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. 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 9.7614 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 5.7121 0 0 3 4 5 6 7 8 9 19 38 39 12 2.6640 0 0 3 4 5 6 7 8 9 46 38 39 3 6.6163 0 2 12 4 5 6 7 8 9 19 29 48 13 3.1084 0 2 0 4 5 6 7 8 9 46 29 48 23 3.5270 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 7.3866 0 2 3 13 5 6 7 8 9 19 29 39 14 3.5461 0 2 3 0 5 6 7 8 9 28 29 39 24 4.3140 0 0 3 13 5 6 7 8 9 19 38 57 124 1.8713 0 0 3 0 5 6 7 8 9 37 56 39 34 4.6945 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 2.5599 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 8.3159 0 2 3 4 23 6 7 8 9 19 29 39 15 4.3235 0 2 3 4 23 6 7 8 9 46 29 39 25 4.8022 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 5.7659 0 2 12 4 14 6 7 8 9 19 29 48 135 2.5903 0 2 0 4 0 6 7 8 9 46 29 48 235 3.2440 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 6.3774 0 2 3 13 23 6 7 8 9 19 29 39 145 3.1887 0 2 3 0 23 6 7 8 9 37 29 39 245 3.6184 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 3.8349 0 2 12 0 0 6 7 8 9 19 29 129 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 8.9972 0 2 3 4 5 24 7 8 9 19 29 39 16 4.6173 0 2 3 4 5 24 7 8 9 37 29 39 26 5.1369 0 0 3 4 5 15 7 8 9 19 38 39 126 2.1381 0 0 3 4 5 0 7 8 9 37 38 39 36 6.3437 0 2 12 4 5 15 7 8 9 19 29 48 136 2.8481 0 2 0 4 5 24 7 8 9 28 29 57 236 3.3358 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 7.0469 0 2 3 13 5 15 7 8 9 28 29 39 146 3.1128 0 2 3 0 5 0 7 8 9 28 29 39 246 4.2828 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 4.9042 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 7.9139 0 2 3 4 14 24 7 8 9 19 38 39 156 4.2713 0 2 3 4 23 24 7 8 9 37 29 39 256 4.2066 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 5.9479 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 3.1464 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 6.1741 0 2 3 13 23 123 7 8 9 19 29 39 1456 3.2750 0 2 3 0 23 0 7 8 9 37 29 39 2456 3.7509 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 4.0695 0 2 12 0 0 0 7 8 9 19 29 129 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 9.8168 0 2 3 4 5 6 25 8 9 19 29 39 17 5.3167 0 2 3 4 5 6 34 8 9 28 29 39 27 5.7793 0 0 3 4 5 6 34 8 9 19 56 39 127 2.7079 0 0 3 4 5 6 34 8 9 46 56 39 37 6.8764 0 2 12 4 5 6 25 8 9 19 29 48 137 3.3637 0 2 0 4 5 6 25 8 9 46 29 48 237 3.4516 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 7.7568 0 2 3 13 5 6 25 8 9 19 29 39 147 3.6987 0 2 3 0 5 6 25 8 9 28 38 39 247 4.4039 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 