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: This variation always uses two dice. Already Dice Dice Dice Dice Dice Dice Dice Dice Dice Dice Dice Flipped Expected Sum Sum Sum Sum Sum Sum Sum Sum Sum Sum Sum Digits Value =2 =3 =4 =5 =6 =7 =8 =9 =10 =11 =12 ---------------------------------------------------------------------------- 0 7.1432 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 2 4.5190 0 3 4 5 6 7 8 9 19 38 39 12 2.3024 0 3 4 5 6 7 8 9 46 38 39 3 5.1068 2 12 4 5 6 7 8 9 19 29 48 13 2.6320 2 0 4 5 6 7 8 9 46 29 48 23 2.8973 0 0 4 5 6 7 8 9 19 56 48 123 1.3443 0 0 4 5 6 7 8 9 46 56 48 4 5.5327 2 3 13 5 6 7 8 9 19 29 39 14 2.9697 2 3 0 5 6 7 8 9 28 29 39 24 3.5086 0 3 13 5 6 7 8 9 19 38 39 124 1.6577 0 3 0 5 6 7 8 9 37 56 39 34 3.7561 2 12 0 5 6 7 8 9 19 29 57 134 1.9685 2 0 0 5 6 7 8 9 28 56 57 234 2.2027 0 0 0 5 6 7 8 9 19 56 57 1234 0.9621 0 0 0 5 6 7 8 9 0 56 57 5 6.1085 2 3 4 23 6 7 8 9 19 29 39 15 3.5110 2 3 4 23 6 7 8 9 46 29 39 25 3.8619 0 3 4 14 6 7 8 9 19 38 39 125 1.9322 0 3 4 0 6 7 8 9 46 38 39 35 4.4945 2 12 4 14 6 7 8 9 19 29 48 135 2.2124 2 0 4 0 6 7 8 9 46 29 48 235 2.7558 0 0 4 14 6 7 8 9 19 47 48 1235 1.3289 0 0 4 0 6 7 8 9 46 47 48 45 4.7872 2 3 13 23 6 7 8 9 19 29 39 145 2.6849 2 3 0 23 6 7 8 9 37 29 39 245 3.0113 0 3 13 0 6 7 8 9 19 38 39 1245 1.5670 0 3 0 0 6 7 8 9 37 38 39 345 3.1360 2 12 0 0 6 7 8 9 19 29 129 1345 1.7766 2 0 0 0 6 7 8 9 28 29 0 2345 1.8576 0 0 0 0 6 7 8 9 19 0 0 12345 0.8573 0 0 0 0 6 7 8 9 0 0 0 6 6.4993 2 3 4 5 24 7 8 9 19 29 39 16 3.7200 2 3 4 5 24 7 8 9 28 29 39 26 4.0148 0 3 4 5 15 7 8 9 19 38 39 126 1.8227 0 3 4 5 0 7 8 9 37 38 39 36 4.8720 2 12 4 5 15 7 8 9 19 29 48 136 2.3916 2 0 4 5 24 7 8 9 28 29 57 236 2.7399 0 0 4 5 15 7 8 9 19 47 48 1236 1.0774 0 0 4 5 0 7 8 9 0 47 48 46 5.1594 2 3 13 5 15 7 8 9 28 29 39 146 2.5710 2 3 0 5 0 7 8 9 28 29 39 246 3.4613 0 3 13 5 15 7 8 9 19 38 39 1246 1.5525 0 3 0 5 0 7 8 9 37 38 57 346 3.8894 2 12 0 5 15 7 8 9 28 29 57 1346 1.9042 2 0 0 5 0 7 8 9 28 29 57 2346 2.2277 0 0 0 5 15 7 8 9 19 0 57 12346 0.9431 0 0 0 5 0 7 8 9 0 0 57 56 5.6673 2 3 4 14 24 7 8 9 19 38 39 156 3.4512 2 3 4 23 24 7 8 9 37 29 39 256 3.2705 0 3 4 14 0 7 8 9 19 38 39 1256 1.7209 0 3 4 0 0 7 8 9 37 47 39 356 4.5663 2 12 4 14 24 7 8 9 19 29 48 1356 2.3315 2 0 4 0 24 7 8 9 28 47 48 2356 2.5720 0 0 4 14 0 7 8 9 19 47 48 12356 1.3374 0 0 4 0 0 7 8 9 0 47 48 456 4.4186 2 3 13 23 123 7 8 9 19 29 39 1456 2.6611 2 3 0 23 0 7 8 9 37 29 39 2456 2.9935 0 3 13 0 0 7 8 9 19 38 39 12456 2.1176 0 3 0 0 0 7 8 9 37 38 39 3456 3.1922 2 