Shut the Box Analysis Cells show end of game probabilities for various Game Options by Bill Butler All Distribution Probability (Pct) of Probability (Pct) of Probability (Pct) of Rights Reserved a given final score a given final score a given final score Can not flip more Sum of Sum of Always use 2 dice Use a single die if than 2 boxes on Flipped Not Flipped No single Sum of Flipped >= 39 any given dice roll Digits Digits die option Not Flipped <= 6 Uses single die option 0 45 0.0000 0.0000 0.0000 1 44 0.0000 0.0000 0.0000 2 43 0.0772 0.0772 0.0772 3 42 0.0000 0.0000 0.0000 4 41 0.0000 0.0000 0.0000 5 40 0.0257 0.0257 0.0257 6 39 0.0386 0.0386 0.0386 7 38 0.0943 0.0943 0.0943 8 37 0.1179 0.1179 0.1179 9 36 0.0386 0.0386 0.0386 10 35 0.1666 0.1666 0.1666 11 34 0.2236 0.2236 0.2236 12 33 0.1992 0.1992 0.1618 13 32 0.2974 0.2974 0.3165 14 31 0.5808 0.5808 0.5714 15 30 0.3438 0.3438 0.4467 16 29 0.5432 0.5432 0.5275 17 28 0.5437 0.5437 0.6627 18 27 0.6768 0.6754 0.7209 19 26 0.9513 0.9573 0.8879 20 25 1.0351 1.0351 1.2326 21 24 1.3955 1.3933 1.3220 22 23 1.5308 1.5314 1.8736 23 22 1.5331 1.5319 1.7598 24 21 1.9181 1.9128 2.2831 25 20 2.3475 2.3559 2.7201 26 19 2.3666 2.3763 2.8970 27 18 2.9363 2.9172 3.2435 28 17 3.2419 3.2450 3.6546 29 16 3.3192 3.3247 3.9444 30 15 3.8512 3.8673 4.3232 31 14 3.9665 3.9788 4.5238 32 13 4.3262 4.2964 4.5456 33 12 4.4780 4.4736 5.0182 34 11 4.9300 4.8915 5.1942 35 10 5.1756 5.1738 5.6187 36 9 5.9095 5.9319 5.9010 37 8 5.5163 5.5426 5.1567 38 7 5.1233 5.1392 4.8736 39 6 4.8189 3.5589 3.3008 40 5 4.7438 3.8515 3.4305 41 4 4.1914 3.8159 3.2465 42 3 3.8068 3.4515 2.9410 43 2 2.8257 2.9880 2.3801 44 1 2.6507 2.7305 2.1179 45 0 7.1432 9.7614 7.4194 Note: At several decision points, there is a tie for the optimal strategy choices. This will also produce minor changes in the probabilities that the game will end at various scores short of winning the game. The probability of winning the game is not changed by any of these alternate strategies. Use "Back" from your browser to returb to the main "Shut the Box" page