Dice, Dice, Baby

 

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Overview

Liar's Dice, or Pirate's Dice, was recently featured in Pirates of the Carribean: Dead Man's Chest, where one of the intrepid heroes attempts to gamble with his soul against a pair of swashbucklers. I happen to think this particular gambling game is rather interesting, so I decided to write up some stuff about it.

Try it out

What you need to play:

  • 2-3 willing players
  • A cup and five dice for each person wanting to play, a Yahtzee set would work great for this purpose

The Rules:

  • At the beginning of the game, each player rolls the dice in their cup, and place it flat down to conceal the dice from the other players
  • Each player in the game, proceeding clockwise, must make consecutively higher bids or challenge the previous player's bid.
  • A bid consists of a number and the value of a die, for example you can bid that there are "Four Sixes" on the table somewhere, or "Seven Fives" or "Three Ones". For a bid to be higher than the previous bid, you need to simply pick a higher number, for example "Three Ones" can be followed by "Four Twos" or "Five Ones" or anything similar.
  • When a bid is challenged, all players open up their cups to reveal all the dice on the table. For example, if you bid "Three Ones" and someone calls you a liar, your bid is correct if between all the players at the table, there are at least three ones between all the players.
  • After a bid is challenged, if it was challenged successfully, the player who was challenged loses a die and the game restarts with the challenging player bidding first. If the challenge fails, the challenging player loses a die and the challenged player bids first.

Examples:

Try it out yourself, you can play a version of the game on the official Disney website.

 

Jack, Will, and Davy all roll their five dice and place them under a cup.

Davy Has: 2, 2, 5, 5, 6

Will Has: 2, 1, 4, 3, 1

Jack Has: 1, 5, 3, 2, 3
  • Davy starts the bidding with "Two Twos".
  • Will has to bid something higher, so he bids "Three Twos".
  • Jack has a two himself so he bids "Four Twos".
  • Davy calls Jack a Liar and challenges the bet. All the dice are shown, and there are four twos on the table. Davy loses a die, and Jack gets to bid first in the next game.

Jack Has: 6, 6, 2, 4, 3

Will Has: 2, 1, 4, 3, 1

Davy Has: 3, 3, 6, 5

  • Jack decides to take a risk and bids "Two Fours", hoping that another player will have a four if he gets challenged.
  • Will has a four himself so he decides to raise the bidding up to "Three Fours".
  • Davy doesn't have any fours and he doesn't feel confident that there might be four of his threes, so he decides to challenge Will's bet by calling him a liar. All the dice are shown, and are only two fours on the table. Will loses a die, and Davy gets to bid first in the next game.

Play continues until only one player has any dice remaining, at which point that player is the winner. The starting bid can be any denomination, from "One Three" to "Five Sixes" if you feel really lucky.

Strategy

  • For any particular game, there will be a best possible bid that can be made. For example, in the previous game, "four threes" is the best possible bid, there's no number which can be bid over that one without making you a liar. As the bidding escalates, you want to be in a position to either bid that number or call someone else before you get there.
  • 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 on the dice on the table. For example, in a two player game, if you bid two fours when you have none, and the next player bids three fours, you can call them on it right away.
  • It may be in your best interests to "jump the bid" on occasion, for example if you have three fours you may want to start the bidding at that value, rather than starting with one four and waiting for the bidding to get back to you, in the hopes that the other players won't be make it all the way around before it's your turn again without lying.

General Strategy:

 

The following table lays out the odds of a particular die showing up under one of the other player's cups depending upon how many dice are still in play. For example, at the start of the game, the odds of any of the other players having one six is 83.8%, and the odds of any of the other players having two sixes is 51.5%.