12 0 0 0 7 8 9 19 29 129 13456 2.3834 2 0 0 0 0 7 8 9 28 29 0 23456 2.4177 0 0 0 0 0 7 8 9 19 0 0 123456 1.5432 0 0 0 0 0 7 8 9 0 0 0 7 7.1253 2 3 4 5 6 25 8 9 19 29 39 17 4.3147 2 3 4 5 6 34 8 9 28 29 39 27 4.5302 0 3 4 5 6 34 8 9 19 56 39 127 2.3181 0 3 4 5 6 34 8 9 46 56 39 37 5.2496 2 12 4 5 6 25 8 9 19 29 48 137 2.8257 2 0 4 5 6 25 8 9 46 29 48 237 2.7715 0 0 4 5 6 16 8 9 19 56 48 1237 1.2555 0 0 4 5 6 0 8 9 46 56 48 47 5.7305 2 3 13 5 6 25 8 9 19 29 39 147 3.0640 2 3 0 5 6 25 8 9 28 38 39 247 3.5042 0 3 13 5 6 16 8 9 19 38 39 1247 1.3952 0 3 0 5 6 0 8 9 0 56 39 347 4.3605 2 12 0 5 6 25 8 9 19 29 156 1347 2.2694 2 0 0 5 6 25 8 9 28 56 0 2347 2.5492 0 0 0 5 6 16 8 9 19 56 156 12347 1.0860 0 0 0 5 6 0 8 9 0 56 0 57 6.4164 2 3 4 23 6 16 8 9 19 29 39 157 3.7441 2 3 4 23 6 34 8 9 28 29 48 257 4.3726 0 3 4 14 6 34 8 9 19 38 39 1257 2.2384 0 3 4 0 6 34 8 9 46 38 39 357 4.7877 2 12 4 14 6 16 8 9 28 29 48 1357 2.1486 2 0 4 0 6 0 8 9 46 29 48 2357 3.0900 0 0 4 14 6 16 8 9 19 146 48 12357 1.4575 0 0 4 0 6 0 8 9 46 0 48 457 5.0370 2 3 13 23 6 16 8 9 19 29 39 1457 2.5048 2 3 0 23 6 0 8 9 28 29 39 2457 3.6551 0 3 13 0 6 16 8 9 19 38 39 12457 1.6361 0 3 0 0 6 0 8 9 0 38 39 3457 4.2535 2 12 0 0 6 16 8 9 28 29 129 13457 2.2005 2 0 0 0 6 0 8 9 28 29 0 23457 3.0221 0 0 0 0 6 16 8 9 19 0 0 123457 1.2860 0 0 0 0 6 0 8 9 0 0 0 67 6.8609 2 3 4 5 15 34 8 9 19 29 39 167 4.1065 2 3 4 5 24 34 8 9 28 29 39 267 4.1259 0 3 4 5 15 34 8 9 19 38 39 1267 1.8519 0 3 4 5 0 34 8 9 0 38 39 367 5.1358 2 12 4 5 15 25 8 9 19 29 48 1367 2.8254 2 0 4 5 24 25 8 9 28 29 48 2367 2.3720 0 0 4 5 15 0 8 9 19 0 48 12367 1.0631 0 0 4 5 0 0 8 9 0 0 48 467 5.2841 2 3 13 5 15 25 8 9 19 38 39 1467 3.2144 2 3 0 5 0 25 8 9 28 38 39 2467 3.2386 0 3 13 5 15 0 8 9 19 38 39 12467 1.5404 0 3 0 5 0 0 8 9 0 38 39 3467 4.9783 2 12 0 5 15 25 8 9 19 29 129 13467 2.7892 2 0 0 5 0 25 8 9 28 29 0 23467 2.4691 0 0 0 5 15 0 8 9 19 0 0 123467 1.0288 0 0 0 5 0 0 8 9 0 0 0 567 5.9761 2 3 4 14 24 34 8 9 19 29 39 1567 4.3117 2 3 4 23 24 34 8 9 28 29 39 2567 4.0781 0 3 4 14 0 34 8 9 19 38 39 12567 2.3620 0 3 4 0 0 34 8 9 0 38 39 3567 5.1790 2 12 4 14 24 124 8 9 19 29 129 13567 2.5806 2 0 4 0 24 0 8 9 28 29 48 23567 2.3791 0 0 4 14 0 0 8 9 19 0 48 123567 1.3889 0 0 4 0 0 0 8 9 0 0 48 4567 4.2338 2 3 13 23 123 0 8 9 19 29 39 14567 2.5563 2 3 0 23 0 0 8 9 28 29 39 24567 2.9064 0 3 13 0 0 0 8 9 19 38 39 124567 2.5206 0 3 0 0 0 0 8 9 0 38 39 34567 3.5108 2 12 0 0 0 0 8 9 19 29 129 134567 3.6523 2 0 0 0 0 0 8 9 28 29 0 234567 3.5494 0 0 0 0 0 0 8 9 19 0 0 1234567 3.0864 