5.4391 0 2 12 0 5 6 25 8 9 19 29 156 1347 2.5914 0 2 0 0 5 6 25 8 9 28 56 0 2347 3.0143 0 0 0 0 5 6 16 8 9 19 56 156 12347 1.1860 0 0 0 0 5 6 0 8 9 0 56 0 57 8.8791 0 2 3 4 23 6 16 8 9 19 29 39 157 4.6634 0 2 3 4 23 6 34 8 9 28 29 48 257 5.4643 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 6.3389 0 2 12 4 14 6 16 8 9 28 29 48 1357 2.6101 0 2 0 4 0 6 0 8 9 46 29 48 2357 3.7116 0 0 0 4 14 6 16 8 9 19 146 48 12357 1.6032 0 0 0 4 0 6 0 8 9 46 0 48 457 7.1084 0 2 3 13 23 6 16 8 9 19 29 39 1457 3.1368 0 2 3 0 23 6 0 8 9 28 29 39 2457 4.4825 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 5.2780 0 2 12 0 0 6 16 8 9 28 29 129 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 9.6654 0 2 3 4 5 15 34 8 9 19 29 39 167 5.1522 0 2 3 4 5 24 34 8 9 28 29 39 267 5.4005 0 0 3 4 5 15 34 8 9 19 38 39 1267 2.2181 0 0 3 4 5 0 34 8 9 0 38 39 367 6.8985 0 2 12 4 5 15 25 8 9 19 29 48 1367 3.4155 0 2 0 4 5 24 25 8 9 28 29 48 2367 2.9914 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 7.6174 0 2 3 13 5 15 25 8 9 28 38 39 1467 3.8917 0 2 3 0 5 0 25 8 9 28 38 39 2467 4.2279 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 6.2731 0 2 12 0 5 15 25 8 9 19 29 129 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 8.6798 0 2 3 4 14 24 34 8 9 19 29 39 1567 5.3265 0 2 3 4 23 24 34 8 9 28 29 39 2567 5.2476 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 6.8644 0 2 12 4 14 24 124 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 6.5634 0 2 3 13 23 123 0 8 9 19 29 39 14567 3.5265 0 2 3 0 23 0 0 8 9 28 29 39 24567 4.1209 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 4.9583 0 2 12 0 0 0 0 8 9 19 29 129 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 11.8771 0 2 3 4 5 6 7 35 9 19 29 39 18 6.5065 0 2 3 4 5 6 7 35 9 46 29 39 28 7.4048 0 0 3 4 5 6 7 35 9 19 47 39 128 3.6767 0 0 3 4 5 6 7 35 9 46 47 39 38 8.3372 0 2 12 4 5 6 7 26 9 19 29 57 138 3.9406 0 2 0 4 5 6 7 26 9 46 29 57 238 4.6603 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 9.7448 0 2 3 13 5 6 7 26 9 19 29 39 148 5.0294 0 2 3 0 5 6 7 35 9 37 29 39 248 6.1017 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 6.6554 0 2 12 0 5 6 7 26 9 19 56 57 1348 3.0274 0 2 0 0 5 6 7 26 9 0 29 57 2348 4.0195 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 10.6783 0 2 3 4 14 6 7 17 9 19 29 39 158 5.5886 0 2 3 4 23 6 7 26 9 46 29 39 258 6.1940 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 7.9628 0 2 12 4 14 6 7 26 9 19 29 246 1358 3.7566 0 2 0 4 0 6 7 26 9 46 29 246 2358 4.7604 0 0 0 4 14 6 7 17 9 46 47 147 12358 2.1433 0 0 0 4 0 6 7 0 9 46 47 0 458 