Optimal Strategy for the Current Shut the Box Payout Table Computer Program by Bill Butler (All Distribution Rights Reserved) Table shows which flip combination should be used given the digit combinations that have already been flipped (left column) and the current dice total (Column Headers). The Expected Value is the average expected return (percent probability of winning) after you have already flipped the digits to the left and are about to roll the dice again. Note: If the sum of the flipped digits is > 38 only 1 die is used. Note: A maximum of two boxes may be flipped per any dice roll. Already Dice Dice Dice Dice Dice Dice Dice Dice Dice Dice Dice Dice Flipped Expected Sum Sum Sum Sum Sum Sum Sum Sum Sum Sum Sum Sum Digits Value =1 =2 =3 =4 =5 =6 =7 =8 =9 =10 =11 =12 --------------------------------------------------------------------------------- 0 7.4194 0 2 3 4 5 6 7 8 9 19 29 39 1 0.0000 0 0 0 0 0 0 0 0 0 0 0 0 2 4.9493 0 0 3 4 5 6 7 8 9 19 38 39 12 2.6330 0 0 3 4 5 6 7 8 9 46 38 39 3 5.4282 0 2 12 4 5 6 7 8 9 19 29 48 13 3.0012 0 2 0 4 5 6 7 8 9 46 29 48 23 3.2495 0 0 0 4 5 6 7 8 9 19 56 48 123 1.5101 0 0 0 4 5 6 7 8 9 46 56 48 4 5.8042 0 2 3 13 5 6 7 8 9 19 29 39 14 3.3457 0 2 3 0 5 6 7 8 9 28 29 39 24 3.8645 0 0 3 13 5 6 7 8 9 19 38 39 124 1.8713 0 0 3 0 5 6 7 8 9 37 56 39 34 4.0007 0 2 12 0 5 6 7 8 9 19 29 57 134 2.2334 0 2 0 0 5 6 7 8 9 28 56 57 234 2.4742 0 0 0 0 5 6 7 8 9 19 56 57 1234 1.0360 0 0 0 0 5 6 7 8 9 0 56 57 5 6.3853 0 2 3 4 14 6 7 8 9 19 29 39 15 4.0303 0 2 3 4 23 6 7 8 9 46 29 39 25 4.2023 0 0 3 4 14 6 7 8 9 19 38 39 125 2.2077 0 0 3 4 0 6 7 8 9 46 38 39 35 4.7659 0 2 12 4 14 6 7 8 9 19 29 48 135 2.5046 0 2 0 4 0 6 7 8 9 46 29 48 235 2.9975 0 0 0 4 14 6 7 8 9 19 47 48 1235 1.4375 0 0 0 4 0 6 7 8 9 46 47 48 45 4.9683 0 2 3 13 23 6 7 8 9 19 29 39 145 2.9994 0 2 3 0 23 6 7 8 9 37 29 39 245 3.2167 0 0 3 13 0 6 7 8 9 19 38 39 1245 1.7211 0 0 3 0 0 6 7 8 9 37 38 39 345 3.1649 0 2 12 0 0 6 7 8 9 19 29 0 1345 1.9619 0 2 0 0 0 6 7 8 9 28 29 0 2345 2.0676 0 0 0 0 0 6 7 8 9 19 0 0 12345 0.9002 0 0 0 0 0 6 7 8 9 0 0 0 6 6.7844 0 2 3 4 5 15 7 8 9 19 29 39 16 4.2100 0 2 3 4 5 24 7 8 9 28 29 39 26 4.4647 0 0 3 4 5 15 7 8 9 19 38 39 126 2.0952 0 0 3 4 5 0 7 8 9 37 38 39 36 5.1158 0 2 12 4 5 15 7 8 9 19 29 48 136 2.7338 0 2 0 4 5 24 7 8 9 28 29 57 236 3.0492 0 0 0 4 5 15 7 8 9 19 47 48 1236 1.2196 0 0 0 4 5 0 7 8 9 0 47 48 46 5.4483 0 2 3 13 5 15 7 8 9 28 29 39 146 2.9285 0 2 3 0 5 0 7 8 9 28 29 39 246 3.8732 0 0 3 13 5 15 7 8 9 19 38 39 1246 1.7630 0 0 3 0 5 0 7 8 9 37 38 57 346 4.1768 0 2 12 0 5 15 7 8 9 28 29 57 1346 2.1676 0 2 0 0 5 0 7 8 9 28 29 57 2346 2.6192 0 0 0 0 5 15 7 8 9 19 0 57 12346 1.0288 0 0 0 0 5 0 7 8 9 0 0 57 56 5.9167 