0 0 0 0 0 0 8 9 0 0 0 8 8.4399 2 3 4 5 6 7 35 9 19 29 39 18 5.2094 2 3 4 5 6 7 35 9 37 29 39 28 5.7478 0 3 4 5 6 7 35 9 19 47 39 128 3.1561 0 3 4 5 6 7 35 9 46 47 39 38 6.2544 2 12 4 5 6 7 17 9 19 29 57 138 3.2649 2 0 4 5 6 7 26 9 46 29 57 238 3.7161 0 0 4 5 6 7 17 9 19 56 57 1238 1.7490 0 0 4 5 6 7 0 9 46 47 57 48 7.0869 2 3 13 5 6 7 26 9 19 29 39 148 4.1679 2 3 0 5 6 7 35 9 37 29 39 248 4.8618 0 3 13 5 6 7 35 9 19 56 39 1248 2.5756 0 3 0 5 6 7 35 9 37 56 39 348 5.1782 2 12 0 5 6 7 26 9 19 29 57 1348 2.6187 2 0 0 5 6 7 26 9 0 29 57 2348 3.4051 0 0 0 5 6 7 17 9 19 56 57 12348 1.5604 0 0 0 5 6 7 0 9 0 56 57 58 7.5821 2 3 4 14 6 7 17 9 19 29 39 158 4.3913 2 3 4 23 6 7 26 9 46 29 39 258 4.8212 0 3 4 14 6 7 17 9 19 47 39 1258 2.2848 0 3 4 0 6 7 0 9 46 47 39 358 6.0011 2 12 4 14 6 7 26 9 19 29 246 1358 3.1360 2 0 4 0 6 7 26 9 46 29 246 2358 3.9630 0 0 4 14 6 7 17 9 46 47 147 12358 1.9547 0 0 4 0 6 7 0 9 46 47 0 458 6.5059 2 3 13 23 6 7 26 9 19 29 39 1458 4.1028 2 3 0 23 6 7 26 9 37 29 39 2458 4.0602 0 3 13 0 6 7 17 9 19 137 39 12458 2.1176 0 3 0 0 6 7 0 9 37 0 39 3458 5.1483 2 12 0 0 6 7 26 9 19 29 129 13458 3.0007 2 0 0 0 6 7 26 9 0 29 0 23458 3.3693 0 0 0 0 6 7 17 9 19 0 0 123458 1.5432 0 0 0 0 6 7 0 9 0 0 0 68 8.2108 2 3 4 5 24 7 35 9 19 29 39 168 4.8501 2 3 4 5 24 7 35 9 37 29 39 268 5.4829 0 3 4 5 15 7 35 9 19 47 39 1268 2.8542 0 3 4 5 0 7 35 9 37 47 39 368 6.3344 2 12 4 5 24 7 17 9 19 29 57 1368 2.6911 2 0 4 5 24 7 0 9 0 29 57 2368 4.0252 0 0 4 5 15 7 17 9 19 47 57 12368 1.5947 0 0 4 5 0 7 0 9 0 47 57 468 6.9437 2 3 13 5 15 7 17 9 37 29 39 1468 4.0273 2 3 0 5 0 7 35 9 37 29 39 2468 5.4184 0 3 13 5 15 7 35 9 19 137 39 12468 2.8892 0 3 0 5 0 7 35 9 37 0 39 3468 5.7985 2 12 0 5 15 7 17 9 19 29 129 13468 2.4520 2 0 0 5 0 7 0 9 0 29 57 23468 3.9609 0 0 0 5 15 7 17 9 19 0 57 123468 1.8519 0 0 0 5 0 7 0 9 0 0 57 568 7.3762 2 3 4 23 24 7 17 9 19 29 39 1568 4.1162 2 3 4 23 24 7 0 9 37 29 39 2568 4.6875 0 3 4 14 0 7 17 9 19 47 39 12568 2.3405 0 3 4 0 0 7 0 9 37 47 39 3568 6.5158 2 12 4 14 24 7 17 9 19 29 129 13568 2.7949 2 0 4 0 24 7 0 9 0 29 0 23568 4.2438 0 0 4 14 0 7 17 9 19 47 147 123568 2.1605 0 0 4 0 0 7 0 9 0 47 0 4568 6.2321 2 3 13 23 123 7 17 9 19 29 39 14568 3.5922 2 3 0 23 0 7 0 9 37 29 39 24568 4.6039 0 3 13 0 0 7 17 9 19 137 39 124568 3.3951 0 3 0 0 0 7 0 9 37 0 39 34568 5.4270 2 12 0 0 0 7 17 9 19 29 129 134568 3.3951 2 0 0 0 0 7 0 9 0 29 0 234568 5.8642 0 0 0 0 0 7 17 9 19 0 0 1234568 3.7037 0 0 0 0 0 7 0 9 0 0 0 78 8.9218 2 3 4 5 6 34 35 9 19 29 39 178 5.9192 2 3 4 5 6 34 35 9 46 29 39 