9.0871 0 2 3 13 23 6 7 26 9 19 29 39 1458 4.9516 0 2 3 0 23 6 7 26 9 37 29 39 2458 5.0512 0 0 3 13 0 6 7 17 9 19 137 39 12458 2.3834 0 0 3 0 0 6 7 0 9 37 0 39 3458 6.3910 0 2 12 0 0 6 7 26 9 19 29 129 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 11.8326 0 2 3 4 5 24 7 35 9 19 29 39 168 6.2173 0 2 3 4 5 24 7 35 9 37 29 39 268 7.2756 0 0 3 4 5 15 7 35 9 19 47 39 1268 3.3936 0 0 3 4 5 0 7 35 9 37 47 39 368 8.5553 0 2 12 4 5 24 7 17 9 19 29 57 1368 3.3350 0 2 0 4 5 24 7 0 9 0 29 57 2368 5.0740 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 9.9074 0 2 3 13 5 15 7 35 9 37 29 39 1468 4.9449 0 2 3 0 5 0 7 35 9 37 29 39 2468 6.7668 0 0 3 13 5 15 7 35 9 19 137 39 12468 3.2493 0 0 3 0 5 0 7 35 9 37 0 39 3468 7.4974 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 10.7560 0 2 3 4 23 24 7 17 9 19 29 39 1568 5.3855 0 2 3 4 23 24 7 0 9 37 29 39 2568 6.2000 0 0 3 4 14 0 7 17 9 19 47 39 12568 2.8635 0 0 3 4 0 0 7 0 9 37 47 39 3568 8.8763 0 2 12 4 14 24 7 17 9 19 29 129 13568 3.5322 0 2 0 4 0 24 7 0 9 0 29 0 23568 5.4527 0 0 0 4 14 0 7 17 9 19 47 147 123568 2.4691 0 0 0 4 0 0 7 0 9 0 47 0 4568 9.5650 0 2 3 13 23 123 7 17 9 19 29 39 14568 4.8011 0 2 3 0 23 0 7 0 9 37 29 39 24568 6.1471 0 0 3 13 0 0 7 17 9 19 137 39 124568 3.8066 0 0 3 0 0 0 7 0 9 37 0 39 34568 7.4074 0 2 12 0 0 0 7 17 9 19 29 129 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 12.9318 0 2 3 4 5 6 34 35 9 19 29 39 178 7.5140 0 2 3 4 5 6 34 35 9 46 29 39 278 8.2762 0 0 3 4 5 6 34 35 9 19 56 39 1278 4.4031 0 0 3 4 5 6 34 35 9 46 56 39 378 9.2067 0 2 12 4 5 6 25 26 9 19 29 129 1378 4.9435 0 2 0 4 5 6 25 26 9 46 29 246 2378 4.6268 0 0 0 4 5 6 16 0 9 19 56 156 12378 2.1691 0 0 0 4 5 6 0 0 9 46 56 0 478 11.3626 0 2 3 13 5 6 16 35 9 19 29 39 1478 5.9151 0 2 3 0 5 6 25 35 9 235 29 39 2478 7.3300 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 8.5701 0 2 12 0 5 6 25 26 9 19 29 129 13478 4.2210 0 2 0 0 5 6 25 26 9 0 29 0 23478 5.1555 0 0 0 0 5 6 16 0 9 19 56 156 123478 2.5034 0 0 0 0 5 6 0 0 9 0 56 0 578 12.4305 0 2 3 4 23 6 34 26 9 19 29 39 1578 7.0925 0 2 3 4 23 6 34 26 9 46 29 39 2578 7.6296 0 0 3 4 14 6 34 134 9 19 146 39 12578 3.6137 0 0 3 4 0 6 34 0 9 46 0 39 3578 9.4625 0 2 12 4 14 6 16 26 9 19 29 129 13578 4.5853 0 2 0 4 0 6 0 26 9 46 29 246 23578 5.6541 0 0 0 4 14 6 16 0 9 19 146 0 123578 2.9321 0 0 0 4 0 6 0 0 9 46 0 0 4578 10.8522 0 2 3 13 23 6 16 26 9 19 29 39 14578 5.3169 0 2 3 0 23 6 0 26 9 0 29 39 24578 6.1185 0 0 3 13 0 6 16 0 9 19 0 39 124578 2.9750 0 0 3 0 0 6 0 0 9 0 0 39 34578 9.4636 0 2 12 0 0 6 16 26 9 19 29 129 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 