

What is 2 fair dice?

If the two dice are fair and independent , each possibility (a,b) is equally likely. Because there are 36 possibilities in all, and the sum of their probabilities must equal 1, each singleton event {(a,b)} is assigned probability equal to 1/36.

Is a 7 sided dice fair?

Making fair dice by ignoring faces

This 7 sided die is fair for ranges 1-5, provided you ignore the 6 and 7th face. As we read above, any prism can be fair provided the ends are "capped" or ignored (see Long Dice). So, a real d7 would be made of a heptagonal prism.