Shut the Box Analysis by Bill Butler All Distribution Rights Reserved All table entrees show the percent probability that a game will end at the specified final score. Can not flip more Can not flip more Sum of Use a single die than 2 boxes on than 2 boxes on Sum of Not Always use 2 if sum of flipped any given dice any given dice Flipped Flipped dice. No single is >= 39 roll. Use roll. Always Digits Digits die option (Not Flipped <= 6) single die option use 2 dice. 0 45 0.0000 0.0000 0.0000 0.0000 1 44 0.0000 0.0000 0.0000 0.0000 2 43 0.0772 0.0772 0.0772 0.0772 3 42 0.0000 0.0000 0.0000 0.0000 4 41 0.0000 0.0000 0.0000 0.0000 5 40 0.0257 0.0257 0.0257 0.0257 6 39 0.0386 0.0386 0.0386 0.0386 7 38 0.0943 0.0943 0.0943 0.0943 8 37 0.1179 0.1179 0.1179 0.1179 9 36 0.0386 0.0386 0.0386 0.0386 10 35 0.1666 0.1666 0.1666 0.1666 11 34 0.2236 0.2236 0.2236 0.2236 12 33 0.1992 0.1992 0.1618 0.1542 13 32 0.2974 0.2974 0.3165 0.2974 14 31 0.5808 0.5808 0.5714 0.6086 15 30 0.3438 0.3438 0.4467 0.4450 16 29 0.5432 0.5432 0.5275 0.5275 17 28 0.5437 0.5437 0.6627 0.6398 18 27 0.6768 0.6754 0.7209 0.7222 19 26 0.9513 0.9573 0.8879 0.8708 20 25 1.0351 1.0351 1.2326 1.2166 21 24 1.3955 1.3933 1.3220 1.3348 22 23 1.5308 1.5314 1.8736 1.9323 23 22 1.5331 1.5319 1.7598 1.8023 24 21 1.9181 1.9128 2.2831 2.3096 25 20 2.3475 2.3559 2.7201 2.7029 26 19 2.3666 2.3763 2.8970 3.1834 27 18 2.9363 2.9172 3.2435 3.5711 28 17 3.2419 3.2450 3.6546 3.8365 29 16 3.3192 3.3247 3.9444 4.0520 30 15 3.8512 3.8673 4.3232 4.4938 31 14 3.9665 3.9788 4.5238 4.5954 32 13 4.3262 4.2964 4.5456 4.5507 33 12 4.4780 4.4736 5.0182 5.0875 34 11 4.9300 4.8915 5.1942 5.5372 35 10 5.1756 5.1738 5.6187 5.6475 36 9 5.9095 5.9319 5.9010 5.8824 37 8 5.5163 5.5426 5.1567 5.0855 38 7 5.1233 5.1392 4.8736 4.8497 39 6 4.8189 3.5589 3.3008 4.1098 40 5 4.7438 3.8515 3.4305 3.9525 41 4 4.1914 3.8159 3.2465 3.1683 42 3 3.8068 3.4515 2.9410 2.9256 43 2 2.8257 2.9880 2.3801 2.0600 44 1 2.6507 2.7305 2.1179 1.7157 45 0 7.1432 9.7614 7.4194 5.3488 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