13.6717 0 2 3 4 5 24 34 35 9 19 29 39 1678 7.7892 0 2 3 4 5 24 34 35 9 235 29 39 2678 8.2662 0 0 3 4 5 15 34 35 9 19 0 39 12678 3.9180 0 0 3 4 5 0 34 35 9 0 0 39 3678 10.0016 0 2 12 4 5 24 25 125 9 19 29 129 13678 4.7468 0 2 0 4 5 24 25 0 9 0 29 0 23678 4.6553 0 0 0 4 5 15 0 0 9 19 0 0 123678 2.1605 0 0 0 4 5 0 0 0 9 0 0 0 4678 11.6446 0 2 3 13 5 15 25 35 9 19 29 39 14678 7.3417 0 2 3 0 5 0 25 35 9 235 29 39 24678 7.7303 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 11.4398 0 2 12 0 5 15 25 125 9 19 29 129 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 12.4069 0 2 3 4 23 24 34 134 9 19 29 39 15678 7.3288 0 2 3 4 23 24 34 0 9 0 29 39 25678 9.2378 0 0 3 4 14 0 34 134 9 19 0 39 125678 5.0154 0 0 3 4 0 0 34 0 9 0 0 39 35678 11.3897 0 2 12 4 14 24 124 0 9 19 29 129 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 11.3569 0 2 3 13 23 123 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 8.4619 0 2 12 0 0 0 0 0 9 19 29 129 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 14.5017 0 2 3 4 5 6 7 8 18 28 38 48 19 8.6943 0 2 3 4 5 6 7 8 45 28 38 48 29 9.4705 0 0 3 4 5 6 7 8 18 46 38 48 129 5.1464 0 0 3 4 5 6 7 8 45 37 38 48 39 10.7384 0 2 12 4 5 6 7 8 18 28 56 57 139 5.8036 0 2 0 4 5 6 7 8 45 28 56 48 239 6.4056 0 0 0 4 5 6 7 8 18 46 47 57 1239 3.2303 0 0 0 4 5 6 7 8 45 46 56 48 49 11.8751 0 2 3 13 5 6 7 8 18 28 56 57 149 6.2750 0 2 3 0 5 6 7 8 36 28 38 57 249 7.6374 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 7.9049 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 4.3892 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 13.4249 0 2 3 4 14 6 7 8 18 28 38 48 159 7.9220 0 2 3 4 23 6 7 8 36 46 38 48 259 8.5915 0 0 3 4 14 6 7 8 18 37 47 48 1259 4.5385 0 0 3 4 0 6 7 8 36 46 38 48 359 10.0464 0 2 12 4 14 6 7 8 18 28 47 48 1359 5.0719 0 2 0 4 0 6 7 8 27 46 47 48 2359 6.3615 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 11.0793 0 2 3 13 23 6 7 8 18 28 38 138 1459 6.4924 0 2 3 0 23 6 7 8 36 28 38 237 2459 7.1956 0 0 3 13 0 6 7 8 18 37 38 138 12459 4.0595 0 0 3 0 0 6 7 8 36 37 38 0 3459 7.0009 0 2 12 0 0 6 7 8 18 28 128 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 14.6694 0 2 3 4 5 15 7 8 18 28 38 48 169 8.6155 0 2 3 4 5 24 7 8 45 28 38 57 269 9.4097 0 0 3 4 5 15 7 8 18 37 38 48 1269 5.0233 0 0 3 4 5 0 7 8 45 37 38 48 369 11.3644 0 2 12 4 5 15 7 8 18 28 47 57 1369 6.3959 0 2 0 4 5 24 7 8 45 28 47 57 2369 6.9352 0 0 0 4 5 15 7 8 18 145 47 48 12369 3.4486 0 0 0 4 5 0 7 8 45 0 47 48 469 12.5326 0 2 3 13 5 15 7 8 18 28 38 57 1469 5.8079 0 2 3 0 5 0 7 8 27 28 38 57 