0 2 3 4 14 24 7 8 9 19 38 39 156 4.0108 0 2 3 4 23 24 7 8 9 37 29 39 256 3.7597 0 0 3 4 14 0 7 8 9 19 38 39 1256 2.0021 0 0 3 4 0 0 7 8 9 37 47 39 356 4.8941 0 2 12 4 14 24 7 8 9 19 29 48 1356 2.7825 0 2 0 4 0 24 7 8 9 28 47 48 2356 3.0178 0 0 0 4 14 0 7 8 9 19 47 48 12356 1.4660 0 0 0 4 0 0 7 8 9 0 47 48 456 4.4888 0 2 3 13 23 0 7 8 9 19 29 39 1456 3.1464 0 2 3 0 23 0 7 8 9 37 29 39 2456 3.3393 0 0 3 13 0 0 7 8 9 19 38 39 12456 2.2891 0 0 3 0 0 0 7 8 9 37 38 39 3456 3.1641 0 2 12 0 0 0 7 8 9 19 29 0 13456 2.5977 0 2 0 0 0 0 7 8 9 28 29 0 23456 2.6749 0 0 0 0 0 0 7 8 9 19 0 0 123456 1.5432 0 0 0 0 0 0 7 8 9 0 0 0 7 7.2781 0 2 3 4 5 6 25 8 9 19 29 39 17 4.8018 0 2 3 4 5 6 34 8 9 28 29 39 27 4.9070 0 0 3 4 5 6 34 8 9 19 56 39 127 2.6579 0 0 3 4 5 6 34 8 9 46 56 39 37 5.4264 0 2 12 4 5 6 25 8 9 19 29 48 137 3.2042 0 2 0 4 5 6 25 8 9 46 29 48 237 3.1233 0 0 0 4 5 6 16 8 9 19 56 48 1237 1.4565 0 0 0 4 5 6 0 8 9 46 56 48 47 5.9779 0 2 3 13 5 6 25 8 9 19 38 39 147 3.4248 0 2 3 0 5 6 25 8 9 28 38 39 247 3.8931 0 0 3 13 5 6 16 8 9 19 38 39 1247 1.6267 0 0 3 0 5 6 0 8 9 0 56 39 347 4.5216 0 2 12 0 5 6 25 8 9 19 29 0 1347 2.5914 0 2 0 0 5 6 25 8 9 28 56 0 2347 2.7571 0 0 0 0 5 6 16 8 9 19 56 0 12347 1.1860 0 0 0 0 5 6 0 8 9 0 56 0 57 6.5993 0 2 3 4 23 6 16 8 9 19 29 39 157 4.3222 0 2 3 4 23 6 34 8 9 28 29 48 257 4.6335 0 0 3 4 14 6 34 8 9 19 38 39 1257 2.5880 0 0 3 4 0 6 34 8 9 46 38 39 357 5.0195 0 2 12 4 14 6 16 8 9 28 29 48 1357 2.4815 0 2 0 4 0 6 0 8 9 46 29 48 2357 3.1972 0 0 0 4 14 6 16 8 9 19 0 48 12357 1.6032 0 0 0 4 0 6 0 8 9 46 0 48 457 5.5923 0 2 3 13 23 6 16 8 9 19 29 39 1457 2.9654 0 2 3 0 23 6 0 8 9 28 29 39 2457 3.9599 0 0 3 13 0 6 16 8 9 19 38 39 12457 1.8490 0 0 3 0 0 6 0 8 9 0 38 39 3457 4.3801 0 2 12 0 0 6 16 8 9 28 29 0 13457 2.4806 0 2 0 0 0 6 0 8 9 28 29 0 23457 3.3350 0 0 0 0 0 6 16 8 9 19 0 0 123457 1.3717 0 0 0 0 0 6 0 8 9 0 0 0 67 6.9480 0 2 3 4 5 15 34 8 9 19 29 39 167 4.5503 0 2 3 4 5 24 34 8 9 28 29 39 267 4.6554 0 0 3 4 5 15 34 8 9 19 38 48 1267 2.1324 0 0 3 4 5 0 34 8 9 0 38 39 367 5.1721 0 2 12 4 5 15 25 8 9 19 29 48 1367 3.1583 0 2 0 4 5 24 25 8 9 28 29 48 2367 2.6318 0 0 0 4 5 15 0 8 9 19 0 48 12367 1.2260 0 0 0 4 5 0 0 8 9 0 0 48 467 5.7083 0 2 3 13 5 15 25 8 9 19 29 39 1467 3.5360 0 2 3 0 5 0 25 8 9 28 38 39 2467 3.8221 0 0 3 13 5 15 0 8 9 19 38 39 12467 1.7947 0 0 3 0 5 0 0 8 9 0 38 39 3467 5.0930 0 2 12 0 5 15 25 8 9 19 29 0 13467 3.1350 0 2 0 0 5 0 25 8 9 28 29 0 23467 3.0378 0 0 0 0 5 15 0 8 9 19 0 0 123467 1.2003 0 0 0 0 5 0 0 8 9 0 0 0 567 5.8882 0 2 3 4 14 24 34 8 9 19 29 39 1567 4.8121 0 2 3 4 23 24 34 8 9 28 29 39 2567 4.5532 0 0 3 4 14 0 34 8 9 19 38 39 12567 2.6920 0 0 3 4 0 0 34 8 9 0 38 39 3567 4.8798 0 2 12 4 14 