Number of plies (half-moves) Number of possible games[2] Number of Checkmates[3] 1 20 0 2 400 0 3 8,902 0 4 197,281 8 5 4,865,609 347 6 119,060,324 10,828 7 3,195,901,860 435,767 8 84,998,978,956 9,852,036 9 2,439,530,234,167 400,191,963 10 69,352,859,712,417 8,790,619,155 11 2,097,651,003,696,806 362,290,010,907 12 62,854,969,236,701,747 8,361,091,858,959 13 1,981,066,775,000,396,239 346,742,245,764,219 14 61,885,021,521,585,529,237 15 2,015,099,950,053,364,471,960