2469 8.5291 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 9.2932 0 2 12 0 5 15 7 8 27 28 128 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 14.2096 0 2 3 4 14 24 7 8 18 37 38 48 1569 8.7958 0 2 3 4 23 24 7 8 27 37 38 48 2569 8.0043 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 11.5859 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 6.4815 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 12.3232 0 2 3 13 23 123 7 8 18 28 38 138 14569 7.2595 0 2 3 0 23 0 7 8 27 28 38 237 24569 8.4662 0 0 3 13 0 0 7 8 18 37 38 138 124569 5.4527 0 0 3 0 0 0 7 8 0 37 38 0 34569 8.9592 0 2 12 0 0 0 7 8 18 28 128 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 16.0787 0 2 3 4 5 6 25 8 18 28 38 48 179 10.2203 0 2 3 4 5 6 25 8 36 28 38 48 279 10.7627 0 0 3 4 5 6 34 8 18 46 38 48 1279 6.0817 0 0 3 4 5 6 34 8 45 46 38 48 379 12.8127 0 2 12 4 5 6 25 8 18 46 56 48 1379 7.0842 0 2 0 4 5 6 25 8 45 28 56 48 2379 7.8213 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 13.9222 0 2 3 13 5 6 25 8 18 28 38 138 1479 7.5600 0 2 3 0 5 6 25 8 36 28 38 0 2479 8.5861 0 0 3 13 5 6 16 8 18 136 38 138 12479 3.7366 0 0 3 0 5 6 0 8 36 0 38 0 3479 10.4191 0 2 12 0 5 6 25 8 18 28 56 156 13479 5.3748 0 2 0 0 5 6 25 8 0 28 56 0 23479 6.6008 0 0 0 0 5 6 16 8 18 0 56 156 123479 3.1293 0 0 0 0 5 6 0 8 0 0 56 0 579 16.1995 0 2 3 4 23 6 16 8 18 28 38 48 1579 9.5680 0 2 3 4 23 6 34 8 36 28 38 48 2579 11.0281 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 12.2660 0 2 12 4 14 6 16 8 18 28 128 48 13579 4.7114 0 2 0 4 0 6 0 8 0 28 0 48 23579 9.3664 0 0 0 4 14 6 16 8 18 46 146 48 123579 4.5139 0 0 0 4 0 6 0 8 0 46 0 48 4579 14.1431 0 2 3 13 23 6 16 8 18 28 38 138 14579 7.5839 0 2 3 0 23 6 0 8 36 28 38 0 24579 10.5781 0 0 3 13 0 6 16 8 18 136 38 138 124579 5.8985 0 0 3 0 0 6 0 8 36 0 38 0 34579 11.3655 0 2 12 0 0 6 16 8 18 28 128 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 17.4266 0 2 3 4 5 15 34 8 18 28 38 48 1679 10.7726 0 2 3 4 5 24 34 8 45 28 38 48 2679 11.3565 0 0 3 4 5 15 34 8 18 145 38 48 12679 6.2800 0 0 3 4 5 0 34 8 45 0 38 48 3679 13.8174 0 2 12 4 5 24 25 8 18 28 128 48 13679 9.3157 0 2 0 4 5 24 25 8 45 28 245 48 23679 8.1662 0 0 0 4 5 15 0 8 18 145 0 48 123679 5.0154 0 0 0 4 5 0 0 8 45 0 0 48 4679 15.3495 0 2 3 13 5 15 25 8 18 28 38 138 14679 7.7175 0 2 3 0 5 0 25 8 0 28 38 0 24679 9.6008 0 0 3 13 5 15 0 8 18 0 38 138 124679 4.4153 0 0 3 0 5 0 0 8 0 0 38 0 34679 13.7446 0 2 12 0 5 15 25 8 18 28 128 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 17.2479 0 2 3 4 23 24 34 8 18 28 38 48 15679 13.0180 0 2 3 4 23 24 34 8 234 