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代达罗斯之殇的期望值问题DOTA2

少_游 2022-05-06 阅读 39
概率论

代达罗斯之殇

出多少把代达罗斯之殇合适呢?
在这里插入图片描述

被动:致命一击 - 普通攻击有30%概率造成225%伤害。
+88 攻击力

期望输出:

E ( a 1 ) = 88 × 225 % × 0.7 + 88 × 0.7 = 121 E(a_1)=88\times225\%\times0.7+88\times0.7=121 E(a1)=88×225%×0.7+88×0.7=121
E ( a 2 ) = 176 × 225 % × ( 0.3 + 0.7 × 0.3 ) + 176 × 0. 7 2 = 288.2 E(a_2)=176\times225\%\times(0.3+0.7\times0.3)+176\times0.7^2=288.2 E(a2)=176×225%×(0.3+0.7×0.3)+176×0.72=288.2
E ( a 3 ) = 264 × 225 % × ( 0.3 + 0.7 × 0.3 + 0. 7 2 × 0.3 ) + 264 × 0. 7 3 = 480.81 E(a_3)=264\times225\%\times(0.3+0.7\times0.3+0.7^2\times0.3)+264\times0.7^3=480.81 E(a3)=264×225%×(0.3+0.7×0.3+0.72×0.3)+264×0.73=480.81
E ( a 4 ) = 352 × 225 % × ( 0.3 + 0.7 × 0.3 + 0. 7 2 × 0.3 + 0. 7 3 × 0.3 ) + 352 × 0. 7 4 = 686.356 E(a_4)=352\times225\%\times(0.3+0.7\times0.3+0.7^2\times0.3+0.7^3\times0.3)+352\times0.7^4=686.356 E(a4)=352×225%×(0.3+0.7×0.3+0.72×0.3+0.73×0.3)+352×0.74=686.356
E ( a 5 ) = 440 × 225 % × ( 0.3 + 0.7 × 0.3 + 0. 7 2 × 0.3 + 0. 7 3 × 0.3 + 0. 7 4 × 0.3 ) + 440 × 0. 7 5 = 897.5615 E(a_5)=440\times225\%\times(0.3+0.7\times0.3+0.7^2\times0.3+0.7^3\times0.3+0.7^4\times0.3)+440\times0.7^5=897.5615 E(a5)=440×225%×(0.3+0.7×0.3+0.72×0.3+0.73×0.3+0.74×0.3)+440×0.75=897.5615
E ( a 6 ) = 528 × 225 % × ( 0.3 + 0.7 × 0.3 + 0. 7 2 × 0.3 + 0. 7 3 × 0.3 + 0. 7 4 × 0.3 + 0. 7 5 × 0.3 ) + 528 × 0. 7 6 = 1110.35166 E(a_6)=528\times225\%\times(0.3+0.7\times0.3+0.7^2\times0.3+0.7^3\times0.3+0.7^4\times0.3+0.7^5\times0.3)+528\times0.7^6=1110.35166 E(a6)=528×225%×(0.3+0.7×0.3+0.72×0.3+0.73×0.3+0.74×0.3+0.75×0.3)+528×0.76=1110.35166

经济/输出比

即每多少钱转化为一点单位攻击力

r 1 = 5150 121 ≈ 42.56 r_1=\frac{5150}{121}\approx42.56 r1=121515042.56
r 2 = 10300 288.2 ≈ 35.74 r_2=\frac{10300}{288.2}\approx35.74 r2=288.21030035.74
r 3 = 15450 480.81 ≈ 32.13 r_3=\frac{15450}{480.81}\approx32.13 r3=480.811545032.13
r 4 = 20600 686.356 ≈ 30.01 r_4=\frac{20600}{686.356}\approx30.01 r4=686.3562060030.01
r 5 = 25750 897.5615 ≈ 28.69 r_5=\frac{25750}{897.5615}\approx28.69 r5=897.56152575028.69
r 6 = 30900 1110.35166 ≈ 27.83 r_6=\frac{30900}{1110.35166}\approx27.83 r6=1110.351663090027.83

在这里插入图片描述

综上,两把代达罗斯之殇最为合理。

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