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#6
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Recursive Mathematica code:
Clear[gamevalue]; gamevalue[black_, white_] := gamevalue[black, white] = If[black == white == 0 || black < 0 || white < 0, 0, Max[0, black/(black + white) (-1 + gamevalue[black - 1, white]) + white/(black + white) (1 + gamevalue[black, white - 1])]] Badly formatted output: Table[gamevalue[i, j], {i, 0, 10}, {j, 0, 10}] 0 1 2 3 4 5 6 7 8 9 10 0 1/2 4/3 9/4 16/5 25/6 36/7 49/8 64/9 81/10 100/11 0 0 2/3 3/2 12/5 10/3 30/7 21/4 56/9 36/5 90/11 0 0 1/5 17/20 58/35 71/28 145/42 527/120 294/55 347/55 1041/143 0 0 0 12/35 1 113/63 93/35 235/66 202/45 777/143 492/77 0 0 0 0 4/9 47/42 21/11 199/72 428/117 705/154 182/33 0 0 0 0 1/15 127/231 284/231 3457/1716 8594/3003 5356/143 1333/286 0 0 0 0 0 61/396 563/858 4583/3432 13606/6435 8449/2860 9319/2431 0 0 0 0 0 0 697/3003 49/65 18457/12870 53683/24310 133097/43758 0 0 0 0 0 0 0 311/1040 10224/12155 74131/48620 106045/46189 0 0 0 0 0 0 0 0 7793/21879 84855/92378 26995/16796 |
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