Yahtzee Proficiency Test: Instructions

[ Overview | Notes | Explanation of Analysis ]

Overview

You play a game of Solitaire Yahtzee and afterwards receive an analysis of how well you have chosen compared to the Optimal Solitaire Yahtzee Player.

To roll the unkept dice: Click Roll button (below Score Card).
To select the dice to keep: check or uncheck Keep checkboxes (below the dice).
Only allowed on first and second roll of each turn!
To score the current roll: Click button next to an empty category.
Before clicking, the score in that category is displayed below the Score Card.
Allowed on any roll; however, you must score your third roll!
Repeat steps above until all thirteen categories have been scored.
To receive an analysis of your choices: Click Analyze button (next to Score Card).
The result is shown in a separate window and can be printed on a single page.
To start a new game: Click New Game button (above Score Card).

Notes

There is no Undo button! Once you click to Roll or Score, your decision is final. Before scoring, the score in that category is displayed below the Score Card.

How to Read the Analysis

When clicking the Analyze button, all your choices are analyzed on the server and a report is returned in a separate window. The report consists of three blocks.

The first block shows a line for each roll. The columns contain the following information:

# = turn number from 1 through 13
Game State =
- set of unscored categories:
  1 = Aces
  2 = Twos
  3 = Threes
  4 = Fours
  5 = Fives
  6 = Sixes
  T = Three of a Kind
  F = Four of a Kind
  H = Full House
  S = Small Straight
  L = Large Straight
  Y = Yahtzee
  C = Chance
- number of points needed in Upper Section to obtain the bonus,
- +/- depending on whether you scored 50 points for Yahtzee or not.
Tot = total score so far
Roll = dice values (sorted); number of rolls left (2, 1, or 0)
You = either the list of the dice values you kept, or the category you scored (see under Game State for the meaning of the category letter codes)
Expect = expected final score for your choice, assuming that all subsequent choices are made optimally
SD = standard deviation in the final score under optimal play after your choice

The following columns are only given if your choice differs from the choice made by the Optimal Solitaire Yahtzee Player (OSYP) in the same situation.

OSYP = OSYP's choice
Expect = expected final score for OSYP's choice
SD = standard deviation in the final score after OSYP's choice
Delta = difference between OSYP's and your expectation, followed by a marker indicating the class (see next block for and explanation of the markers)

The second block counts all your choices in various classes:

Choices identical to the Optimal Solitaire Yahtzee Player (OSYP).
Choices not identical to OSYP but with (almost) the same expectation.
Choices that differ from 0.01 to 1.00 from OSYP.
Choices that differ from 1.00 to 5.00 from OSYP.
Choices that differ 5.00 or more from OSYP.

Finally, the mean difference in expected final score per choice is shown. Aim for a value below 0.2.

The third block consists of the Score Card.

_N_E_W_: The fourth block explains the advantage of OSYP's choice over your choice, by showing a breakdown of the difference in (expected) final score per aspect. For example, if the game record contains

 # Game State        Tot Roll       You  Expect SD   OSYP  Expect SD  Delta
-- ----------------- --- -------  -----  ------ --  -----  ------ --  -----
   ...
 7 _2__5_TF__LYC;15- 103 12344;2  1234_  243.10 38  234__  243.41 38   0.31 *

then you may want to know why keeping 234 is better than keeping 1234, since the latter certainly makes it easier to obtain a Large Straight. The breakdown in the fourth block will contain the lines

 #   G |  1    2    3    4    5    6 |  U |  T    F    H    S    L    Y    C |  E 
-- ----+---- ---- ---- ---- ---- ----+----+---- ---- ---- ---- ---- ---- ----+----
    ...
 7  0.3|  .   0.5   .    .  -0.2   . | 0.4|-0.0  0.2   .    .  -0.4  0.1 -0.1| 0.0

This shows that the expected loss of about 0.3 points in the final score (under G) is mainly due to an expected loss in your final scores for Twos (0.5 under 2) and the Upper Section Bonus (0.4 under U), etc. It is true that your choice has an advantage over OSYP when it comes to the expected final score for Large Straight (-0.4 under L). But that advantage is not big enough to compensate for the losses.