24 0 8 9 19 29 48 13567 3.2779 0 2 0 4 0 24 0 8 9 28 29 48 23567 3.2064 0 0 0 4 14 0 0 8 9 19 0 48 123567 1.6461 0 0 0 4 0 0 0 8 9 0 0 48 4567 4.6903 0 2 3 13 23 0 0 8 9 19 29 39 14567 3.5265 0 2 3 0 23 0 0 8 9 28 29 39 24567 3.8123 0 0 3 13 0 0 0 8 9 19 38 39 124567 2.8635 0 0 3 0 0 0 0 8 9 0 38 39 34567 3.5965 0 2 12 0 0 0 0 8 18 19 29 0 134567 4.0809 0 2 0 0 0 0 0 8 9 28 29 0 234567 4.0638 0 0 0 0 0 0 0 8 9 19 0 0 1234567 3.0864 0 0 0 0 0 0 0 8 9 0 0 0 8 8.5755 0 2 3 4 5 6 7 17 9 19 29 39 18 5.7871 0 2 3 4 5 6 7 35 9 37 29 39 28 6.1995 0 0 3 4 5 6 7 17 9 19 47 39 128 3.6167 0 0 3 4 5 6 7 35 9 46 47 39 38 6.5761 0 2 12 4 5 6 7 26 9 19 29 57 138 3.7291 0 2 0 4 5 6 7 26 9 46 29 57 238 4.1971 0 0 0 4 5 6 7 17 9 19 56 57 1238 2.0062 0 0 0 4 5 6 7 0 9 46 47 57 48 7.3144 0 2 3 13 5 6 7 26 9 19 29 39 148 4.6088 0 2 3 0 5 6 7 35 9 37 29 39 248 5.3580 0 0 3 13 5 6 7 35 9 19 56 39 1248 2.9326 0 0 3 0 5 6 7 35 9 37 56 39 348 5.5688 0 2 12 0 5 6 7 26 9 19 29 57 1348 3.0274 0 2 0 0 5 6 7 26 9 0 29 57 2348 3.8652 0 0 0 0 5 6 7 17 9 19 56 57 12348 1.6975 0 0 0 0 5 6 7 0 9 0 56 57 58 7.8091 0 2 3 4 14 6 7 17 9 19 29 39 158 5.0961 0 2 3 4 23 6 7 26 9 46 29 39 258 5.1507 0 0 3 4 14 6 7 17 9 19 47 39 1258 2.7006 0 0 3 4 0 6 7 0 9 46 47 39 358 6.2437 0 2 12 4 14 6 7 26 9 19 29 0 1358 3.4479 0 2 0 4 0 6 7 26 9 46 29 0 2358 4.1774 0 0 0 4 14 6 7 17 9 46 47 0 12358 2.1433 0 0 0 4 0 6 7 0 9 46 47 0 458 6.7657 0 2 3 13 23 6 7 26 9 19 29 39 1458 4.5058 0 2 3 0 23 6 7 26 9 37 29 39 2458 4.2291 0 0 3 13 0 6 7 17 9 19 0 39 12458 2.3834 0 0 3 0 0 6 7 0 9 37 0 39 3458 5.2581 0 2 12 0 0 6 7 26 9 19 29 0 13458 3.3093 0 2 0 0 0 6 7 26 9 0 29 0 23458 3.7894 0 0 0 0 0 6 7 17 9 19 0 0 123458 1.6461 0 0 0 0 0 6 7 0 9 0 0 0 68 8.2872 0 2 3 4 5 24 7 35 9 19 29 39 168 5.4789 0 2 3 4 5 24 7 35 9 37 29 39 268 6.1019 0 0 3 4 5 15 7 35 9 19 47 39 1268 3.2908 0 0 3 4 5 0 7 35 9 37 47 39 368 6.4262 0 2 12 4 5 24 7 17 9 19 29 57 1368 3.1293 0 2 0 4 5 24 7 0 9 0 29 57 2368 4.5396 0 0 0 4 5 15 7 17 9 19 47 57 12368 1.8690 0 0 0 4 5 0 7 0 9 0 47 57 468 7.1099 0 2 3 13 5 15 7 35 9 19 29 39 1468 4.4682 0 2 3 0 5 0 7 35 9 37 29 39 2468 5.6694 0 0 3 13 5 15 7 35 9 19 0 39 12468 3.2493 0 0 3 0 5 0 7 35 9 37 0 39 3468 6.2086 0 2 12 0 5 15 7 17 9 19 29 57 13468 2.8978 0 2 0 0 5 0 7 0 9 0 29 57 23468 4.8354 0 0 0 0 5 15 7 17 9 19 0 57 123468 2.0576 0 0 0 0 5 0 7 0 9 0 0 57 568 7.4314 0 2 3 4 23 24 7 17 9 19 29 39 1568 4.9414 0 2 3 4 23 24 7 0 9 37 29 39 2568 5.3148 0 0 3 4 14 0 34 17 9 19 47 39 12568 2.8635 0 0 3 4 0 0 7 0 9 37 47 39 3568 6.9559 0 2 12 4 14 24 7 17 9 19 29 0 13568 3.5322 0 2 0 4 0 24 7 0 9 0 29 0 23568 4.8354 0 0 0 4 14 0 7 17 9 19 47 0 123568 2.4691 0 0 0 4 0 0 7 0 9 0 47 0 4568 6.7844 0 2 