MEZARPOLY

When should you call bluff? A card-counting probability guide

21 October 2026 · 4 min read

In Bluff (also known as Cheat or I Doubt It), half of winning is lying convincingly and the other half is calling "BLUFF!" at the right moment. Here we work out how likely a claim is from the cards in your hand: first a simple rule that catches certain lies, then probability tables for one-deck and two-deck tables.

1. A certain lie: your cards plus the claim go over 4
2. Probability table: one deck, 4 players
3. Claims get weaker as hands shrink
4. Two decks: 104 cards, 6–8 players
5. The player who opens the round is different
6. The cost of a call is the size of the pile
7. When you lie, use the table in reverse

A certain lie: your cards plus the claim go over 4

With one deck there are exactly 4 cards of each rank (8 with two decks). If an opponent says "three 9s" and you hold two 9s, they cannot possibly have played three 9s: 2 + 3 = 5, which is more than 4. Calling that play is risk-free: the liar takes the pile and you start the next round.

Keep counting through the round. The named rank does not change until the round ends, and the number of cards claimed for it adds up on the table. If earlier plays, the last play and your own cards add up to more than 4, at least one play was a lie. But note that you can only call "BLUFF!" on the last play. When the total goes over, the lie may have been in an earlier play. The last play is only a certain lie if it goes over the limit on its own, together with your cards.

Probability table: one deck, 4 players

A certain lie is rare; most of the time you are weighing odds. The table below shows the chance that an opponent really holds as many cards as they claim, assuming the cards were dealt at random. Row: how many of that rank you hold. Column: how many cards the opponent claimed. The numbers assume the opponent holds 13 cards, as at the start of the game.

A "—" means the claim is impossible, so it is a certain lie. Three lessons from the table:

• Even when you hold none of that rank, a claim of "three" is true only about 9.9% of the time.
• When you hold one, a claim of "two" is true roughly one time in four (25.3%).
• A claim of "one" is usually true. Calling a single card usually costs you.

Claims get weaker as hands shrink

The fewer cards an opponent holds, the more suspicious the same claim becomes. For an opponent with 6 cards left:

Even when you hold none of that rank, an opponent with 6 cards left saying "two" is telling the truth only 10.4% of the time. Late in the game, big claims are mostly lies.

Two decks: 104 cards, 6–8 players

At crowded tables (two decks are recommended for 6 or more players) there are 8 cards of each rank and claims become more believable. The certain-lie limit rises to 8. With 6 players and an opponent holding 17 cards:

With two decks, a claim of "two" is close to a coin flip even when you hold none (49.0%). At a crowded table, wait for stronger evidence before calling.

The player who opens the round is different

The tables are for players who must play a rank someone else chose. The player who opens the round picks the rank and usually names the one they hold most of, so their claim is true more often than the table suggests. Calling the opening play is riskier than calling the plays that follow.

The cost of a call is the size of the pile

• If you are wrong, you take the whole pile. With 3 cards in the pile, a wrong call costs little; with 20 it can cost you the game. Call freely on small piles and only with strong evidence on big ones.
• Almost always call a player who plays their last cards. If you don't, the game ends and they win. If you are wrong, the game still ends; the only cost is taking the pile and dropping in the standings (the other players are ranked by how many cards they hold).
• The window to call is short (6 seconds by default, then the next card is played). Know your own counts in advance so the maths is done before the play comes round.
• Remember who gets caught. Mezarpoly's bots do: they call more readily on players who have been caught lying before, and they want stronger evidence as the pile grows.

When you lie, use the table in reverse

Your opponents can do the same maths. A claim of "one" draws the least suspicion; make big claims like "three" or "four" only when you really hold them. If you are going to lie, lie small: saying "one" instead of "two" clearly lowers the chance of being caught. When you play your last cards, expect everyone to call: the safest game-ending play is a true one.

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