Liar’s Dice Odds & Bid Checker
Work out whether a Liar’s Dice bid is likely — and see why the "k ones equals 2k+1" rule is a bidding ladder, not a statement about odds.
Ones are wild, so every unknown die is a third — not a sixth
This is the expensive mistake. Ones count as every other face, so an unknown die matches whatever you are bidding one time in three. The expected count doubles, and so does the height the bidding reaches.
| Dice on the table | Expect, of any face | Expect, of ones | A 50/50 bid is about |
|---|---|---|---|
| 5 | 1.67 | 0.83 | 2 |
| 10 | 3.33 | 1.67 | 3 |
| 15 | 5.00 | 2.50 | 5 |
| 20 | 6.67 | 3.33 | 7 |
| 25 | 8.33 | 4.17 | 8 |
| 30 | 10.00 | 5.00 | 10 |
With twenty-five dice out, expect 8.33 of any face — not 4.17. Beginners fold at bids that are comfortably below average.
And “k ones equals 2k+1 of a face” is not an odds rule
Every rulebook gives that conversion for switching a bid into or out of ones, and it is stated so flatly that it reads like a claim about likelihood. It is not — it is the legal ordering of bids. As a statement about odds it is wrong, and worse the higher you go. With twenty unknown dice:
| Bid | Chance | Ranked equal to | Chance of that | Fair equivalent |
|---|---|---|---|---|
| 1 one | 97.4% | 3 of a face | 98.2% | 3.2 |
| 2 ones | 87.0% | 5 of a face | 84.8% | 4.8 |
| 3 ones | 67.1% | 7 of a face | 52.1% | 6.2 |
| 4 ones | 43.3% | 9 of a face | 19.1% | 7.5 |
| 5 ones | 23.1% | 11 of a face | 3.8% | 8.7 |
| 6 ones | 10.2% | 13 of a face | 0.4% | 9.9 |
Calling five ones is not a bold equivalent of eleven sixes. At 23.1% against 3.8% it is six times as likely, and the fair exchange is about 8.7 of a face, not eleven. By six ones the ratio is 27×.
It is not uniformly harsh, though, and that is worth knowing at the table: at the very bottom of the ladder it is generous, and the crossover moves as dice come and go — 0 rungs at 10 dice, 0 rungs at 15 dice, 1 rung at 20 dice, 2 rungs at 25 dice, 3 rungs at 30 dice. Early in a game the first few rungs are a fair deal or better; late on, with few dice left, every rung overshoots.
How to use
- Enter how many dice you cannot see, and the bid on the table.
- Type your own dice — wild ones are counted for you.
- Read the chance the bid is good before you call.
- Check the ones ladder before switching a bid into or out of ones.
Frequently asked questions
What is the probability of a face in Liar’s Dice?
One in three, not one in six, because ones are wild and count as every other face. That doubles the expected count: with twenty-five dice on the table expect 8.33 of any face rather than 4.17. Folding to a bid below that average is the commonest beginner mistake.
Is a bid of k ones really equal to 2k+1 of a face?
Only as a bidding ladder. As a statement about odds it is wrong and grows worse the higher you go: with twenty unknown dice, five ones is 23.1% while eleven of a face is 3.8% — six times as likely — and by six ones the ratio is twenty-seven to one.
What is a fair swap for a bid of ones?
Closer to double than double-plus-one, and it is not a whole number. With twenty unknown dice, five ones is about as likely as 8.7 of an ordinary face, not the eleven the ladder ranks it beside. This page works the equivalent out exactly rather than quoting a rule of thumb.
Is the ones rule always harsh?
No, and the crossover moves with the table. With ten or fifteen unknown dice every rung overshoots, but at twenty the first rung is generous, at twenty-five the first two are, and at thirty the first three. Early in a game the bottom of the ladder is a fair deal or better; late on it never is.
Do my own dice count as wild too?
Your own ones count towards any ordinary face you bid, so a hand of 3, 3, 5, 1, 6 holds three threes. When the bid is ones themselves, only the actual ones count, because ones are not wild for their own face.
How many of a face should I expect?
A third of every die you cannot see, plus whatever you hold. Ten unknown dice give 3.33, twenty give 6.67, thirty give ten. A bid at or just under that figure is usually safe, and the fifty-fifty point sits a little above it.
How are these numbers worked out?
From the binomial distribution, checked against an exhaustive count of every way up to eight dice can fall — a plain tally rather than a formula — so the maths behind the big tables is verified on the small cases first.
Does this send anything anywhere?
No. Everything is worked out in your browser and nothing is stored or uploaded.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.