Shut the Box and Liar's Dice: rules, scoring and odds

Shut the Box: how to play

You need a box of numbered tiles (1 to 9 is the classic, some boxes go to 10 or 12) and two dice. Every tile starts open, meaning standing up.

1. Roll both dice and add them. Say you roll a 6 and a 3: the total is 9.
2. Shut tiles that add up to the total. With everything open you could shut the 9, or the 6 and the 3, or 5 + 3 + 1, or 4 + 3 + 2, among others. Pick one set. You can only use open tiles, and each tile once.
3. Roll again and do the same with the tiles that are left.
4. Your turn ends when a roll gives you no set of open tiles that matches the total, or when the whole box is shut.
5. Score what is still standing. If 1, 4 and 7 are still open you have 12 points. Lower is better, and a shut box is zero.

House rules that change the game

What you may shut. The usual rule is any open tiles that sum to the roll. A stricter version only lets you shut the single tile equal to the total, or the two tiles showing on the dice (and only if the dice differ). The strict version is far harder; see the table below.

One die. Near the end, a total of two dice is often too big for the small tiles left. Groups handle it differently: never roll one die, roll one die automatically once the open tiles add up to 6 or less, or let the player choose one die or two once every tile from 7 up is shut.

Box size. 9 tiles is standard. 10-tile and 12-tile boxes exist and make a shut box much rarer.

Three ways to score

Liar's Dice: how to play

Each player has a cup with the same number of dice (five is the usual). The goal is to be the last player with a die.

1. Everyone rolls in secret. Shake your cup, peek at your own dice, keep them hidden.
2. Bid on the whole table. A bid like "four fives" claims that, counting every cup together, there are at least four dice showing five. Nobody knows more than their own cup, so a bid is a mix of what you hold and what you guess.
3. Each bid must go up. Either more dice ("five fives" after "four fives") or the same number of a higher face ("four sixes" after "four fives").
4. Or call it. Instead of raising, say "Liar!" if you think the last bid is too high. Everyone lifts their cups and counts. If there are at least as many as bid, the bid held and the caller loses a die. If there are fewer, the bidder loses a die.
5. Next round. Re-roll and go again; in Nine Down the player who lost the die opens the next round. A player with no dice is out. Last cup standing wins.

Wild ones

A common option: every 1 counts as whatever face is being bid, so a bid on fives is met by fives and ones together. The exception is a bid on ones themselves. Once anyone bids on ones in a round, nothing is wild until the cups are lifted. Turning wild ones off makes ones an ordinary face, and the odds fall to one in six per die.

"Spot on"

An optional extra call. Instead of "Liar!" you can say the last bid is exactly right. If the count matches the bid exactly, the bidder loses a die; if not, you lose one. It is risky because exact counts are less likely than "at least" counts.

A simple way to judge a bid

Count the dice in your own cup that match. Subtract that from the bid to see how many matching dice you need from the other cups. Then look up in the table below how likely that is. A bid that needs only one or two from many hidden dice is usually safe; a bid that needs half of them or more is where bluffing lives.

The odds, calculated exactly

Shut the Box: chance of shutting the whole box

These are exact figures for a player who always makes the move that gives the best chance of shutting the box.

The 9-tile figures match published single-player analyses of the game.

Your first roll in a 9-tile box

With any-combination moves and the one-die-at-6-or-less rule, here is how likely each first total is, which move keeps the best chance of shutting the box afterwards, and what that chance is.

The pattern: shut the one big tile when you can. High tiles are hard to remove later, because only a few rolls make them, while low tiles can be made by many combinations.

Liar's Dice: at least this many matches among unseen dice

"Unseen dice" are the dice in cups other than yours. Read across for how many matching dice you need from them. Without wild ones, each unseen die matches with probability 1 in 6.

Example. You hold two fives in a five-dice cup, with ones wild, and a rival has just bid "six fives" with ten dice unseen. Both of your fives count, so you need 4 more from the 10 unseen dice: 44.1%. So the bid holds about 44% of the time, and a "Liar!" call would be right about 56% of the time.

These assume every unseen die is a fair, independent roll. Real opponents bid for reasons, so their bids tell you something too. In a bid on ones, or with wild ones off, use the first table.

Quick answers