278 6.3099 0 3 4 5 6 34 35 9 19 56 39 1278 3.7485 0 3 4 5 6 34 35 9 46 56 39 378 6.7255 2 12 4 5 6 25 26 9 19 29 129 1378 4.0571 2 0 4 5 6 25 26 9 46 29 246 2378 3.5294 0 0 4 5 6 16 0 9 19 56 156 12378 1.7833 0 0 4 5 6 0 0 9 46 56 0 478 8.0131 2 3 13 5 6 16 35 9 19 29 39 1478 4.8219 2 3 0 5 6 25 35 9 235 29 39 2478 5.6491 0 3 13 5 6 16 35 9 19 56 39 12478 2.6978 0 3 0 5 6 0 35 9 0 56 39 3478 6.5629 2 12 0 5 6 25 26 9 19 29 129 13478 3.5780 2 0 0 5 6 25 26 9 0 29 0 23478 4.1924 0 0 0 5 6 16 0 9 19 56 156 123478 2.2634 0 0 0 5 6 0 0 9 0 56 0 578 8.6028 2 3 4 23 6 34 26 9 19 29 39 1578 5.4758 2 3 4 23 6 34 26 9 46 29 39 2578 5.9256 0 3 4 14 6 34 134 9 19 146 39 12578 2.9878 0 3 4 0 6 34 0 9 46 0 39 3578 6.6687 2 12 4 14 6 16 26 9 19 29 129 13578 3.5837 2 0 4 0 6 0 26 9 46 29 246 23578 4.4624 0 0 4 14 6 16 0 9 19 146 0 123578 2.6235 0 0 4 0 6 0 0 9 46 0 0 4578 6.8644 2 3 13 23 6 16 26 9 19 29 39 14578 4.0309 2 3 0 23 6 0 26 9 0 29 39 24578 4.5525 0 3 13 0 6 16 0 9 19 0 39 124578 2.5206 0 3 0 0 6 0 0 9 0 0 39 34578 7.1888 2 12 0 0 6 16 26 9 19 29 129 134578 4.8868 2 0 0 0 6 0 26 9 0 29 0 234578 6.0185 0 0 0 0 6 16 0 9 19 0 0 1234578 3.0864 0 0 0 0 6 0 0 9 0 0 0 678 9.1422 2 3 4 5 24 34 35 9 19 29 39 1678 5.9261 2 3 4 5 24 34 35 9 235 29 39 2678 5.9214 0 3 4 5 15 34 35 9 19 0 39 12678 3.1207 0 3 4 5 0 34 35 9 0 0 39 3678 6.9344 2 12 4 5 24 25 125 9 19 29 129 13678 3.6694 2 0 4 5 24 25 0 9 0 29 0 23678 3.4979 0 0 4 5 15 0 0 9 19 0 0 123678 1.8519 0 0 4 5 0 0 0 9 0 0 0 4678 7.1759 2 3 13 5 15 25 35 9 19 29 39 14678 5.9099 2 3 0 5 0 25 35 9 235 29 39 24678 5.7613 0 3 13 5 15 0 35 9 19 0 39 124678 4.1152 0 3 0 5 0 0 35 9 0 0 39 34678 8.8477 2 12 0 5 15 25 125 9 19 29 129 134678 5.1440 2 0 0 5 0 25 0 9 0 29 0 234678 4.9383 0 0 0 5 15 0 0 9 19 0 0 1234678 2.4691 0 0 0 5 0 0 0 9 0 0 0 5678 7.9432 2 3 4 23 24 34 134 9 19 29 39 15678 5.5255 2 3 4 23 24 34 0 9 0 29 39 25678 7.3560 0 3 4 14 0 34 134 9 19 0 39 125678 4.4753 0 3 4 0 0 34 0 9 0 0 39 35678 8.3462 2 12 4 14 24 124 0 9 19 29 129 135678 4.1667 2 0 4 0 24 0 0 9 0 29 0 235678 3.8580 0 0 4 14 0 0 0 9 19 0 0 1235678 1.8519 0 0 4 0 0 0 0 9 0 0 0 45678 6.5072 2 3 13 23 123 0 0 9 19 29 39 145678 3.3436 2 3 0 23 0 0 0 9 0 29 39 245678 2.7778 0 3 13 0 0 0 0 9 19 0 39 1245678 4.0123 0 3 0 0 0 0 0 9 0 0 39 345678 4.4753 2 12 0 0 0 0 0 9 19 29 129 1345678 6.1728 2 0 0 0 0 0 0 9 0 29 0 2345678 8.3333 0 0 0 0 0 0 0 9 19 0 0 12345678 11.1111 0 0 0 0 0 0 0 9 0 0 0 9 10.1502 2 3 4 5 6 7 8 18 28 38 48 19 6.9434 2 3 4 5 6 7 8 45 28 38 48 29 7.2701 0 3 4 5 6 7 8 18 46 