Bluff poker

Final Project for the Multi Agent Systems Course

By Marten Schutten (s1777475) and Michiel van de Steeg (s1793489)

Bluff poker is an easy dice game, which can be played with any number of players, and for which one only needs three dice, a cup to throw the dice with and a flat surface to throw the dice on. The goal is to deliver penalties to your opponents by being able to outbid or outbluff them. In this section, a thorough explanation of the game will be given. An explanation in Dutch can also be found at wikipedia. The explanation given here is mainly based on this source.

First we will give an impression of how a regular turn is played (which describes the mnain mechanics of the game). We will then present the way in which the resulting value of the dice is determined.

A regular turn

When it's a players' turn, the player throws the dice, and makes a bid. Then the next player can do one of two things: either believe the bid, or call a bluff. The implications of both of these actions will now be viewed. Finally we will describe some of the special situations which can occur during th game (such as starting a new round)

Believe

Believing a bid, means that the next player believes that the result of the other players' dice are actually of the same value as (or higher than) the bid. The next player now has to make a new bid, exceeding the bid of the previous player. He can do this in one out of two ways: passing the cup along blindly, or try to rethrow the dice in order to get a new (better) result.

Passing the cup along blindly, implies that you think that the previous player bid lower than his actual result. You just make a bid, without looking at the dice, and have faith that the previous player actually rolled higher than you bid.

Rerolling means that you have to reroll at least one of the dice, in order to improve the result of the dice. You may throw each die one, however do not have to throw them all, and may choose to throw them not at the same time. For example, I first may choose to reroll the lowest die and then, when I failed to exceed the previous players' bid, reroll another die (or both).

A player may choose whether he either throws the dice open or closed, i.e. either under the cup, or in such a way that the other players can view the result. All dice can either be hidden under the cup, or be open. Hence, when we throw one die closed, the other two dice will be revealed to the other players.

Once a player is content with its result, or he can't throw any more dice, he has to make a new bid, exceeding the previous players' bid.

Call bluff

When the next player calls a bluff, the cup is lifted and all dice are revealed. When the resulting value is equal to or higher than the previous players' bid, the next player receives a penalty. When the previous player actually bluffed (and bid a higher value than actually was thrown), the previous player recieves a penalty.

Values of the dice

As stated in the previous section, there are three dice, which result in a single value. The resulting value consists of a factor of hundreds, a factor of tens, and a factor of ones. The highest die determines determines the hundreds, the second highest value determines the tens, and the final value determines the ones. For example, when we throw a 5, 3 and 2, the resulting value is 532. When we throw 3,6 and 1, the resulting value will be 631.

When one of the values is doubled it of course doesn't matter in which order they are placed, since they are the same. Hence, when we throw 6,6 and 3, the value is 663. And 3, 1 and 1 results in 311.

It speaks for itself which of two values is higher, however there is one exception. When we throw a triplet (i.e. that all dice have the same value), we have a special occasion. These values are called pokers. A poker is always higher than a non-poker, however there are some special rules when throwing a poker, which wll be explianed with the other special occasions.

In total there are 56 different possible results. In the table below we give a short overview of the results, from high to low.

666 652 552 441
555 651 551 433
444 644 544 432
333 643 543 431
222 642 542 422
111 641 541 421
665 633 533 411
664 632 532 332
663 631 531 331
662 622 522 322
661 621 521 321
655 611 511 311
654 554 443 221
653 553 442 211

Special Situations

Starting a new round

When a player has received a penalty, a new round is started. This round has to be set up by the player who recieved a penalty. This first turn is different from a regular turn. During their first turn, a player always throws all dice. After looking at the dice, the player can decide to make a bid, or reroll the dice. After rerolling the player can look again and make a bid or reroll a second time. However, after rolling a third time the player can not look at the dice anymore, and has to make a blind bid. Note that during the first turn, it is not possible to reroll a subset of the dice.

Pokers

As stated before, pokers are the highest values in the game and occur when a triplet is thrown (i.e. 111). When a player bids a poker, things slightly change. The next player can either believe a bid or call a bluff. When he thinks the previous player bluffs things remain the same, however things slightly change when a bid of a poker is believed.

When a player believes that a poker is thrown he has three chances to throw a poker himself. The dice are thrown open, and in the first turn all dice are thrown. After the first throw a player can choose to rethrow any number of the dice, as long as the number of throws doesn't exceed three. If the player isn't able to throw a poker, he receives a penalty. When he throws a poker of an equal or higher value, no penalties are applied. Finally, when a higher poker is thrown the previous player receives a penalty.

Winning the game

This last one isn't really a special situation, but rather a special rule. The game doesn't know a winner, only a loser. Once a player reaches a penalty of 7 he loses the game, and the game is over (or starts over completely).