One of the mini-games in Read Dead Redemption is Liar’s Dice.

Liars dice is a game of incomplete information which distinguishes it from games like chess and backgammon where you can always see what your opponent is doing. The art of liars dice is filling the gaps in the incomplete information provided by your opponents bidding, and at the same time preventing your opponents from discovering any more than what you want them to know about your roll.

Originating in South America and originally going by the name of Perudo, this game is inherently engaging for students.

Rules:

•2 to 4 people are the ideal number of players

•Each player starts with 5 six-sided dice and something to conceal their roll

•All players initially roll their dice for everybody to see. Highest numerical total starts play

•The ‘One’ is wild

•All players now roll their dice so that they are concealed from the other players

•Each player in the game, proceeding clockwise, must make consecutively higher bids or call ‘liar’.

•A bid consists of a number and the value of a die. For example a bid of ‘Three Sixes’ could be followed by “Four fives” or “Six fours”

•As long as the bid is either numerically greater or contains more of the one bid it is valid. For example, if player 1 bids ‘Four Sixes’ player 2 could bid either ‘Five Sixes’ or ‘Five Fives’ as 5 x 5 = 25 which is greater than 4 x 6 =24

•If the opening bid consists of ‘Ones’, ‘Ones’ are no longer wild

•When a player is called ‘liar’, all players reveal their dice. For example, if you bid ‘Four Sixes’ and someone calls you ‘liar’ your bid is correct if between all players at the table, there are at least ‘Four Sixes’

•If you are caught ‘lying’ you lose a dice and play resumes. If there is at least the number of dice that you bid the person who unsuccessfully called you a ‘liar’ loses a dice and play resumes

•The last player with dice is the winner (of course, as with any game, there are variations to these rules)

The skill of liars dice consists of knowing when to tell the truth and when to ‘bluff’ and also when to call someone’s bluff. Obviously the optimum strategy is to mix bluffing with statistical estimation of what’s on the table.

Since the other players have to base their estimation of the dice on what you bid, if you can get away with a bluff in the early rounds you can affect their estimates of what’s on the table. 

For example, all players roll their dice. Player 1 has 3 3 4 5 2, Player 2 has 6 6 3 2 4 and Player 3 has 6 1 3 3 5. Player 1 opens the bidding and bids ‘Three Sixes’. Player 2 has two sixes himself so bids ‘Four sixes’. Player 3 also has a six and a one so bids ‘Five Sixes’. Player 1 holds no sixes so can fairly confidently call liar with the odds being in his favour.

The early bluff is misleading information designed to skew the perception of the other players. When a player makes a bid that the information he has does not support, that bid is likely to be accurate based on simple probability, but other players will think the bid was made because the player had some part of the bid in his own dice. This in turn causes the other players to inflate their own bids based around that value, increasing the likelihood that those bids will be false.

Once other players are aware that you like to bluff with an opening bid, it can be to your advantage to start semi-bluffing. Lets say you have the opening bid and you roll 6 6 1 3 2. Bid ‘Five Sixes’. Player 2 thinks that you are bluffing and calls you ‘liar’. The probability is definitely in your favour that Player 2 and Player 3 have each got either a one or a six.

Position is one of the key elements affecting virtually every bid in liars dice. The game is heavily weighted in favour of the player acting first. Aggressiveness in this position ensures that you control the round. For example, an opening bid of ‘Three Twos’ is relatively weak and gives the other players a lot of room to move, potentially exposing yourself to a precarious situation later in the round. By demonstrating weakness on the opening bid, you have relinquished your powerful position to the next player who can then take control of the round. A much more dominating and aggressive bid might be ‘Five Fives’ or ‘Four Sixes’. An aggressive opening like this one puts pressure on the other players immediately and gives you control of the round.

A complete strategy of liars dice is inherently complex because it takes into account not only the dice that each player is holding but also the state of the game in general. After experimentation you will find that certain players exhibit certain tendencies and that their are subtle differences in game play between a game involving two players and a game involving more than two.

Good liars dice players, to one degree or another tend to possess knowledge of game theory and the following characteristics:

•Mathematical proficiency – Ability to accurately calculate probabilities

•Reading skill – Ability to determine if a player is telling the truth or is obviously bluffing

•Flexibility – The ability to modify their approach to the game based on their opponents and what their opponents ‘know’ of their game

•Awareness – Constantly scanning opponents, looking for clues that assist in decision making

•Aggression – An attacking dominating style

The movie, Pirates of the Caribbean: Dead Mans Chest, also gives a variation of Liars Dice (seen below) and an online version of ‘Pirates Dice’ has been created by Disney, where you get to wager your soul as you play against Davey Jones and his crew.

I have provided here a brief overview of an opinion on liars dice. It is not meant to be comprehensive, but instead is provided to guide thinking when developing your own strategy and to help you guide students in their own exploration of this game. 

Feedback welcome.