38 48 129 4.4180 0 3 4 5 6 7 8 45 37 38 48 39 7.9704 2 12 4 5 6 7 8 18 28 56 57 139 4.8384 2 0 4 5 6 7 8 45 28 56 48 239 5.1545 0 0 4 5 6 7 8 18 46 47 57 1239 2.8657 0 0 4 5 6 7 8 45 46 56 48 49 8.4973 2 3 13 5 6 7 8 18 28 38 57 149 5.1316 2 3 0 5 6 7 8 36 28 38 57 249 6.0188 0 3 13 5 6 7 8 18 37 56 57 1249 3.2574 0 3 0 5 6 7 8 36 37 56 57 349 6.0642 2 12 0 5 6 7 8 18 28 56 57 1349 3.7292 2 0 0 5 6 7 8 27 28 56 57 2349 3.6751 0 0 0 5 6 7 8 18 0 56 57 12349 1.9504 0 0 0 5 6 7 8 0 0 56 57 59 9.3617 2 3 4 14 6 7 8 18 28 38 48 159 6.2362 2 3 4 23 6 7 8 27 46 38 48 259 6.6459 0 3 4 14 6 7 8 18 37 47 48 1259 3.9122 0 3 4 0 6 7 8 36 46 38 48 359 7.4761 2 12 4 14 6 7 8 18 28 47 48 1359 4.2374 2 0 4 0 6 7 8 27 46 47 48 2359 5.2726 0 0 4 14 6 7 8 18 46 47 48 12359 2.8292 0 0 4 0 6 7 8 0 46 47 48 459 7.9719 2 3 13 23 6 7 8 18 28 38 138 1459 5.4043 2 3 0 23 6 7 8 36 28 38 237 2459 5.8885 0 3 13 0 6 7 8 18 37 38 138 12459 3.7080 0 3 0 0 6 7 8 36 37 38 0 3459 5.5741 2 12 0 0 6 7 8 18 28 128 0 13459 3.6223 2 0 0 0 6 7 8 27 28 0 0 23459 3.5044 0 0 0 0 6 7 8 18 0 0 0 123459 1.9290 0 0 0 0 6 7 8 0 0 0 0 69 9.9970 2 3 4 5 15 7 8 18 28 38 48 169 6.6781 2 3 4 5 24 7 8 45 28 38 57 269 7.0851 0 3 4 5 15 7 8 18 37 38 48 1269 4.2686 0 3 4 5 0 7 8 45 37 38 48 369 8.3494 2 12 4 5 15 7 8 18 28 47 57 1369 5.3305 2 0 4 5 24 7 8 45 28 47 48 2369 5.6156 0 0 4 5 15 7 8 18 145 47 48 12369 3.0864 0 0 4 5 0 7 8 45 0 47 48 469 8.7134 2 3 13 5 15 7 8 18 28 38 57 1469 4.5958 2 3 0 5 0 7 8 27 28 38 57 2469 6.6222 0 3 13 5 15 7 8 18 37 38 138 12469 3.1336 0 3 0 5 0 7 8 0 37 38 57 3469 7.0287 2 12 0 5 15 7 8 27 28 128 57 13469 3.8109 2 0 0 5 0 7 8 27 28 0 57 23469 4.4239 0 0 0 5 15 7 8 18 0 0 57 123469 2.3148 0 0 0 5 0 7 8 0 0 0 57 569 9.5440 2 3 4 14 24 7 8 18 37 38 48 1569 6.8417 2 3 4 23 24 7 8 27 37 38 48 2569 5.7828 0 3 4 14 0 7 8 18 37 38 48 12569 3.5537 0 3 4 0 0 7 8 0 37 38 48 3569 8.2819 2 12 4 14 24 7 8 18 28 128 48 13569 5.2726 2 0 4 0 24 7 8 27 28 47 48 23569 4.9576 0 0 4 14 0 7 8 18 0 47 48 123569 3.6265 0 0 4 0 0 7 8 0 0 47 48 4569 8.0861 2 3 13 23 123 7 8 18 28 38 138 14569 5.5898 2 3 0 23 0 7 8 27 28 38 237 24569 6.4172 0 3 13 0 0 7 8 18 37 38 138 124569 4.9383 0 3 0 0 0 7 8 0 37 38 0 34569 6.6422 2 12 0 0 0 7 8 18 28 128 0 134569 6.2500 2 0 0 0 0 7 8 27 28 0 0 234569 5.6327 0 0 0 0 0 7 8 18 0 0 0 1234569 4.6296 0 0 0 0 0 7 8 0 0 0 0 79 10.9475 2 3 4 5 6 25 8 18 28 38 48 179 8.0450 2 3 4 5 6 25 8 36 28 38 48 279 8.0957 0 3 4 5 6 34 8 18 46 38 48 1279 5.1250 0 3 4 5 6 34 8 45 46 38 48 379 9.3588 2 12 4 5 6 16 8 18 46 56 