| Next Move | Normal Probability | Adjusted Probability |
|---|
Learn about the probability calculations behind the tool.
The normal probability is the chance a claim is true based on all unknown dice in the game, treating them as a single random pool. It doesn't consider the claimant's hand or bluffing.
First, we count how many dice in your hand contribute to the claim. Ones are wild and count as any number.
Next, we calculate the total number of dice that are unknown to you. This includes the dice held by all other players. We also determine the remaining needed dice to meet the claim.
We use the binomial formula to find the probability of getting exactly the required number of dice (or more) from the unknown pool.
Generic Formula:
Example:
| \(k\) | Formula | Value |
|---|
Finally, we sum the probabilities of getting exactly the number of matches we need and all higher possibilities.
The adjusted probability is a more sophisticated calculation that factors in the claimant's dice and a bluffing model using Bayesian inference. It's the probability the claim is true, given that the claimant made it.
Look at your dice and count how many show the claimed number. Ones are wild and count as any number. The remaining needed dice must come from other players.
We calculate the probability each possible number of claimant dice contribute to the claim using the binomial formula. The example table below shows the probabilities for \(k = 0\) to matches from the claimant's dice.
Generic Formula:
| \(k\) | Formula | Value |
|---|
The claim might be exaggerated. We estimate the probability of the claim being made given a certain number of matches \(K\) a player holds, considering a fixed bluff rate.
This is based on the formula: \(P(\text{claim} | K=k) = 1.0\) if \(k \ge \text{threshold}\), else bluffRate.
We use Bayes' Theorem to adjust the prior probabilities based on the fact that a claim was made. This gives us a new probability distribution for the number of matches the claimant holds, called the posterior probability. The formula is:
Generic Formula:
| \(k\) | Formula | Value |
|---|
For each possible number of matches the claimant holds (\(K\)), we calculate the probability that the remaining unknown dice satisfy the claim. We use a binomial tail sum for this.
Generic Formula:
| \(k\) | Formula | Value |
|---|
Finally, we multiply the posterior probabilities by the probability the claim is true for each \(K\) and sum them up. This is the final adjusted probability the claim is likely true, considering both dice probability and bluffing.
Generic Formula:
| \(k\) | Posterior | \(P(\\text{true}|k)\) | Weighted Product |
|---|
This Liar’s Dice Probability Calculator helps players analyze probabilities to make better decisions. Liar’s Dice is a game of skill, psychology, and probability. While intuition plays a big role, understanding the math behind the game can give you a sharper edge.
Try it out, refine your gameplay, and take your Liar’s Dice strategy to the next level!
1,2,3).