How to play Liar's Dice (Perudo)
Four players, five dice each, rolled in secret under a cup. You can see your own five and nobody else's. A bid is a quantity and a face — "four fives" — and it is a claim about every die on the table, yours included, not just your own cup. Play passes round; each player must raise the standing bid or call.
Ones are wild. A one counts as any face, so "four fives" is satisfied by any mix of fives and ones adding to four. The exception matters: for a bid of aces, a one is only a one. That is why a bid of aces is worth roughly double the same quantity of any other face, and why the rules make you halve to enter them and double-and-add-one to leave.
Instead of raising you may call dudo — "I doubt it". Every cup is lifted and the matching dice are counted. If there really are that many or more, the bid stood and you lose a die; if there are fewer, the bidder loses one. Exactly the number bid means the bid stood, because a bid claims at least — which is the off-by-one that decides one challenge in six.
You may also call calza (exact): a claim that the standing bid is precisely right, not merely true. Get it exactly and you take a die back, up to your starting five; get it wrong and you pay one. The bidder is unaffected either way, which surprises people. A player on zero dice is out, and the last player still holding dice wins.
The rule almost every table gets wrong
Ask a casual Liar's Dice player whether "six twos" beats "five sixes" and most will say no — that the face can never go down. It can. Raising the quantity frees the face completely; the face only has to climb if you are keeping the quantity where it is. A table playing the wrong version has deleted most of its own legal moves, which makes sixes absurdly strong and turns the endgame into a staring contest.
This board does not argue the point, it draws it. The grid under the table is the whole bid space: quantities down the side, the six faces across, and every cell that is a legal raise from the standing bid is lit. After "five sixes" the row for six is lit end to end — ones through sixes — and the row for five is lit only where the face exceeds six, which is nowhere. You learn the law by looking at the shape rather than by being told it.
What the numbers on the grid mean
Each lit cell carries the probability that the bid is true, and it is exact rather than simulated. Your own matching dice are known — they are not a probability at all — so the only uncertainty is in the dice you cannot see. Each unseen die matches with probability 1/3 when aces are wild and the bid is not aces, and 1/6 for a bid of aces or in a palifico round. The number of hits among the n unseen dice is therefore Binomial(n, p), and the chance the bid is true is the upper tail P(X ≥ quantity − your own hits).
Two consequences you will feel within a round. First, your own cup moves the number a long way: holding three fours makes "six fours" a far better bid than the table average would suggest, and the grid shows that immediately. Second, a bid that is 60% true is not necessarily a good bid, because the player after you gets to raise it — the grid prices honesty, not strategy, and the page will not pretend those are the same thing.
Can you trust the dice?
Liar's Dice is nothing but hidden dice, so "trust us" is a weak answer and we do not give it. Before the first roll the page publishes the SHA-256 hash of a server seed. You may type a seed of your own; if you do not, one is generated for you. Every die of every round is a pure function of the two seeds and its index, so the whole game is fixed before you see a single face, and it cannot depend on how you are doing or on what the bots are holding.
When the game ends, the server seed is revealed. Hash it yourself, check it against the commitment you were shown at the start, and re-derive every die on the verification page. If one die had been altered, the seeds would not reproduce the game you played.
What these bots can and cannot do
They compute. Each bot values the standing bid and every raise available to it from its own cup and the number of dice it cannot see, using the same function that prints your numbers — it is never shown another player's dice, so it cannot cheat by construction. The three levels are three settings of the same published thresholds, and which of them is hardest was measured, not decided. The first attempt made the top level a bot that overbid and challenged thin — the intuitive picture of a dangerous player. Played head to head it was no better than chance.
What actually separates a strong Perudo bot from a weak one turned out to be a single number: how unlikely a bid has to look before it stops raising and calls. A 27-point sweep, 300 games a cell, scored as how often the reference bot beats three copies of a tune — 0.250 is chance:
Challenge at 32% and the reference wins 0.301, so that tune is worse than chance. At 25%, 0.251 — level. At 18%, 0.211 — clearly stronger. Confirmed at 800 games on two independent seed sets, where the standard error is 1.5%, so the ends sit about six standard errors apart. Jumpy, Steady and Patient are those three points, in that order.
The finding is worth more than the bots are: the losing move in this game is calling dudo too soon, not bidding too boldly — the opposite of the advice most tables give. And the patient setting makes the better game as well as the harder one, at 4.2 bids a round against Jumpy's 2.4, because it does not end the round the moment the arithmetic dips below even money. What it is not is a strength claim against a human: it is a tournament between three settings of one bot, and it says only that they differ and in which direction.
The honest limitation, stated plainly: they do not read you. A real opponent treats your jump to "eight fours" as evidence about your cup, hesitates, and has tells. These have none of that, and no amount of correct probability substitutes for it. What you get here is the arithmetic half of the game played properly and a board that teaches you to price a bid; the psychological half needs people, and live tables for this game are not built yet.
Frequently asked questions
Can you bid a lower face than the last player?
Yes, if you raise the quantity. "Five sixes" is legally beaten by "six twos". The face only has to climb when the quantity stays the same. This is the most misremembered rule in the game.
Are ones wild?
Yes in Perudo — except for a bid of aces, where a one is only a one, and except in a palifico round, where nothing is wild.
What if the count is exactly the number bid?
The bid stood, because a bid claims at least that many. The challenger loses the die. If you thought it was exactly right you should have called calza instead.
How many aces to switch to ones?
Half the standing quantity rounded up — after "eight fives" you may say "four aces". To leave aces you double and add one: after "four aces" the next bid must be at least nine of something.
What is palifico?
The round after a player first drops to one die. That player opens, aces are dead, and the face they name is locked for the whole round — everyone else may only raise the quantity.
Is Perudo the same as Liar's Dice?
Perudo is one branch of the Liar's Dice family and it is the one played here: five dice, aces wild, calza and palifico. It is not the Milton Bradley game sold as Bluff, whose exact call costs every other player a die instead of returning one to the caller.
Is it free?
Yes — no signup, no ads, no coins, nothing to buy, and the odds panel is not a paid hint.