48 1379 5.7723 2 0 4 5 6 25 8 45 46 56 48 2379 6.1543 0 0 4 5 6 16 8 45 46 56 48 12379 3.4379 0 0 4 5 6 0 8 45 46 56 48 479 9.8107 2 3 13 5 6 25 8 18 28 38 138 1479 6.1410 2 3 0 5 6 25 8 36 28 38 0 2479 6.5972 0 3 13 5 6 16 8 18 136 38 138 12479 3.1129 0 3 0 5 6 0 8 36 0 38 0 3479 7.8411 2 12 0 5 6 25 8 18 28 128 156 13479 4.5410 2 0 0 5 6 25 8 0 28 56 0 23479 5.3819 0 0 0 5 6 16 8 18 0 56 156 123479 2.8292 0 0 0 5 6 0 8 0 0 56 0 579 10.9725 2 3 4 23 6 16 8 18 28 38 48 1579 7.2643 2 3 4 23 6 34 8 36 28 38 48 2579 8.2590 0 3 4 14 6 34 8 18 46 38 48 12579 5.3584 0 3 4 0 6 34 8 36 46 38 48 3579 8.6048 2 12 4 14 6 16 8 18 28 128 48 13579 3.6308 2 0 4 0 6 0 8 0 28 0 48 23579 7.5360 0 0 4 14 6 16 8 18 46 146 48 123579 4.0509 0 0 4 0 6 0 8 0 46 0 48 4579 9.1435 2 3 13 23 6 16 8 18 28 38 138 14579 5.8456 2 3 0 23 6 0 8 36 28 38 0 24579 8.4234 0 3 13 0 6 16 8 18 136 38 138 124579 5.2726 0 3 0 0 6 0 8 36 0 38 0 34579 8.6934 2 12 0 0 6 16 8 18 28 128 0 134579 4.5653 2 0 0 0 6 0 8 0 28 0 0 234579 7.7160 0 0 0 0 6 16 8 18 0 0 0 1234579 3.8580 0 0 0 0 6 0 8 0 0 0 0 679 11.4125 2 3 4 5 15 34 8 18 28 38 48 1679 8.0328 2 3 4 5 24 34 8 45 28 38 48 2679 8.1819 0 3 4 5 15 34 8 18 145 38 48 12679 5.1290 0 3 4 5 0 34 8 45 0 38 48 3679 9.5854 2 12 4 5 24 25 8 18 28 128 48 13679 7.6217 2 0 4 5 24 25 8 45 28 245 48 23679 6.4172 0 0 4 5 15 0 8 18 145 0 48 123679 4.4753 0 0 4 5 0 0 8 45 0 0 48 4679 9.8665 2 3 13 5 15 25 8 18 28 38 138 14679 6.0821 2 3 0 5 0 25 8 0 28 38 0 24679 7.0730 0 3 13 5 15 0 8 18 0 38 138 124679 3.6780 0 3 0 5 0 0 8 0 0 38 0 34679 10.2238 2 12 0 5 15 25 8 18 28 128 0 134679 6.7387 2 0 0 5 0 25 8 0 28 0 0 234679 6.3272 0 0 0 5 15 0 8 18 0 0 0 1234679 3.0864 0 0 0 5 0 0 8 0 0 0 0 5679 10.8432 2 3 4 23 24 34 8 18 28 38 48 15679 10.2023 2 3 4 23 24 34 8 234 28 38 48 25679 8.4426 0 3 4 14 0 34 8 18 0 38 48 125679 6.2500 0 3 4 0 0 34 8 0 0 38 48 35679 11.5998 2 12 4 14 24 124 8 18 28 128 48 135679 5.5941 2 0 4 0 24 0 8 0 28 0 48 235679 4.9383 0 0 4 14 0 0 8 18 0 0 48 1235679 5.0926 0 0 4 0 0 0 8 0 0 0 48 45679 8.9120 2 3 13 23 123 0 8 18 28 38 138 145679 4.4496 2 3 0 23 0 0 8 0 28 38 0 245679 6.3272 0 3 13 0 0 0 8 18 0 38 138 1245679 7.0988 0 3 0 0 0 0 8 0 0 38 0 345679 7.7160 2 12 0 0 0 0 8 18 28 128 0 1345679 9.1049 2 0 0 0 0 0 8 0 28 0 0 2345679 11.1111 0 0 0 0 0 0 8 18 0 0 0 12345679 13.8889 0 0 0 0 0 0 8 0 0 0 0 89 12.3004 2 3 4 5 6 7 17 27 37 47 57 189 9.7351 2 3 4 5 6 7 26 27 37 47 57 289 10.1895 0 3 4 5 6 7 17 36 46 47 57 1289 6.9716 0 3 4 5 6 7 35 45 46 47 57 389 10.6151 2 12 4 5 6 7 17 27 46 