Appendix

Table A. The Reddere Integral

Programmed by Norman Wattenberger, Casino Vérité.

Table B. Yahtzee Strategies

Notes: Column A lists the 252 possible five-dice configurations. Column B designates dice to be fixed assuming that the configuration shown in Column A represents the first throw of the dice. Column C designates dice to be fixed assuming the configuration of Column A represents the second roll of the dice. Column D indicates the scoring category to be selected assuming the Column A configuration represents the final throw of the dice.

Courtesy of Phil Woodward.

Table C (A). EORs—Dealer’s Up-Card 2

Table C (B). EORs—Dealer’s Up-Card 3

Table C (C). EORs—Dealer’s Up-Card 4

Table C (D). EORs—Dealer’s Up-Card 5

Table C (E). EORs—Dealer’s Up-Card 6

Table C (F). EORs—Dealer’s Up-Card 7

Table C (G). EORs—Dealer’s Up-Card 8

Table C (H). EORs—Dealer’s Up-Card 9

Table C (I). EORs—Dealer’s Up-Card T

Table C (J). EORs—Dealer’s Up-Card A

Table D. Player’s Exact Expectation When Holding 16 vs. a 10

Table E. Optimal Strategy for All Cards Exposed

Table F. Mathematical Expectations as a Function of Dealer’s Cards

Table G. Double-Exposure Optimal Strategy

– = Stand
db = Double down; if doubling not permitted, then hit
dbs = Double down; if doubling not permitted, then stand
H = Hit
S = Split

Courtesy of Stanford Wong.

Table H. Double-Exposure Hi-Lo Strategy Numbers (TCs)

– = Stand
db = Double down; if doubling not permitted, then hit
dbs = Double down; if doubling not permitted, then stand
H = Hit
S = Split
H/– = Hit or stand, never split
number = Stand (or double or split) at a count per deck equal to or greater than the number; hit (or do not split) at a count per deck less than the number

^* Split if count per deck is less than the number; otherwise hit

Courtesy of Stanford Wong.

Table I. Blackarat Strategy (Single Deck), Bonus Pays 5 to 1

Programmed by Norman Wattenberger, Casino Vérité.

Table J. Blackarat Strategy (Six Decks), Bonus Pays 5 to 1

Programmed by Norman Wattenberger, Casino Vérité.

Table K. Expectations for Several Blackarat Bonuses

Single Deck:
Six Decks:

Table L. Outcomes of Positions in Dodgem

Courtesy of Elwyn Berlekamp.