3 13 23 0 7 17 9 19 29 39 14568 4.4925 0 2 3 0 23 0 7 0 9 37 29 39 24568 4.9126 0 0 3 13 0 0 7 17 9 19 0 39 124568 3.8066 0 0 3 0 0 0 7 0 9 37 0 39 34568 5.6584 0 2 12 0 0 0 7 17 27 19 29 0 134568 3.9095 0 2 0 0 0 0 7 0 9 0 29 0 234568 6.4815 0 0 0 0 0 0 7 17 9 19 0 0 1234568 3.7037 0 0 0 0 0 0 7 0 9 0 0 0 78 8.8249 0 2 3 4 5 6 34 35 9 19 29 39 178 6.3497 0 2 3 4 5 6 34 35 9 46 29 39 278 6.5183 0 0 3 4 5 6 34 35 9 19 56 39 1278 4.2660 0 0 3 4 5 6 34 35 9 46 56 39 378 6.5988 0 2 12 4 5 6 25 26 9 19 29 0 1378 4.5320 0 2 0 4 5 6 25 26 9 46 29 0 2378 4.0390 0 0 0 4 5 6 16 0 9 19 56 0 12378 2.1691 0 0 0 4 5 6 0 0 9 46 56 0 478 8.0477 0 2 3 13 5 6 16 35 9 19 29 39 1478 4.9549 0 2 3 0 5 6 25 35 9 0 29 39 2478 6.5187 0 0 3 13 5 6 16 35 9 19 56 39 12478 3.2036 0 0 3 0 5 6 0 35 9 0 56 39 3478 6.8606 0 2 12 0 5 6 25 26 9 19 29 0 13478 4.2210 0 2 0 0 5 6 25 26 9 0 29 0 23478 4.5382 0 0 0 0 5 6 16 0 9 19 56 0 123478 2.5034 0 0 0 0 5 6 0 0 9 0 56 0 578 8.1935 0 2 3 4 14 6 34 26 9 19 29 39 1578 6.4223 0 2 3 4 23 6 34 26 9 46 29 39 2578 5.4696 0 0 3 4 14 6 34 0 9 19 0 39 12578 3.6137 0 0 3 4 0 6 34 0 9 46 0 39 3578 7.2082 0 2 12 4 14 6 16 26 9 19 29 0 13578 3.9680 0 2 0 4 0 6 0 26 9 46 29 0 23578 4.4196 0 0 0 4 14 6 16 0 9 19 0 0 123578 2.9321 0 0 0 4 0 6 0 0 9 46 0 0 4578 8.0951 0 2 3 13 23 6 16 26 9 19 29 39 14578 4.6996 0 2 3 0 23 6 0 26 9 0 29 39 24578 5.1955 0 0 3 13 0 6 16 0 36 19 0 39 124578 2.9750 0 0 3 0 0 6 0 0 9 0 0 39 34578 7.3803 0 2 12 0 0 6 16 26 9 19 29 0 134578 5.4870 0 2 0 0 0 6 0 26 9 0 29 0 234578 6.7644 0 0 0 0 0 6 16 0 9 19 0 0 1234578 3.3951 0 0 0 0 0 6 0 0 9 0 0 0 678 8.5465 0 2 3 4 5 24 34 35 9 19 29 39 1678 6.3957 0 2 3 4 5 24 34 35 9 0 29 39 2678 6.9383 0 0 3 4 5 15 34 35 9 19 0 39 12678 3.6094 0 0 3 4 5 0 34 35 9 0 0 39 3678 6.4184 0 2 12 4 5 24 25 0 9 19 29 0 13678 4.1295 0 2 0 4 5 24 25 0 9 0 29 0 23678 3.9180 0 0 0 4 5 15 0 0 45 19 0 0 123678 2.1605 0 0 0 4 5 0 0 0 9 0 0 0 4678 7.7303 0 2 3 13 5 15 25 35 9 19 29 39 14678 5.4898 0 2 3 0 5 0 25 35 9 0 29 39 24678 6.4958 0 0 3 13 5 15 0 35 9 19 0 39 124678 4.6125 0 0 3 0 5 0 0 35 9 0 0 39 34678 7.5817 0 2 12 0 5 15 25 0 9 19 29 0 134678 5.8299 0 2 0 0 5 0 25 0 9 0 29 0 234678 6.5329 0 0 0 0 5 15 0 0 9 19 0 0 1234678 3.0864 0 0 0 0 5 0 0 0 9 0 0 0 5678 6.5189 0 2 3 4 23 24 34 0 9 19 29 39 15678 6.0943 0 2 3 4 23 24 34 0 9 0 29 39 25678 6.1514 0 0 3 4 14 0 34 0 9 19 0 39 125678 5.0154 0 0 3 4 0 0 34 0 9 0 0 39 35678 6.9916 0 2 12 4 14 24 0 0 9 19 29 0 135678 5.6584 0 2 0 4 0 24 0 0 9 0 29 0 235678 5.9414 0 0 0 4 14 0 0 0 9 19 0 0 1235678 2.7778 0 0 0 4 0 0 0 0 9 0 0 0 45678 7.8075 0 2 3 13 23 0 0 0 9 19 29 39 145678 5.6670 0 2 3 0 23 0 0 0 9 0 29 39 245678 5.8128 0 0 3 13 0 0 0 0 9 19 0 39 