56 57 1389 7.2838 2 0 4 5 6 7 26 45 46 47 57 2389 7.5574 0 0 4 5 6 7 17 45 46 56 57 12389 4.7711 0 0 4 5 6 7 0 45 46 47 57 489 11.3456 2 3 13 5 6 7 26 27 37 56 57 1489 8.0930 2 3 0 5 6 7 35 27 37 56 57 2489 8.9578 0 3 13 5 6 7 17 36 37 56 57 12489 6.2586 0 3 0 5 6 7 35 36 37 56 57 3489 8.5662 2 12 0 5 6 7 17 27 127 56 57 13489 6.1257 2 0 0 5 6 7 26 27 0 56 57 23489 5.6456 0 0 0 5 6 7 17 0 0 56 57 123489 4.1667 0 0 0 5 6 7 0 0 0 56 57 589 12.2279 2 3 4 14 6 7 17 27 37 47 237 1589 8.7395 2 3 4 23 6 7 26 27 46 47 237 2589 9.3921 0 3 4 14 6 7 17 36 37 47 147 12589 5.4141 0 3 4 0 6 7 0 36 37 47 0 3589 10.4135 2 12 4 14 6 7 26 27 46 47 147 13589 7.7032 2 0 4 0 6 7 26 27 46 47 246 23589 8.1404 0 0 4 14 6 7 17 0 46 47 147 123589 5.4784 0 0 4 0 6 7 0 0 46 47 0 4589 11.2340 2 3 13 23 6 7 17 27 37 137 237 14589 9.4865 2 3 0 23 6 7 26 27 37 236 237 24589 9.6708 0 3 13 0 6 7 17 36 37 137 0 124589 6.7901 0 3 0 0 6 7 0 36 37 0 0 34589 9.2721 2 12 0 0 6 7 17 27 127 0 0 134589 8.1019 2 0 0 0 6 7 26 27 0 0 0 234589 6.6358 0 0 0 0 6 7 17 0 0 0 0 1234589 4.6296 0 0 0 0 6 7 0 0 0 0 0 689 12.7986 2 3 4 5 24 7 17 27 37 47 57 1689 9.9308 2 3 4 5 24 7 35 27 37 47 57 2689 9.9666 0 3 4 5 15 7 17 45 37 47 57 12689 7.9733 0 3 4 5 0 7 35 45 37 47 57 3689 11.6577 2 12 4 5 24 7 17 27 127 47 57 13689 7.1631 2 0 4 5 24 7 0 27 0 47 57 23689 10.5710 0 0 4 5 15 7 17 45 145 47 57 123689 6.3272 0 0 4 5 0 7 0 45 0 47 57 4689 12.1778 2 3 13 5 15 7 17 27 37 137 57 14689 8.6077 2 3 0 5 0 7 35 27 37 0 57 24689 11.8570 0 3 13 5 15 7 17 135 37 137 57 124689 7.4074 0 3 0 5 0 7 35 0 37 0 57 34689 11.1368 2 12 0 5 15 7 17 27 127 0 57 134689 5.7099 2 0 0 5 0 7 0 27 0 0 57 234689 7.7160 0 0 0 5 15 7 17 0 0 0 57 1234689 6.4815 0 0 0 5 0 7 0 0 0 0 57 5689 13.2416 2 3 4 23 24 7 17 27 37 47 147 15689 10.1723 2 3 4 23 24 7 0 27 37 47 237 25689 9.0664 0 3 4 14 0 7 17 0 37 47 147 125689 5.2469 0 3 4 0 0 7 0 0 37 47 0 35689 12.2299 2 12 4 14 24 7 17 27 127 47 147 135689 7.0216 2 0 4 0 24 7 0 27 0 47 0 235689 8.7963 0 0 4 14 0 7 17 0 0 47 147 1235689 8.3333 0 0 4 0 0 7 0 0 0 47 0 45689 11.3169 2 3 13 23 123 7 17 27 37 137 237 145689 8.3333 2 3 0 23 0 7 0 27 37 0 237 245689 9.8765 0 3 13 0 0 7 17 0 37 137 0 1245689 10.1852 0 3 0 0 0 7 0 0 37 0 0 345689 10.9568 2 12 0 0 0 7 17 27 127 0 0 1345689 12.0370 2 0 0 0 0 7 0 27 0 0 0 2345689 13.8889 0 0 0 0 0 7 17 0 0 0 0 12345689 16.6667 0 0 0 0 0 7 0 0 0 0 0 789 13.3937 2 3 4 5 6 16 35 36 46 56 156 1789 11.5981 2 3 4 5 6 34 26 36 46 56 246 2789 11.7998 0 3 4 5 6 16 35 45 46 56 156 12789 10.2752 0 3 4 5 6 34 35 