```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 ``` ```Output of http://codepad.org/iwY04MTf ************************************* '1 Die diff' is the average amount of armies the aggressor loses minus the average amount of armies the defender loses, if the defender rolls 1 die. '2 Dice diff' is the average amount of armies the aggressor loses minus the average amount of armies the defender loses, if the defender rolls 2 dice. A (x,y) battle loss means that the aggressor looses an average of x armies and the defender looses an average of y armies. Aggressor dice: (1, 1) -> 1 Die diff: 1.0000; 2 Dice diff: 2.0000 => Use 2: it results in (2.0000,0.0000) battle loss. Aggressor dice: (1, 2) -> 1 Die diff: 0.6667; 2 Dice diff: 1.9444 => Use 2: it results in (1.9722,0.0278) battle loss. Aggressor dice: (1, 3) -> 1 Die diff: 0.3333; 2 Dice diff: 1.7778 => Use 2: it results in (1.8889,0.1111) battle loss. Aggressor dice: (1, 4) -> 1 Die diff: 0.0000; 2 Dice diff: 1.5000 => Use 2: it results in (1.7500,0.2500) battle loss. Aggressor dice: (1, 5) -> 1 Die diff: -0.3333; 2 Dice diff: 1.1111 => Use 2: it results in (1.5556,0.4444) battle loss. Aggressor dice: (1, 6) -> 1 Die diff: -0.6667; 2 Dice diff: 0.6111 => Use 2: it results in (1.3056,0.6944) battle loss. Aggressor dice: (2, 2) -> 1 Die diff: 0.6667; 2 Dice diff: 1.3333 => Use 2: it results in (1.6667,0.3333) battle loss. Aggressor dice: (2, 3) -> 1 Die diff: 0.3333; 2 Dice diff: 1.1667 => Use 2: it results in (1.5833,0.4167) battle loss. Aggressor dice: (2, 4) -> 1 Die diff: 0.0000; 2 Dice diff: 0.8889 => Use 2: it results in (1.4444,0.5556) battle loss. Aggressor dice: (2, 5) -> 1 Die diff: -0.3333; 2 Dice diff: 0.5000 => Use 2: it results in (1.2500,0.7500) battle loss. Aggressor dice: (2, 6) -> 1 Die diff: -0.6667; 2 Dice diff: 0.0000 => Use 2: it results in (1.0000,1.0000) battle loss. Aggressor dice: (3, 3) -> 1 Die diff: 0.3333; 2 Dice diff: 0.6667 => Use 2: it results in (1.3333,0.6667) battle loss. Aggressor dice: (3, 4) -> 1 Die diff: 0.0000; 2 Dice diff: 0.3889 => Use 2: it results in (1.1944,0.8056) battle loss. Aggressor dice: (3, 5) -> 1 Die diff: -0.3333; 2 Dice diff: 0.0000 => Use 2: it results in (1.0000,1.0000) battle loss. Aggressor dice: (3, 6) -> 1 Die diff: -0.6667; 2 Dice diff: -0.5000 => Use 2: it results in (0.7500,1.2500) battle loss. Aggressor dice: (4, 4) -> 1 Die diff: 0.0000; 2 Dice diff: 0.0000 => Use 2: it results in (1.0000,1.0000) battle loss. Aggressor dice: (4, 5) -> 1 Die diff: -0.3333; 2 Dice diff: -0.3889 => Use 1: it results in (0.3333,0.6667) battle loss. Aggressor dice: (4, 6) -> 1 Die diff: -0.6667; 2 Dice diff: -0.8889 => Use 1: it results in (0.1667,0.8333) battle loss. Aggressor dice: (5, 5) -> 1 Die diff: -0.3333; 2 Dice diff: -0.6667 => Use 1: it results in (0.3333,0.6667) battle loss. Aggressor dice: (5, 6) -> 1 Die diff: -0.6667; 2 Dice diff: -1.1667 => Use 1: it results in (0.1667,0.8333) battle loss. Aggressor dice: (6, 6) -> 1 Die diff: -0.6667; 2 Dice diff: -1.3333 => Use 1: it results in (0.1667,0.8333) battle loss. The average army loss is 0.7735 for the aggressor and 0.7728 for the defender assuming the defender plays the ideal strategy. ```