1245678 5.2469 0 0 3 0 0 0 0 0 9 0 0 39 345678 5.6842 0 2 12 0 0 0 0 0 9 19 29 0 1345678 7.7160 0 2 0 0 0 0 0 0 9 0 29 0 2345678 10.1852 0 0 0 0 0 0 0 0 9 19 0 0 12345678 11.1111 0 0 0 0 0 0 0 0 9 0 0 0 9 10.1919 0 2 3 4 5 6 7 8 18 28 38 48 19 7.7370 0 2 3 4 5 6 7 8 36 28 38 48 29 7.7873 0 0 3 4 5 6 7 8 18 46 38 48 129 5.0714 0 0 3 4 5 6 7 8 45 37 38 48 39 8.3189 0 2 12 4 5 6 7 8 18 28 56 57 139 5.5714 0 2 0 4 5 6 7 8 45 28 56 48 239 5.7516 0 0 0 4 5 6 7 8 18 46 56 57 1239 3.2303 0 0 0 4 5 6 7 8 45 46 56 48 49 8.5610 0 2 3 13 5 6 7 8 18 28 38 57 149 5.8279 0 2 3 0 5 6 7 8 36 28 38 57 249 6.3932 0 0 3 13 5 6 7 8 18 37 56 57 1249 3.7286 0 0 3 0 5 6 7 8 36 37 56 57 349 6.3165 0 2 12 0 5 6 7 8 18 28 56 57 1349 4.3072 0 2 0 0 5 6 7 8 27 28 56 57 2349 4.1963 0 0 0 0 5 6 7 8 18 0 56 57 12349 2.1219 0 0 0 0 5 6 7 8 0 0 56 57 59 9.4345 0 2 3 4 23 6 7 8 18 28 38 48 159 7.0656 0 2 3 4 23 6 7 8 36 28 38 48 259 7.1565 0 0 3 4 14 6 7 8 18 37 38 48 1259 4.5385 0 0 3 4 0 6 7 8 36 46 38 48 359 7.7618 0 2 12 4 14 6 7 8 18 28 47 48 1359 4.8790 0 2 0 4 0 6 7 8 27 46 47 48 2359 5.8042 0 0 0 4 14 6 7 8 18 46 47 48 12359 3.0907 0 0 0 4 0 6 7 8 0 46 47 48 459 7.7114 0 2 3 13 23 6 7 8 18 28 38 0 1459 5.7636 0 2 3 0 23 6 7 8 36 28 38 0 2459 5.9059 0 0 3 13 0 6 7 8 18 37 38 0 12459 4.0595 0 0 3 0 0 6 7 8 36 37 38 0 3459 5.3803 0 2 12 0 0 6 7 8 18 28 0 0 13459 4.0638 0 2 0 0 0 6 7 8 27 28 0 0 23459 3.9823 0 0 0 0 0 6 7 8 18 0 0 0 123459 2.0576 0 0 0 0 0 6 7 8 0 0 0 0 69 10.0909 0 2 3 4 5 15 7 8 18 28 38 48 169 7.4961 0 2 3 4 5 24 7 8 45 28 38 57 269 7.5163 0 0 3 4 5 15 7 8 18 37 38 48 1269 4.8947 0 0 3 4 5 0 7 8 45 37 38 48 369 8.4687 0 2 12 4 5 15 7 8 18 28 47 48 1369 6.0101 0 2 0 4 5 24 7 8 45 28 47 57 2369 5.6920 0 0 0 4 5 15 7 8 18 0 47 48 12369 3.4486 0 0 0 4 5 0 7 8 45 0 47 48 469 8.7679 0 2 3 13 5 15 7 8 18 28 38 57 1469 5.4072 0 2 3 0 5 0 7 8 27 28 38 57 2469 7.2345 0 0 3 13 5 15 7 8 18 37 38 57 12469 3.6651 0 0 3 0 5 0 7 8 0 37 38 57 3469 7.3737 0 2 12 0 5 15 7 8 27 28 0 57 13469 4.4796 0 2 0 0 5 0 7 8 27 28 0 57 23469 5.4227 0 0 0 0 5 15 7 8 18 0 0 57 123469 2.5720 0 0 0 0 5 0 7 8 0 0 0 57 569 9.4661 0 2 3 4 14 24 7 8 18 28 38 48 1569 7.8741 0 2 3 4 23 24 7 8 27 37 38 48 2569 6.9084 0 0 3 4 14 0 7 8 18 37 38 48 12569 4.2824 0 0 3 4 0 0 7 8 0 37 38 48 3569 8.8201 0 2 12 4 14 24 7 8 18 28 47 48 13569 6.5972 0 2 0 4 0 24 7 8 27 28 47 48 23569 6.0957 0 0 0 4 14 0 7 8 18 0 47 48 123569 4.0123 0 0 0 4 0 0 7 8 0 0 47 48 4569 8.0439 0 2 3 13 23 0 7 8 18 28 38 0 14569 6.4879 0 2 3 0 23 0 7 8 27 28 38 0 24569 6.7687 0 0 3 13 0 0 7 8 18 37 38 0 124569 5.4527 0 0 3 0 0 0 7 8 0 37 38 0 34569 6.1964 0 2 12 0 0 0 7 17 18 28 0 0 134569 6.8930 0 2 0 0 0 0 7 8 27 28 0 0 234569 6.4043 0 0 