36 46 56 345 3789 12.5743 2 12 4 5 6 16 26 45 46 56 156 13789 11.1711 2 0 4 5 6 25 26 45 46 56 246 23789 9.6386 0 0 4 5 6 16 0 45 46 56 156 123789 6.6358 0 0 4 5 6 0 0 45 46 56 0 4789 13.4502 2 3 13 5 6 25 26 36 136 56 156 14789 11.5112 2 3 0 5 6 25 26 36 235 56 0 24789 12.5129 0 3 13 5 6 16 35 36 136 56 156 124789 7.4588 0 3 0 5 6 0 35 36 0 56 0 34789 10.8603 2 12 0 5 6 16 26 126 0 56 156 134789 8.2819 2 0 0 5 6 25 26 0 0 56 0 234789 8.4105 0 0 0 5 6 16 0 0 0 56 156 1234789 8.6420 0 0 0 5 6 0 0 0 0 56 0 5789 14.2768 2 3 4 23 6 16 26 36 46 146 246 15789 12.9415 2 3 4 23 6 34 26 36 46 236 246 25789 12.3778 0 3 4 14 6 16 134 36 46 146 0 125789 7.7932 0 3 4 0 6 34 0 36 46 0 0 35789 11.6770 2 12 4 14 6 16 26 126 46 146 246 135789 7.6775 2 0 4 0 6 0 26 0 46 0 246 235789 11.4198 0 0 4 14 6 16 0 0 46 146 0 1235789 10.6481 0 0 4 0 6 0 0 0 46 0 0 45789 12.8987 2 3 13 23 6 16 26 36 136 236 1236 145789 10.9311 2 3 0 23 6 0 26 36 0 236 0 245789 12.5000 0 3 13 0 6 16 0 36 136 0 0 1245789 12.6543 0 3 0 0 6 0 0 36 0 0 0 345789 13.5802 2 12 0 0 6 16 26 126 0 0 0 1345789 14.6605 2 0 0 0 6 0 26 0 0 0 0 2345789 16.6667 0 0 0 0 6 16 0 0 0 0 0 12345789 13.8889 0 0 0 0 6 0 0 0 0 0 0 6789 14.3704 2 3 4 5 15 34 35 45 145 245 345 16789 13.0873 2 3 4 5 24 25 35 45 235 245 345 26789 11.3169 0 3 4 5 15 34 35 45 145 0 345 126789 10.3395 0 3 4 5 0 34 35 45 0 0 345 36789 13.0273 2 12 4 5 15 25 125 45 145 245 1245 136789 12.1914 2 0 4 5 24 25 0 45 0 245 0 236789 11.8827 0 0 4 5 15 0 0 45 145 0 0 1236789 12.9630 0 0 4 5 0 0 0 45 0 0 0 46789 13.9660 2 3 13 5 15 25 35 135 235 1235 0 146789 12.2942 2 3 0 5 0 25 35 0 235 0 0 246789 14.5062 0 3 13 5 15 0 35 135 0 0 0 1246789 15.1235 0 3 0 5 0 0 35 0 0 0 0 346789 15.8951 2 12 0 5 15 25 125 0 0 0 0 1346789 17.2840 2 0 0 5 0 25 0 0 0 0 0 2346789 13.8889 0 0 0 5 15 0 0 0 0 0 0 12346789 11.1111 0 0 0 5 0 0 0 0 0 0 0 56789 14.7441 2 3 4 14 24 34 134 234 1234 0 0 156789 15.5093 2 3 4 23 24 34 0 234 0 0 0 256789 15.8179 0 3 4 14 0 34 134 0 0 0 0 1256789 17.5926 0 3 4 0 0 34 0 0 0 0 0 356789 18.2099 2 12 4 14 24 124 0 0 0 0 0 1356789 14.3519 2 0 4 0 24 0 0 0 0 0 0 2356789 11.1111 0 0 4 14 0 0 0 0 0 0 0 12356789 8.3333 0 0 4 0 0 0 0 0 0 0 0 456789 14.6605 2 3 13 23 123 0 0 0 0 0 0 1456789 11.4198 2 3 0 23 0 0 0 0 0 0 0 2456789 8.3333 0 3 13 0 0 0 0 0 0 0 0 12456789 5.5556 0 3 0 0 0 0 0 0 0 0 0 3456789 5.5556 2 12 0 0 0 0 0 0 0 0 0 13456789 2.7778 2 0 0 0 0 0 0 0 0 0 0 23456789 0.0000 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 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.