28 38 48 25679 11.4862 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 16.2916 0 2 12 4 14 24 124 8 18 28 128 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 16.0051 0 2 3 13 23 123 0 8 18 28 38 138 145679 7.7975 0 2 3 0 23 0 0 8 0 28 38 0 245679 10.5453 0 0 3 13 0 0 0 8 18 0 38 138 1245679 8.6420 0 0 3 0 0 0 0 8 0 0 38 0 345679 13.0273 0 2 12 0 0 0 0 8 18 28 128 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 18.7212 0 2 3 4 5 6 7 17 45 46 47 57 189 12.5063 0 2 3 4 5 6 7 26 27 37 47 57 289 13.7636 0 0 3 4 5 6 7 17 36 46 47 57 1289 8.2419 0 0 3 4 5 6 7 35 45 46 47 57 389 15.0517 0 2 12 4 5 6 7 17 27 46 56 57 1389 8.9360 0 2 0 4 5 6 7 26 45 46 47 57 2389 9.8926 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 16.9438 0 2 3 13 5 6 7 26 27 37 56 57 1489 10.2290 0 2 3 0 5 6 7 35 27 37 56 57 2489 12.0656 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 11.8281 0 2 12 0 5 6 7 17 27 127 56 57 13489 7.3131 0 2 0 0 5 6 7 26 27 0 56 57 23489 7.0945 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 18.8183 0 2 3 4 14 6 7 17 36 46 47 237 1589 11.6698 0 2 3 4 23 6 7 26 27 46 47 237 2589 12.9133 0 0 3 4 14 6 7 17 36 37 47 147 12589 6.5801 0 0 3 4 0 6 7 0 36 37 47 0 3589 15.2953 0 2 12 4 14 6 7 26 27 46 47 147 13589 9.5057 0 2 0 4 0 6 7 26 27 46 47 246 23589 10.3009 0 0 0 4 14 6 7 17 0 46 47 147 123589 6.0957 0 0 0 4 0 6 7 0 0 46 47 0 4589 17.0596 0 2 3 13 23 6 7 17 27 37 137 237 14589 11.7541 0 2 3 0 23 6 7 26 27 37 236 237 24589 12.4143 0 0 3 13 0 6 7 17 36 37 137 0 124589 7.5874 0 0 3 0 0 6 7 0 36 37 0 0 34589 12.2128 0 2 12 0 0 6 7 17 27 127 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 20.5412 0 2 3 4 5 24 7 17 45 37 47 57 1689 13.5645 0 2 3 4 5 24 7 35 27 37 47 57 2689 14.4276 0 0 3 4 5 15 7 17 45 37 47 57 12689 9.5850 0 0 3 4 5 0 7 35 45 37 47 57 3689 16.8810 0 2 12 4 5 24 7 17 45 127 47 57 13689 9.0706 0 2 0 4 5 24 7 0 27 0 47 57 23689 13.5674 0 0 0 4 5 15 7 17 45 145 47 57 123689 7.3302 0 0 0 4 5 0 7 0 45 0 47 57 4689 18.9751 0 2 3 13 5 15 7 35 27 37 137 57 14689 11.0039 0 2 3 0 5 0 7 35 27 37 0 57 24689 15.6121 0 0 3 13 5 15 7 17 135 37 137 57 124689 8.6934 0 0 3 0 5 0 7 35 0 37 0 57 34689 15.5993 0 2 12 0 5 15 7 17 27 127 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 21.0516 0 2 3 4 23 24 7 17 27 37 47 147 15689 13.8460 0 2 3 4 23 24 7 0 27 37 47 237 25689 13.1173 0 0 3 4 14 0 7 17 0 37 47 147 125689 7.0216 0 0 3 4 0 0 7 0 0 37 47 0 35689 18.9558 0 2 12 4 14 24 7 17 27 127 47 147 135689 10.2623 0 2 0 4 0 24 7 0 27 0 47 0 235689 12.9630 0 0 0 4 14 0 7 17 0 0 47 147 1235689 9.7222 0 0 0 4 