Similarly, if you're playing against 1 player, and he has all five dice left, the odds of him having 1 six is 59.8%, the odds of him having 2 sixes is 19.6 %, and the odds of him having three sixes is 3.5%. So you'd be relatively safe in bidding one more six than you have. (e.g., if you have 1 six you might bid two and hope he'll have another one)

 

Odds of matching
a particular die 

1 die to match

2 dice to match

3 dice to match

10 dice remaining

83.8%

51.5%

22.4%

9 dice remaining

80.6%

45.7%

17.8%

8 dice remaining

76.7%

39.5%

13.5%

7 dice remaining

72.1%

33.0%

9.6%

6 dice remaining

66.5%

26.3%

6.2%

5 dice remaining

59.8%

19.6%

3.5%

4 dice remaining

51.8%

13.1%

1.6%

3 dice remaining

42.1%

7.4%

.5%

2 dice remaining

30.5%

2.8%

0%

1 dice remaining

16.7%

0%

0%

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alternate Rules

  • In the movie, the game is simply played "elimination" style where a player loses the game instantly, rather than making the viewers endure at least 10 successive rounds of the same game, world series of poker style.
  • Also in the movie, the betting rules follow a different variation than the online version of the game. A bid is higher than the previous bid if either the number of dice is higher (three twos beats two twos) or if number is the same and the value of the die picked is higher (three twos beats three ones)
  • A more complex variation of the game involves making "ones" wild. Thus, if there are 8 dice on the table with 2 ones, 3 threes, and 3 fives, "five threes" and "five fives" are both winning bets, since the ones can represent any value which is bid on. When bidding ones you bid strictly on the number of ones on the table. Bidding "one one" beats any bid of two of anything and is beaten by three of anything. Similarly, "two ones" beats four of anything and is beaten by five of anything, three ones beats six and loses to seven, etc
  • In some variations you can bet that the previous bid was exactly correct. After this the dice are shown, and if you were wrong, you lose a die, but if you were right, you get a die back.

Summary of the Game Played in POTC:Dead Man's Chest

Arrrr, thar be spoilers ahead, matey!

 

The Stakes

Davy Jones is wagering the key to his heart, so to speak.
Will Turner is wagering an eternity of servitude aboard the Flying Dutchman.
Bill Turner is matching Will Turner's wager, he currently owes a debt to the Dutchman of at least 90 years of service.

If Will or Bill loses, the Dutchman gains the loser's soul for eternity. If Davy loses, the Turners gain control of the key. Will and Bill aren't in a position to exchange information or collude together unfortunately.

The Dice

Davy's Dice: 5, 4, 5, 5, 5
Will's Dice: 5, 5, 5, 1, 2
Bill's Dice: 3, 2, 3, 2, 2

 

Davy has the strongest roll with four of the same die to cushion his bets. The best possible bid is seven fives.

The Bids:


1. Bill bids three twos. This, strictly speaking, is the only honest bid of the entire game, since this is the only time any player bids when he knows for sure that he can make his bid.

2.Davy bids four fours. A flat out bluff, if Davy had been called at this point he would have lost. He has only one four to back his bid up with.

3. Will bids four fives. A fairly safe bet, he's counting on at least one other player having a five should he get called a liar.

4. Bill bids six threes. Bill exaggerates the strength of the threes in his hand while hoping Davy will take the bait and make a strong threes bid on top of his. Since it's a bluff Bill would have lost had he been called.

5. Davy bids seven fives. And at this point, Davy has hit the best possible bet in the game by adding what he guesses are Will's three fives to his own.

6. Will bids eight fives. Will's on shaky ground at this point, hoping there are more fives out there than the ones Davy was betting on. Bill looks at Will at this point and figures Will is going to lose since Bill knows he doesn't have any fives to add to the pool.

7. Bill bids twelve fives. Bill ups the bidding to a ridiculous level to make sure Will won't lose the game. Bill knows for a fact that there can't be twelve fives on the table since he has five out of the fifteen dice in his possession. Bill simply figures that it doesn't matter what he bids at this point, so he'll take the bid and lose the game.

8. Davy calls Bill a liar. The dice are shown, there are only seven fives on the table, so Bill loses and Will gets to walk away.

 

 

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