Liar's Dice Psychology, Probability, and Bidding Strategy Guide

Want to drink less? Master the dice game! Wrong calls lead to trouble, and carelessness leads to dizziness!

I. Bidding Strategy

For a 4-player game:

Never start bidding with quantity of 1. It's better to start with 3 or 4 dice. These quantities have high probability, and the game usually escalates quickly, likely reaching maximum bids within the next one or two players. Check the probability section below for details!
If you start with quantity of 1, after one round when it's your turn again, if the previous player puts you in a difficult bidding position, you'll have no choice but to challenge them!
It's best to start with a bluff. For example, bid "three 3s" when you don't have any 3s. Nobody will challenge this early. Watch if others follow with 3s. If not, players will gradually start bidding their most frequent numbers as the quantities increase!

II. Psychological Strategy

When playing with skilled players, if someone bids "four of something" in the first round and you don't have any of that number, challenge immediately as the next player! They might be bluffing!
When it's your turn and you're stuck, don't just increase the quantity based on your most frequent number. Instead, follow the previous player's number but increase the quantity!

Example: If the previous player bids "five 4s" and you have two 3s, even if you believe there are five 4s, don't bid "six 3s" - bid "six 4s" instead, even if you don't have any 4s!

Later in the game, players who hesitate more are likely bidding their actual most frequent numbers. Consider challenging based on your dice!
Don't be overly conservative by always starting with "three 3s" or "three 4s". While these could be bluffs, others won't challenge. Sometimes be aggressive based on your dice and bid five! Let others challenge you! Mix truth with lies for the best strategy!

III. Dice Probability Calculations!

Since your dice are known, we calculate probabilities for the other three players' 15 dice.

Standard Version (No Wild Dice)

1 of a kind: 100%
2 of a kind: 93.5%
3 of a kind: 74%
4 of a kind: 46.7%
5 of a kind: 23%
6 of a kind: 8.8%

Version with Wild Dice

Probabilities for the other three players:

1 of a kind: 100%
2 of a kind: ≈100%
3 of a kind: 98.5%
4 of a kind: 92.3%
5 of a kind: 79.3%
6 of a kind: 59.8%
7 of a kind: 38.4%
8 of a kind: 10.5%

These are all the strategies and psychological insights I can think of for the dice game, also known as Liar's Dice.