0 0 7 0 0 0 47 0 45689 21.1163 0 2 3 13 23 123 7 17 27 37 137 237 145689 12.7058 0 2 3 0 23 0 7 0 27 37 0 237 245689 15.2778 0 0 3 13 0 0 7 17 0 37 137 0 1245689 12.0370 0 0 3 0 0 0 7 0 0 37 0 0 345689 17.5926 0 2 12 0 0 0 7 17 27 127 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 22.0818 0 2 3 4 5 6 16 35 45 46 56 156 1789 15.6689 0 2 3 4 5 6 34 26 36 46 56 246 2789 16.8774 0 0 3 4 5 6 16 35 45 46 56 156 12789 12.1656 0 0 3 4 5 6 34 35 36 46 56 345 3789 18.8665 0 2 12 4 5 6 16 26 45 46 56 156 13789 13.8682 0 2 0 4 5 6 25 26 45 46 56 246 23789 13.1644 0 0 0 4 5 6 16 0 45 46 56 156 123789 8.3076 0 0 0 4 5 6 0 0 45 46 56 0 4789 21.1283 0 2 3 13 5 6 25 26 36 136 56 156 14789 14.4976 0 2 3 0 5 6 25 26 36 235 56 0 24789 17.3768 0 0 3 13 5 6 16 35 36 136 56 156 124789 9.5422 0 0 3 0 5 6 0 35 36 0 56 0 34789 16.1623 0 2 12 0 5 6 16 26 126 0 56 156 134789 10.7767 0 2 0 0 5 6 25 26 0 0 56 0 234789 11.6770 0 0 0 0 5 6 16 0 0 0 56 156 1234789 9.7222 0 0 0 0 5 6 0 0 0 0 56 0 5789 23.0306 0 2 3 4 23 6 16 26 36 46 146 246 15789 17.7226 0 2 3 4 23 6 34 26 36 46 236 246 25789 17.7641 0 0 3 4 14 6 16 134 36 46 146 0 125789 10.5195 0 0 3 4 0 6 34 0 36 46 0 0 35789 19.9481 0 2 12 4 14 6 16 26 126 46 146 246 135789 11.2912 0 2 0 4 0 6 0 26 0 46 0 246 235789 16.2423 0 0 0 4 14 6 16 0 0 46 146 0 1235789 12.0370 0 0 0 4 0 6 0 0 0 46 0 0 45789 24.1455 0 2 3 13 23 6 16 26 36 136 236 1236 145789 15.9851 0 2 3 0 23 6 0 26 36 0 236 0 245789 18.4928 0 0 3 13 0 6 16 0 36 136 0 0 1245789 14.3519 0 0 3 0 0 6 0 0 36 0 0 0 345789 20.7433 0 2 12 0 0 6 16 26 126 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 24.4831 0 2 3 4 5 15 34 35 45 145 245 345 16789 19.0015 0 2 3 4 5 24 25 35 45 235 245 345 26789 18.8186 0 0 3 4 5 15 34 35 45 145 0 345 126789 14.0175 0 0 3 4 5 0 34 35 45 0 0 345 36789 22.5394 0 2 12 4 5 15 25 125 45 145 245 1245 136789 16.9496 0 2 0 4 5 24 25 0 45 0 245 0 236789 16.8210 0 0 0 4 5 15 0 0 45 145 0 0 1236789 14.3519 0 0 0 4 5 0 0 0 45 0 0 0 46789 25.8145 0 2 3 13 5 15 25 35 135 235 1235 0 146789 17.4126 0 2 3 0 5 0 25 35 0 235 0 0 246789 20.8333 0 0 3 13 5 15 0 35 135 0 0 0 1246789 16.6667 0 0 3 0 5 0 0 35 0 0 0 0 346789 22.9938 0 2 12 0 5 15 25 125 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 26.4832 0 2 3 4 14 24 34 134 234 1234 0 0 156789 21.6692 0 2 3 4 23 24 34 0 234 0 0 0 256789 21.6049 0 0 3 4 14 0 34 134 0 0 0 0 1256789 18.9815 0 0 3 4 0 0 34 0 0 0 0 0 356789 24.2284 0 2 12 4 14 24 124 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 33.3333 1 2 3 13 23 123 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.