Liar's Dice: Rules, Bidding Odds and When to Call a Bluff
Quick answer
In liar's dice, every player rolls their dice in secret, then players take turns bidding on how many dice of one face are on the whole table, raising each time, until someone calls the last bid a lie. On average, one in six of the hidden dice shows any given face, or one in three if 1s are wild. A bid is more likely true than false when it's at or below that average plus what you can see in your own cup.
| Players | 2 to 6 or more |
|---|---|
| Equipment | 5 dice and a cup per player |
| Expected count of a face (hidden dice) | 1 in 6 of them, or 1 in 3 if 1s are wild |
| Also called | Perudo, Dudo, bluff dice |
Liar's dice is a bluffing game, but behind every bid sits a simple probability question: how many dice on the table are likely to show that face? Learn the rules, then use the calculator to check any bid before you raise it or call it a lie.
How to play liar's dice
- Everyone rolls five dice under a cup and looks at their own dice in secret.
- The first player bids a quantity and a face, such as "four 3s", meaning at least four dice on the whole table show a 3.
- Each next player must raise: bid more dice of any face, or the same number of a higher face (some groups have different raising rules).
- Or call "liar" (in Perudo, "dudo") on the previous bid.
- Everyone reveals. If the bid was true, the caller loses a die; if it was false, the bidder loses a die.
- The last player with dice wins.
In many versions, especially Perudo, 1s are wild: they count toward any face that's bid.
Liar's dice bid calculator
Enter what you know: total dice in play, how many are yours, and how many of your own dice match the face being bid.
Is this bid likely true?
The maths behind every bid
Each hidden die matches the bid face with probability 1/6, or 1/3 if 1s are wild. The number of matches among the hidden dice follows a binomial distribution:
P(at least k matches among n hidden dice) = Σ C(n, i) × pⁱ × (1 − p)ⁿ⁻ⁱ, for i = k to np = 1/6 without wilds, 1/3 with wild 1s. Expected matches = n × p.
So with 15 hidden dice and no wilds, you'd expect 15 ÷ 6 = 2.5 of any face. If a bid needs 2 or fewer from the hidden dice, it's usually true; if it needs 5 or more, it's usually a lie.
Odds tables
Chance that at least k of the hidden dice show the bid face:
| At least | 5 hidden dice | 10 hidden | 15 hidden | 20 hidden | 25 hidden |
|---|---|---|---|---|---|
| 1 | 59.8% | 83.8% | 93.5% | 97.4% | 99.0% |
| 2 | 19.6% | 51.5% | 74.0% | 87.0% | 93.7% |
| 3 | 3.5% | 22.5% | 46.8% | 67.1% | 81.1% |
| 4 | 0.3% | 7.0% | 23.2% | 43.3% | 61.8% |
| 5 | 0.0% | 1.5% | 9.0% | 23.1% | 40.6% |
| 6 | 0.0% | 0.2% | 2.7% | 10.2% | 22.8% |
| 7 | 0.0% | 0.0% | 0.7% | 3.7% | 10.9% |
| 8 | 0.0% | 0.0% | 0.1% | 1.1% | 4.5% |
| At least | 5 hidden dice | 10 hidden | 15 hidden | 20 hidden | 25 hidden |
|---|---|---|---|---|---|
| 1 | 86.8% | 98.3% | 99.8% | 100.0% | 100.0% |
| 2 | 53.9% | 89.6% | 98.1% | 99.7% | 99.9% |
| 3 | 21.0% | 70.1% | 92.1% | 98.2% | 99.6% |
| 4 | 4.5% | 44.1% | 79.1% | 94.0% | 98.5% |
| 5 | 0.4% | 21.3% | 59.6% | 84.8% | 95.4% |
| 6 | 0.0% | 7.7% | 38.2% | 70.3% | 88.8% |
| 7 | 0.0% | 2.0% | 20.3% | 52.1% | 77.8% |
| 8 | 0.0% | 0.3% | 8.8% | 33.9% | 63.0% |
To use the tables, subtract your own matching dice from the bid. If the bid is "seven 4s", you hold two 4s and there are 20 hidden dice, the hidden dice need at least five 4s. Without wilds that's true about 23.1% of the time, so calling liar is a good bet. With wild 1s it's about 84.8%, so the bid is probably safe.
Liar's dice strategy
- Start from the expected count. Hidden dice ÷ 6 (or ÷ 3 with wilds), plus your own matches, is the bid that's roughly a coin flip. Bids well below it are safe, well above it are risky.
- Bid on faces you hold. Your own dice are certain; every one you hold makes the bid more likely true.
- Watch other players' bids. A player who keeps bidding a face probably holds some. That information isn't in the maths, which is what makes the game more than arithmetic.
- As dice disappear, re-do the maths. With fewer dice on the table, the expected counts shrink and bold bids become bluffs more often.
More dice games
- Farkle: rules, scoring and odds
- Yahtzee odds
- Online dice roller
Frequently asked questions
How many of a face should I expect in liar's dice?
For each hidden die, the chance of showing a particular face is 1 in 6, so expect one sixth of the hidden dice to match. If 1s are wild, a die matches if it shows the face or a 1, so expect a third. Add the matching dice you can see in your own cup.
When should I call liar?
When the bid is clearly above what's likely. With 20 hidden dice and no wilds, you'd expect about 3.3 of any face; a bid needing 6 or more from those hidden dice is true only about 10% of the time. Use the calculator to check any bid.
Are 1s wild in liar's dice?
In many versions, including Perudo, yes: 1s count as every face, and bidding on 1s themselves follows special rules. In others, 1s are just 1s. Agree before you start, because it doubles the expected count of every face.
Sources
- Liar's dice — Wikipedia
- Two Basic Rules of Probability — OpenStax, Rice University. Multiplication rule; independent events