0 0 0 0 7 8 18 0 0 0 1234569 4.6296 0 0 0 0 0 0 7 8 0 0 0 0 79 10.6862 0 2 3 4 5 6 16 8 18 28 38 48 179 8.7386 0 2 3 4 5 6 25 8 36 28 38 48 279 8.5080 0 0 3 4 5 6 16 8 18 46 38 48 1279 5.9103 0 0 3 4 5 6 34 8 45 46 38 48 379 9.2775 0 2 12 4 5 6 25 8 18 28 56 48 1379 6.6127 0 2 0 4 5 6 25 8 45 28 56 48 2379 6.9124 0 0 0 4 5 6 16 8 45 46 56 48 12379 4.0231 0 0 0 4 5 6 0 8 45 46 56 48 479 9.2471 0 2 3 13 5 6 25 8 18 28 38 0 1479 6.9119 0 2 3 0 5 6 25 8 36 28 38 0 2479 6.6635 0 0 3 13 5 6 16 8 18 0 38 0 12479 3.7366 0 0 3 0 5 6 0 8 36 0 38 0 3479 8.1415 0 2 12 0 5 6 25 8 18 28 56 0 13479 5.3748 0 2 0 0 5 6 25 8 0 28 56 0 23479 5.8292 0 0 0 0 5 6 16 8 18 0 56 0 123479 3.1293 0 0 0 0 5 6 0 8 0 0 56 0 579 10.7064 0 2 3 4 23 6 16 8 18 28 38 48 1579 8.3251 0 2 3 4 23 6 34 8 36 28 38 48 2579 8.7714 0 0 3 4 14 6 34 8 18 46 38 48 12579 6.4215 0 0 3 4 0 6 34 8 36 46 38 48 3579 8.7108 0 2 12 4 14 6 16 8 18 28 0 48 13579 4.3256 0 2 0 4 0 6 0 8 0 28 0 48 23579 7.8232 0 0 0 4 14 6 16 8 18 46 0 48 123579 4.5139 0 0 0 4 0 6 0 8 0 46 0 48 4579 9.7039 0 2 3 13 23 6 16 8 18 28 38 0 14579 6.8123 0 2 3 0 23 6 0 8 36 28 38 0 24579 7.4146 0 0 3 13 0 6 16 8 18 0 38 0 124579 5.8985 0 0 3 0 0 6 0 8 36 0 38 0 34579 8.6516 0 2 12 0 0 6 16 26 18 28 0 0 134579 5.3541 0 2 0 0 0 6 0 8 0 28 0 0 234579 8.6677 0 0 0 0 0 6 16 8 18 0 0 0 1234579 4.2438 0 0 0 0 0 6 0 8 0 0 0 0 679 11.1141 0 2 3 4 5 15 34 35 18 28 38 48 1679 8.8390 0 2 3 4 5 24 34 8 45 28 38 48 2679 8.5647 0 0 3 4 5 15 34 8 18 0 38 48 12679 5.8942 0 0 3 4 5 0 34 8 45 0 38 48 3679 8.9975 0 2 12 4 5 24 25 8 18 28 0 48 13679 7.7725 0 2 0 4 5 24 25 8 45 28 0 48 23679 5.8513 0 0 0 4 5 15 0 8 18 0 0 48 123679 5.0154 0 0 0 4 5 0 0 8 45 0 0 48 4679 9.4494 0 2 3 13 5 15 25 8 18 28 38 0 14679 6.8316 0 2 3 0 5 0 25 35 0 28 38 0 24679 7.8004 0 0 3 13 5 15 0 35 18 0 38 0 124679 4.4153 0 0 3 0 5 0 0 8 0 0 38 0 34679 10.2723 0 2 12 0 5 15 25 8 18 28 0 0 134679 7.6732 0 2 0 0 5 0 25 8 0 28 0 0 234679 8.3591 0 0 0 0 5 15 0 8 18 0 0 0 1234679 3.8580 0 0 0 0 5 0 0 8 0 0 0 0 5679 9.3832 0 2 3 4 23 24 34 8 18 28 38 48 15679 9.9316 0 2 3 4 23 24 34 8 0 28 38 48 25679 9.3257 0 0 3 4 14 0 34 8 18 0 38 48 125679 7.4074 0 0 3 4 0 0 34 8 0 0 38 48 35679 10.2731 0 2 12 4 14 24 0 8 18 28 0 48 135679 7.9604 0 2 0 4 0 24 0 8 0 28 0 48 235679 8.0633 0 0 0 4 14 0 0 8 18 0 0 48 1235679 6.2500 0 0 0 4 0 0 0 8 0 0 0 48 45679 10.9775 0 2 12 13 23 0 0 8 18 28 38 0 145679 7.7975 0 2 3 0 23 0 0 8 0 28 38 0 245679 7.7675 0 0 3 13 0 0 0 8 18 0 38 0 1245679 8.6420 0 0 3 0 0 0 0 8 0 0 38 0 345679 7.4717 0 2 12 0 0 0 0 8 18 28 0 0 1345679 11.0340 0 2 0 0 0 0 0 8 0 28 0 0 2345679 13.4259 0 0 0 0 0 0 0 8 18 0 0 0 12345679 13.8889 0 0 0 0 0 0 0 8 0 0 0 0 89 11.7248 0 2 3 4 