Embedded Files
An app by Timothy Dewey
Yazee, a classic dice game
Yazee, a classic dice game
Description
Description
Yazee is an exciting game of strategy. It is easy to learn, but difficult to master. Hone your skills using a hint that reveals the optimal choices. A Yazee (5 of a kind) is 50 points, but a second Yazee yields a bonus of 100 points. Choose you favorite background color. Set a name for high scores, keep track of your average score, and challenge your friends on Game Center.
Rules
Rules
A game of Yazee consists of 13 turns. Each of turn is up to 3 rolls of 5 dice. After each roll, decide which dice to hold and which dice to roll. After 3 rolls, choose one category that has not yet been chosen. The score for the turn depends on the dice and the category. There are six upper categories (1's through 6's). For each upper category, the score is the sum of the dice which hold the value of the category. For example, a final roll of 3,3,2,2,1 would score 6 points in the 3's category, 4 points in the 2's category, 1 point in the 1's category, and 0 points in the 4's, 5's, or 6's category. If a total of 63 points or more is scored in the upper section, a bonus of 35 points is awarded. The lower section has 7 categories (3K, 4K, FH, SM, LG, CH, YZ). Below is the summary of the 7 lower categories.
3K (3 of a Kind): The score is the sum of all the dice if there are at least 3 dice with the same value and 0 otherwise.
4K (4 of a Kind): The score is the sum of all the dice if there are at least 4 dice with the same value and 0 otherwise.
FH (Full House): The score is 25 if there are 3 dice with one value and 2 dice with another value (or if the roll is a Joker) and 0 otherwise.
SM (Small Straight): The score is 30 if the values of the dice contain 4 consecutive (or if the roll is a Joker) and 0 otherwise.
LG (Large Straight): The score is 40 if the values of the dice are 5 consecutive values (or if the roll is a Joker) and 0 otherwise.
YZ (Yazee): The score is 50 if all 5 dice have the same value and 0 otherwise.
Joker: A Joker is a 5 of a Kind when the YZ category is filled AND the upper category corresponding to the value of the 5 dice is filled. A Joker can be used as 25 points in FH, 30 in SM, or 40 in LG. It can also be played in any other open category for the usual score. If YZ is filled with 50 points, then a Joker (or any 5 of a Kind) yields a 100 point bonus.
About Yazee
About Yazee
Yazee is capable of computing the optimal decision at any point in a Yazee game. The decision is optimal in the sense that it maximizes the expected value of the final score of the game. This means that to maximize the average score over a large number of games, the hint provided by Yazee is the best choice to make. Yazee determines this score using several precomputed tables.
The main table is a list of the expected score for the remainder of the game at the end of a turn. The computation of a similar table is described in [1]. There are over 200 billion possible ways to fill in a Yazee score card, but we can condense this to about 500,000 states of a Yazee game. This table takes just 2 MB (in [1] a 6 MB table is mentioned). The Yazee table is compressed by using single precision floating point, and removing the unreachable states. That is, we removed any state that had expected value 0 since this is an illegal state based on the rules of Yazee. Below is a histogram of 150,000 scores resulting from optimal play.
Contact timothydewey.apps+yazee@gmail.com or td.yazee@gmail.com for support.
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