Bluff!

The board/dice game is by Richard Borg and published by Paul Lamond Games. Postal adaptation by Richard Smith 2000.

F2F Rules Summary

Each player starts with 5 dice which he rolls secretly and conceals under a black pot. The first player makes a bid such as "six threes", and places the red dice on the appropriate square (in this case the 6, with the number 3 showing on the dice). The bidder is claiming that at least 6 of all the dice (his own dice which he can see, plus the other players' dice which he can't) are a three or a star. The star is a "joker" which replaces the 6 on each dice. Note that a player can bid stars (see board).

The next player may either challenge the current bidder, or make a new bid which must be higher than the previous one (n.b. six fours is higher than six threes).

Additionally (not in all versions of the rules but is allowed in the VP game), a player may change the odds by exposing one or more dice, and re-rolling the remainder in his pot. The bid must of course be announced before the re-roll, and at least one die must remain concealed.

Play continues until a challenge is made, when all dice are revealed:

• If the bidder is short then he loses the number of dice he is short by. For example if the bid was ten fours, and only 8 (including stars) were present, he loses two.
• If the bid is spot on, all players lose one dice except the bidder.
• If the bid is over, then the challenger loses the number of dice in excess.

Remaining dice are then rerolled and bidding then resumes with the successful bidder or challenger. The last player to have any dice left wins.

Postal Rules

The postal version is played with exactly 5 players, and there are 5 mini-games (one challenge only) taking place simultaneously. The players are numbered 1 to 5 by random determination.

• Mini-game 1: Each player has 5 dice and player 1 bids first.
• Mini-game 2: Each player has 4 dice and player 2 bids first.
• Mini-game 3: Each player has 3 dice and player 3 bids first.
• Mini-game 4: Each player has 2 dice and player 4 bids first.
• Mini-game 5: Each player has 1 dice and player 5 bids first.

Players are emailed or posted details of their holdings in each mini-game every turn.

At the conclusion of each mini-game, "virtual" dice are removed (i.e. for scoring purposes only). The winner is the player with the highest number of virtual dice remaining (all players start with 5) when all mini-games are complete.

NMRs: In the event of an NMR you raise one in whatever the previous bidder said. So, faced with a bid of 6 3's the NMRer would automatically bid 7 3's. Should the opening bidder NMR, he automatically bids one 1, thus losing the advantage of bidding first.

VARIANT: One-on-One Algorithm Challenge

by Richard Smith 2002

One of the trickiest situations in a game of Bluff! is what to bid when it's down to one dice versus one. Going first is a mixed blessing in this situation, as is getting a star.

Following articles in Variable Pig regarding whether or not there really is a "winning" strategy, it was decided to put it to the test by means of a competition between robot players, each programmed with their own algorithm. The robot players play each other on a round robin to determine the best overall. Subsequently the winning algorithm might be tested against human opponents (who do not know what the algorithm is) in real games of Bluff!

The competition works as follows:

Each algorithm "plays" all the others on a one v. one basis. Each "game" consists of drawing up two grids of all 36 combinations, one for each player going first. If there are plenty of algorithms submitted then the game can be played on a single round basis. Alternatively, the game can be run over a number of rounds - the first batch of algorithms play off and the results (but not the details of the algorithms) are printed and other players may then submit algorithms to challenge the existing ones.

Each player submits a set of rules for when bidding first, and one for when going second. These rules can be as simple or complex as the player wishes. An example of very simple algorithm is:
Going first, always open one 5, then challenge thereafter
Going second, always challenge

Rules can be conditional on the value of your own dice and on opponent's bids.

Players' algorithms are secret until after the game.