5 6 7 17 27 46 47 57 189 10.5694 0 2 3 4 5 6 7 26 27 37 56 57 289 10.3564 0 0 3 4 5 6 7 17 36 37 47 57 1289 8.0361 0 0 3 4 5 6 7 35 45 46 47 57 389 10.7323 0 2 12 4 5 6 7 17 27 46 56 57 1389 8.3701 0 2 0 4 5 6 7 26 45 46 47 57 2389 8.5902 0 0 0 4 5 6 7 17 45 46 56 57 12389 5.5213 0 0 0 4 5 6 7 0 45 46 47 57 489 11.0572 0 2 3 13 5 6 7 17 27 37 56 57 1489 8.9257 0 2 3 0 5 6 7 35 27 37 56 57 2489 9.5927 0 0 3 13 5 6 7 17 36 37 56 57 12489 7.3045 0 0 3 0 5 6 7 35 36 37 56 57 3489 8.3046 0 2 12 0 5 6 7 17 27 0 56 57 13489 7.3131 0 2 0 0 5 6 7 26 27 0 56 57 23489 6.6315 0 0 0 0 5 6 7 17 0 0 56 57 123489 4.6039 0 0 0 0 5 6 7 0 0 0 56 57 589 11.8871 0 2 3 4 14 6 16 17 36 37 47 0 1589 9.7493 0 2 3 4 23 6 7 26 27 46 47 0 2589 9.6833 0 0 3 4 14 6 7 17 36 37 47 0 12589 6.5801 0 0 3 4 0 6 7 0 36 37 47 0 3589 10.5755 0 2 12 4 14 6 7 26 27 46 47 0 13589 8.5798 0 2 0 4 0 6 7 26 27 46 47 0 23589 8.5262 0 0 0 4 14 6 7 17 0 46 47 0 123589 6.0957 0 0 0 4 0 6 7 0 0 46 47 0 4589 10.4085 0 2 3 13 23 6 7 17 27 37 0 0 14589 9.0535 0 2 3 0 23 6 7 26 27 37 0 0 24589 9.6408 0 0 3 13 0 6 16 17 36 37 0 0 124589 7.5874 0 0 3 0 0 6 7 0 36 37 0 0 34589 8.6013 0 2 12 0 0 6 16 17 27 0 0 0 134589 9.0792 0 2 0 0 0 6 7 26 27 0 0 0 234589 7.7932 0 0 0 0 0 6 7 17 0 0 0 0 1234589 5.0926 0 0 0 0 0 6 7 0 0 0 0 0 689 12.6065 0 2 3 4 5 15 34 17 27 37 47 57 1689 10.8655 0 2 3 4 5 24 7 35 27 37 47 57 2689 10.3395 0 0 3 4 5 15 7 17 45 37 47 57 12689 9.1221 0 0 3 4 5 0 7 35 45 37 47 57 3689 10.2231 0 2 12 4 5 24 7 17 45 0 47 57 13689 8.1447 0 2 0 4 5 24 7 0 27 0 47 57 23689 10.4810 0 0 0 4 5 15 7 17 45 0 47 57 123689 7.3302 0 0 0 4 5 0 7 0 45 0 47 57 4689 10.6360 0 2 3 13 5 15 7 35 27 37 0 57 14689 9.7994 0 2 3 0 5 0 25 35 27 37 0 57 24689 10.3652 0 0 3 13 5 15 7 17 0 37 0 57 124689 8.6934 0 0 3 0 5 0 7 35 0 37 0 57 34689 12.2299 0 2 12 0 5 15 25 17 27 0 0 57 134689 7.2788 0 2 0 0 5 0 7 0 27 0 0 57 234689 10.6481 0 0 0 0 5 15 7 17 0 0 0 57 1234689 7.4074 0 0 0 0 5 0 7 0 0 0 0 57 5689 10.6707 0 2 3 4 23 24 7 17 27 37 47 0 15689 11.9320 0 2 3 4 23 24 34 0 27 37 47 0 25689 11.2140 0 0 3 4 14 0 34 17 0 37 47 0 125689 7.0216 0 0 3 4 0 0 7 0 0 37 47 0 35689 13.5545 0 2 12 4 14 24 7 17 27 0 47 0 135689 10.2623 0 2 0 4 0 24 7 0 27 0 47 0 235689 10.1852 0 0 0 4 14 0 7 17 0 0 47 0 1235689 9.7222 0 0 0 4 0 0 7 0 0 0 47 0 45689 14.1718 0 2 12 13 23 0 7 17 27 37 0 0 145689 9.9280 0 2 3 0 23 0 7 0 27 37 0 0 245689 9.7222 0 0 3 13 0 0 7 17 0 37 0 0 1245689 12.0370 0 0 3 0 0 0 7 0 0 37 0 0 345689 9.2593 0 2 12 0 0 0 7 17 27 0 0 0 1345689 14.3519 0 2 0 0 0 0 7 0 27 0 0 0 2345689 16.6667 0 0 0 0 0 0 7 17 0 0 0 0 12345689 16.6667 0 0 0 0 0 0 7 0 0 0 0 0 789 13.5322 0 2 12 13 14 15 16 26 45 46 56 0 1789 11.5336 0 2 3 4 