Bluff is a game for two or more players; each of them has a set of five 6-sided dice, some of which are visible to the other players, and some of which are hidden - only their owner can watch them.
Dice combinations have different values: in ascending order,
Within each category, the highest-valued dice have priority. Three two's are better than three ones; three two's and a six are better than three two's and a four.
At the beginning of the game, each player rolls all of the dice and keeps the resulting combination hidden. Then, each player declares a score; this score might match the actual dice rolled, might be underestimated, or might be a bluff.
Whoever declares the highest score receives one point from all of the other players; the second highest bidder receives one point from lower score bidders; and so on, down to the player who declared the lowest score, who pays one point to every other player in the game.
At this point, each player has to decide whether to trust other players' bids, or to call someone else's bluff. If player A declares that player B bluffed, and player B was not bluffing, A pays one point to B. If B was bluffing, on the other hand, two points are transferred from B to A.
Declaring a wildly high score, therefore, is not a wise strategy: one will gain one point per player in the first phase, but will lose twice the amount when every other player will call the bluff.
Never bluffing leads to somewhat better results; however, it is not the optimal choice, as will be proven with a simplified model.
The best strategy consists in bluffing only some of the times: the opponents will be confused into calling a bluff when one is not bluffing, and vice versa.
After every player has decided which bids to trust, the computer will reveal to everyone which players were bluffing and which players were not bluffing. The actual values of the dice, however, are not disclosed.
Each player can now reroll any amount of dice (none, all, or some). The number of rerolled dice is notified to everyone; the actual rerolled dice are kept private. Then, every player has to reveal the values of two dice to the other players; the choice of which dice is up to the player.
At this point, the game starts anew, with the added quirk that some of the dice are visible. There is another turn of bidding and another turn of trusting/not trusting other players' bids.
After the second hand of the game is over, the reroll-show-bid-trust process is repeated once more. This time, however, four out of five dice are visible: each player gets to keep only one die hidden.
Once the third hand is complete, the game is over. It is possible to restart from the beginning, rerolling all the dice.
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