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Every call in liar's dice comes down to one question: how likely is that bid to be true? You can work it out. Each unseen die is an independent roll, so the number of matching dice follows a binomial distribution. This page gives you the numbers, so you do not have to do the sums at the table.
If you do not know the rules yet, start with how to play liar's dice.
The number to remember
How many dice you expect to match depends on the rule set. The two must never be mixed up (see wild ones vs straight ones).
| Bid on | Chance one die matches | Expected matches |
|---|---|---|
| Wild ones, face 2 to 6 | 1 in 3 (the face or a 1) | dice on the table ÷ 3 |
| Wild ones, bidding on 1s | 1 in 6 (only 1s count) | dice on the table ÷ 6 |
| Straight ones, any face | 1 in 6 | dice on the table ÷ 6 |
Bids well below the expected number are usually safe. Bids above it get risky quickly, and the further above, the closer a bid is to a pure bluff.
Wild ones: bids on 2 to 6
The biggest bid that still holds at least 75 %, 50 % and 25 % of the time, before anyone looks at their own dice. Players start with five dice, so ten dice is a two-player game, fifteen is three players, and thirty is a full table of six.
| Dice on the table | Holds 75 % | Holds 50 % | Holds 25 % |
|---|---|---|---|
| 5 | 1 | 2 | 2 |
| 10 | 2 | 3 | 4 |
| 15 | 4 | 5 | 6 |
| 20 | 5 | 7 | 8 |
| 30 | 8 | 10 | 12 |
Read it as: with ten dice in play, a bid of three of a face holds at least half the time, and a bid of four holds at least a quarter of the time.
Straight ones: any face
The same table for straight ones. It also applies to a bid on 1s under wild ones, since only the 1s count there.
| Dice on the table | Holds 75 % | Holds 50 % | Holds 25 % |
|---|---|---|---|
| 5 | 0 | 1 | 1 |
| 10 | 1 | 2 | 2 |
| 15 | 1 | 2 | 3 |
| 20 | 2 | 3 | 4 |
| 30 | 4 | 5 | 6 |
A 0 means that even a bid of one cannot be called safe before you look at your own dice. Bids are much lower in straight ones, and a single die matters more.
Your own dice change everything
The tables assume you know nothing. In a real game you know your own dice, so you subtract them from the bid and only the dice you cannot see are uncertain.
Wild ones, ten dice on the table. You hold 4, 4, 1, 2 and 5. Two 4s plus the wild 1 give you three matching dice, and five dice are unknown. How likely is each bid on 4s to hold?
| Bid | Chance it holds |
|---|---|
| three 4s | 100 % (you hold them) |
| four 4s | 87 % |
| five 4s | 54 % |
| six 4s | 21 % |
| seven 4s | under 5 % |
Straight ones, ten dice on the table. You hold 4, 4, 3, 2 and 5. Two matching dice, five unknown.
| Bid | Chance it holds |
|---|---|
| two 4s | 100 % (you hold them) |
| three 4s | 60 % |
| four 4s | 20 % |
| five 4s | under 4 % |
The same hand, the same number of dice, and very different odds. That is why the two rule sets play so differently.
When to call liar
Whoever is wrong loses a die. If the bid holds, the caller loses it. If it does not, the bidder does. So as a starting point:
- If the bid holds less than half the time, calling liar wins more often than it loses.
- If it holds more than half the time, raising is usually better than calling.
In the wild ones example above, calling liar on “five 4s” is a bad call: the bid holds 54 % of the time, so the caller loses the die more often than not. “Six 4s” holds only 21 % of the time, so that is a bluff.
The catch: bids are not random
These odds treat every unseen die as a fresh roll. But when an opponent raises, they usually did so for a reason: they hold the face, or want you to think they do. A player who bids a face three times in a row is probably holding it, and that makes their bid more likely to be true than the table says. Good players mix the maths with a read on the person. See the strategy guide for how.