5 6 34 26 36 46 56 0 2789 10.9218 0 0 3 4 5 6 16 35 45 46 56 0 12789 11.3169 0 0 3 4 5 6 34 35 36 46 56 0 3789 10.5538 0 2 12 4 5 6 16 26 45 46 56 0 13789 12.3250 0 2 0 4 5 6 25 26 45 46 56 0 23789 11.1883 0 0 0 4 5 15 16 0 45 46 56 0 123789 8.3076 0 0 0 4 5 6 0 0 45 46 56 0 4789 10.7981 0 2 3 13 5 6 25 26 36 0 56 0 14789 11.3340 0 2 3 0 5 6 25 26 36 0 56 0 24789 13.5445 0 0 3 13 5 15 16 35 36 0 56 0 124789 9.5422 0 0 3 0 5 6 0 35 36 0 56 0 34789 11.6570 0 2 12 0 5 15 16 26 0 0 56 0 134789 10.7767 0 2 0 0 5 6 25 26 0 0 56 0 234789 8.8992 0 0 0 0 5 6 16 0 0 0 56 0 1234789 9.7222 0 0 0 0 5 6 0 0 0 0 56 0 5789 10.4673 0 2 3 4 23 6 16 26 36 46 0 0 15789 14.7001 0 2 3 4 23 24 34 26 36 46 0 0 25789 11.7477 0 0 3 13 14 6 16 0 36 46 0 0 125789 10.5195 0 0 3 4 0 6 34 0 36 46 0 0 35789 14.8984 0 2 12 4 14 24 16 26 0 46 0 0 135789 8.5134 0 2 0 4 0 6 0 26 0 46 0 0 235789 10.6867 0 0 0 4 14 6 16 0 0 46 0 0 1235789 12.0370 0 0 0 4 0 6 0 0 0 46 0 0 45789 16.1515 0 2 12 13 23 6 16 26 36 0 0 0 145789 10.4295 0 2 3 0 23 6 0 26 36 0 0 0 245789 10.1595 0 0 3 13 0 6 16 0 36 0 0 0 1245789 14.3519 0 0 3 0 0 6 0 0 36 0 0 0 345789 9.6322 0 2 12 0 0 6 16 26 0 0 0 0 1345789 16.6667 0 2 0 0 0 6 0 26 0 0 0 0 2345789 18.9815 0 0 0 0 0 6 16 0 0 0 0 0 12345789 16.6667 0 0 0 0 0 6 0 0 0 0 0 0 6789 9.6811 0 2 3 4 5 15 34 35 45 0 0 0 16789 14.3304 0 2 3 4 23 24 25 35 45 0 0 0 26789 15.4150 0 0 3 13 14 15 34 35 45 0 0 0 126789 11.2397 0 0 3 4 5 0 34 35 45 0 0 0 36789 13.1602 0 2 12 4 14 15 25 0 45 0 0 0 136789 11.3940 0 2 0 4 5 24 25 0 45 0 0 0 236789 8.4877 0 0 0 4 5 15 0 0 45 0 0 0 1236789 14.3519 0 0 0 4 5 0 0 0 45 0 0 0 46789 15.1235 0 2 12 13 23 15 25 35 0 0 0 0 146789 9.0792 0 2 3 0 5 0 25 35 0 0 0 0 246789 9.7222 0 0 3 13 5 15 0 35 0 0 0 0 1246789 16.6667 0 0 3 0 5 0 0 35 0 0 0 0 346789 9.1049 0 2 12 0 5 15 25 0 0 0 0 0 1346789 18.9815 0 2 0 0 5 0 25 0 0 0 0 0 2346789 22.2222 1 0 0 0 5 15 0 0 0 0 0 0 12346789 16.6667 0 0 0 0 5 0 0 0 0 0 0 0 56789 12.3800 0 2 12 13 14 24 34 0 0 0 0 0 156789 10.5581 0 2 3 4 23 24 34 0 0 0 0 0 256789 7.7160 0 0 3 4 14 0 34 0 0 0 0 0 1256789 18.9815 0 0 3 4 0 0 34 0 0 0 0 0 356789 7.5617 0 2 12 4 14 24 0 0 0 0 0 0 1356789 22.2222 0 2 0 4 0 24 0 0 0 0 0 0 2356789 22.2222 1 0 0 4 14 0 0 0 0 0 0 0 12356789 16.6667 0 0 0 4 0 0 0 0 0 0 0 0 456789 16.6667 1 2 3 13 23 0 0 0 0 0 0 0 1456789 22.2222 0 2 3 0 23 0 0 0 0 0 0 0 2456789 22.2222 1 0 3 13 0 0 0 0 0 0 0 0 12456789 16.6667 0 0 3 0 0 0 0 0 0 0 0 0 3456789 22.2222 1 2 12 0 0 0 0 0 0 0 0 0 13456789 16.6667 0 2 0 0 0 0 0 0 0 0 0 0 23456789 16.6667 1 0 0 0 0 0 0 0 0 0 0 0 123456789 100.0000 0 0 0 0 0 0 0 0 0 0 0 0 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 return to the main "Shut the Box" page.