# Liar S Dice Board Pdf Download

## Liar's Dice: A Game of Bluffing and Probability

Liar's dice is a game that involves rolling dice, hiding them from other players, and making bids on the number of dice showing a certain face. The game can be played with two or more players, each with a cup and five six-sided dice. The game is also known as Perudo, Dudo, Cachito, or Diception.

The game has two variants: single hand and full hand. In single hand, each player rolls their own dice and bids on the total number of dice of a certain face among all players. In full hand, each player rolls all their dice at once and bids on the number of dice of a certain face in their own hand. The rules for each variant are explained below.

## Liar S Dice Board Pdf Download

## Single Hand Liar's Dice

The rules for single hand liar's dice are as follows:

Each player shakes their cup and rolls their dice, keeping them hidden from other players.

The first player makes an opening bid, stating a quantity and a face value. For example, "three fours" means that there are at least three dice showing four among all players.

The next player can either accept the bid or challenge it. To accept the bid, the player must raise it by either increasing the quantity or the face value, or both. For example, if the previous bid was "three fours", the next player can bid "four fours", "three fives", "four fives", etc. The face value can never be lowered, and the quantity can only be lowered if the face value is raised to six (the highest value).

If a player challenges the bid, all players reveal their dice and count the number of dice matching the face value of the bid. If the bid is equal to or higher than the actual number, the bidder wins and the challenger loses one die. If the bid is lower than the actual number, the challenger wins and the bidder loses one die.

The player who lost a die starts the next round with a new bid. The game continues until only one player has dice left, who is declared the winner.

Some variations of single hand liar's dice include:

Using one or more wild cards, such as ones or sixes, that can match any face value.

Allowing players to re-roll some or all of their dice before making a bid.

Using different types of dice, such as eight-sided or ten-sided dice.

## Full Hand Liar's Dice

The rules for full hand liar's dice are similar to single hand, but with some differences:

Each player shakes their cup and rolls all their dice at once, keeping them hidden from other players.

The first player makes an opening bid, stating a quantity and a face value. For example, "two fours" means that the player has at least two dice showing four in their own hand.

The next player can either accept the bid or challenge it. To accept the bid, the player must raise it by either increasing the quantity or the face value, or both. For example, if the previous bid was "two fours", the next player can bid "three fours", "two fives", "three fives", etc. The face value can never be lowered, and the quantity can only be lowered if the face value is raised to six (the highest value).

If a player challenges the bid, only the bidder and the challenger reveal their dice and compare them. If the bid is equal to or higher than the actual number in the bidder's hand, the bidder wins and the challenger loses one die. If the bid is lower than the actual number in the bidder's hand, the challenger wins and the bidder loses one die.

The player who lost a die starts the next round with a new bid. The game continues until only one player has dice left, who is declared the winner.

Some variations of full hand liar's dice include:

Using one or more wild cards, such as ones or sixes, that can match any face value.

Allowing players to re-roll some or all of their dice before making a bid.

Using different types of dice, such as eight-sided or ten-sided dice.

## Liar's Dice and Binomial Random Variables

Liar's dice is a game that involves probability, as players need to estimate the likelihood of certain combinations of dice rolls among all players. One way to calculate these probabilities is by using binomial random variables. A binomial random variable is the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure. For example, rolling a die is a trial, and getting a four is a success. The probability of success is the same for each trial.

The binomial formula gives the probability of getting exactly k successes in n trials, where p is the probability of success for each trial:

$$P(X=k) = \binomnk p^k (1-p)^n-k$$

For example, if we roll five dice and want to know the probability of getting exactly two fours, we can use the binomial formula with n = 5, k = 2, and p = 1/6:

$$P(X=2) = \binom52 (\frac16)^2 (\frac56)^3 \approx 0.16$$

We can also use the binomial formula to calculate the probability of getting at least k successes in n trials, by adding up the probabilities of getting k, k+1, k+2, ..., n successes:

$$P(X \geq k) = \sum_i=k^n \binomni p^i (1-p)^n-i$$

For example, if we roll five dice and want to know the probability of getting at least two fours, we can use the binomial formula with n = 5, k = 2, and p = 1/6:

$$P(X \geq 2) = \sum_i=2^5 \binom5i (\frac16)^i (\frac56)^5-i \approx 0.20$$

The binomial formula can help us make better bids in liar's dice, by estimating the probability of certain combinations of dice rolls among all players. For example, if there are four players with five dice each, and we want to know the probability of having at least ten sixes among all players, we can use the binomial formula with n = 20 (the total number of dice), k = 10 (the number of sixes), and p = 1/6 (the probability of rolling a six):

$$P(X \geq 10) = \sum_i=10^20 \binom20i (\frac16)^i (\frac56)^20-i \approx 0.001$$

This means that there is only a 0.1% chance of having at least ten sixes among all players, so this would be a very risky bid to make or accept.

## Liar's Dice Board PDF

If you want to play liar's dice at home, you can download and print a liar's dice board PDF from [this link]. The board has spaces for up to six players, each with five dice. You can also use your own cups and dice if you prefer. The board also has a summary of the rules for both single hand and full hand variants. Have fun bluffing and bidding!