My Stuff

This is where I put things that have temporarily captivated me.

Liar's Dice Calculator

I was recently unaware of the wonderful game Liar's Dice, but fortunately some of my good friends were kind enought to explain the rules to me. Basically Liar's Dice is a game that requires a little knowledge of probability, a propensity for bluffing, and a nose for BS, figuratively speaking.


The basics

  • Each player starts with five six-sided dice with a dice cup used for concealment.
  • Liar's Dice Cups
  • Every round each player rolls a "hand" of dice under their cup and looks at their hand while keeping it concealed from the other players.
  • The first player begins bidding, announcing any face value and the number of dice that the player believes are showing that value under all of the cups in the game.
  • Ones are often wild, always counting as the face of the current bid.
  • Each player has two choices during their turn: to make a higher bid, or challenge the previous bid - typically with a call of "Liar!"
  • Raising the bid means either increasing the quantity, the face value, or both.
  • If the current player challenges the previous bid, all dice are revealed. If the bid is valid (at least as many of the face value and any wild ones are showing as were bid), the bidder wins. Otherwise, the challenger wins.
  • For all of the rules and math behind the game, go here.

The Fun Part

The key to accurate bidding is quickly calculating the "expected quantity" (EQ). This is just the quantity of any dice face that has the highest probability of being correct.
  • For six-sided dice, this is 1/6 the number of dice in play, rounded down. So, for 18 dice on the table, the EQ of any face is 3, with about 59% probability. Interestingly, if you miscalculated or just wing it with a guess of 5, the probability that you are correct drops to 11%. And unless you're Le Chiffre, the only way you could know that is by using my awesome calculator, so keep reading.
  • When ones are wild, it is 1/3 the number of dice in play, rounded down. This is because ones are just as likely to be rolled as any other face value. So, for 18 dice on the table, the EQ of any face is 6, again, with about 59% probability.
  • Depending on what you have under your own cup, adjust your bid or expectations up or down.
  • Note that this only helps you understand the odds of various quantities of faces showing up - it will not help you when people start bluffing. Unfortunately that's outside the scope of this calculator!
So, when the bidding starts, whether it's you or someone else doing the bidding, you know where things stand. But what if you want to play it safe and increase the probability of your bid to something higher than the EQ? What if you want to play it risky and decrease the probability by going lower than the EQ to put the next bidder on ice? Or, what if people continue to bid higher and higher? It would be nice to know the exact probability of deviating higher or lower from the EQ, wouldn't it?

The Calculator

This is where a nifty little calculator comes in handy. It will allow you to:
  • Know the exact probability of any quantity of face value being present based on the number of dice currently on the table.
  • Adjust the calculation depending on whether ones are wild.

It does not, however, calculate exact odds of each face based on what you have under your own cup. I've assumed if you are using this, you are 1) cheating, so you'll need to be quick and discreet, 2) likely on a mobile device, so inputting 6 fields in rapid succession would be difficult and time consuming.

Lastly, given the fact that there is an element of bluffing involved, even if you are exact, it will not always win you the hand. Generally, it is helpful to simply have an idea as to the probability of the number you are about to bid so you can either increase the bid or call "Liar!" with a certain level of confidence.

And now, ladies and gentlemen, I give you the Icelandic Snow Owl! Er, the Liar's Dice Calculator.