YahtzeeSolver

java.lang.Object
- YahtzeeSolver

```
public class YahtzeeSolver
extends java.lang.Object
```
YahtzeeSolver - a class for retrograde analysis of Upper Section Yahtzee. Working backwards turn-by-turn from the YahtzeeWidgets with only 1 unscored category remaining, each widget of a turn has its expected score value computed as a retrograde analysis from the last scoring decision backwards to the first reroll decision. For the final turn, the last scoring decision is based on the score plus the end game bonus of 35 or 0 depending on whether or not the upper bonus limit has been reached. On early turns, scoring decisions are based on the score plus the expected score of corresponding next-turn widgets. For the second (and then first) reroll, one will either immediately score or select a reroll of one or more dice such that expected future score is maximized. The expectation of the widget at the beginning of the turn may then simply be computed as the expectation of an arbitrary roll where all dice are rerolled. If there is a tie between actions, scoring is chosen over rerolling, and lesser category/reroll indices are chosen over greater.

Field Summary

Fields
Modifier and Type	Field and Description
`static int`	`ALL_SCORED` constant encoding the fact that all categories have been scored (game end)
`static int[][]`	`catRollIdScore` Lookup table of score gained, indexed by score category index and the roll id.
`static int`	`NUM_CATS` number of scoring categories
`static int`	`NUM_DICE` number of total dice
`static int`	`NUM_RANKS` number of dice ranks
`static int`	`NUM_ROLLS` number of unique sorted rolls for all dice
`static int`	`UNKNOWN` constant for indicating that a nonnegative integer is unknown
`static java.util.TreeMap<java.lang.Integer,java.util.TreeMap<java.lang.Integer,YahtzeeWidget>>`	`widgetMap` Multilevel map allowing lookup of YahtzeeWidget objects indexed by scored categories id and current score (truncated at the upper section bonus limit).
`static java.util.ArrayList<java.util.TreeSet<YahtzeeWidget>>`	`widgets` List of YahtzeeWidget sets grouped according to 0-based turn number.

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`getExpScore()` Return the expected score for optimal play of Upper Section Yahtzee.
`static java.lang.Object[]`	`getOptimalActionAndScore(boolean[] scoredCatsArr, int[] currentRoll, int numRerollsTaken, int score)` Given a boolean array indicating scored categories, an array with the current roll, the number of rerolls that have been taken this turn, and the current score, return a length 2 Object array where the first Object is an Integer encoding the optimal action, and the second is a Double indicating the score expected from that action assuming continued optimal play.
`static void`	`main(java.lang.String[] args)`
`static int`	`playGame()` Simulate an optimally played game and return the final score.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - NUM_DICE
```
public static final int NUM_DICE
```
    number of total dice
    
    See Also:
    
    Constant Field Values
  - NUM_RANKS
```
public static final int NUM_RANKS
```
    number of dice ranks
    
    See Also:
    
    Constant Field Values
  - NUM_ROLLS
```
public static final int NUM_ROLLS
```
    number of unique sorted rolls for all dice
  - NUM_CATS
```
public static final int NUM_CATS
```
    number of scoring categories
  - UNKNOWN
```
public static final int UNKNOWN
```
    constant for indicating that a nonnegative integer is unknown
    
    See Also:
    
    Constant Field Values
  - ALL_SCORED
```
public static final int ALL_SCORED
```
    constant encoding the fact that all categories have been scored (game end)
  - widgets
```
public static java.util.ArrayList<java.util.TreeSet<YahtzeeWidget>> widgets
```
    List of YahtzeeWidget sets grouped according to 0-based turn number. widgets.get(0) contains the single game beginning widget, whereas widgets.get(NUM_CATS - 1) contains all game widgets for the last turn.
  - widgetMap
```
public static java.util.TreeMap<java.lang.Integer,java.util.TreeMap<java.lang.Integer,YahtzeeWidget>> widgetMap
```
    Multilevel map allowing lookup of YahtzeeWidget objects indexed by scored categories id and current score (truncated at the upper section bonus limit). For example, widgetMap.get(42).get(63) returns a widget corresponding to scoredCat 42 and having achieved the upper section bonus limit of 63.
  - catRollIdScore
```
public static int[][] catRollIdScore
```
    Lookup table of score gained, indexed by score category index and the roll id.
- Method Detail
  - getOptimalActionAndScore
```
public static java.lang.Object[] getOptimalActionAndScore(boolean[] scoredCatsArr,
                                                          int[] currentRoll,
                                                          int numRerollsTaken,
                                                          int score)
```
    Given a boolean array indicating scored categories, an array with the current roll, the number of rerolls that have been taken this turn, and the current score, return a length 2 Object array where the first Object is an Integer encoding the optimal action, and the second is a Double indicating the score expected from that action assuming continued optimal play. The optimal action is encoded as follows: If the action is less than the number of scoring categories (NUM_CATS), then the action is to score in the given category index (0 for 1s, 1 for 2s, etc.). If the action is greater than or equal to NUM_CATS, then the player is to reroll with reroll id equal to the action number minus NUM_CATS.
    
    Parameters:
    
    scoredCatsArr - a boolean array indicating scored categories
    
    currentRoll - an array with the current roll
    
    numRerollsTaken - the number of rerolls that have been taken this turn
    
    score - the current score a length 2 Object array where the first Object is an Integer encoding the optimal action, and the second is a Double indicating the score expected from that action assuming continued optimal play.
    
    Returns:
    
    a length 2 Object array where the first Object is an Integer encoding the optimal action, and the second is a Double indicating the score expected from that action assuming continued optimal play. The optimal action is encoded as follows: If the action is less than the number of scoring categories (NUM_CATS), then the action is to score in the given category index (0 for 1s, 1 for 2s, etc.). If the action is greater than or equal to NUM_CATS, then the player is to reroll with reroll id equal to the action number minus NUM_CATS.
  - getExpScore
```
public static double getExpScore()
```
    Return the expected score for optimal play of Upper Section Yahtzee.
    
    Returns:
    
    the expected score for optimal play of Upper Section Yahtzee
  - playGame
```
public static int playGame()
```
    Simulate an optimally played game and return the final score.
    
    Returns:
    
    the final score
  - main
```
public static void main(java.lang.String[] args)
```

Class YahtzeeSolver

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

NUM_DICE

NUM_RANKS

NUM_ROLLS

NUM_CATS

UNKNOWN

ALL_SCORED

widgets

widgetMap

catRollIdScore

Method Detail

getOptimalActionAndScore

getExpScore

playGame

main