设金额:
A=A胜,B=B胜,C=平局,M=总预算
设赔率:
a=A胜,b=B胜,c=平局
如果A胜赢:
① Aa - A - B - C ≥ 0 =>> A(a-1) ≥ B + C
如果B胜赢:
② Bb - A - B - C ≥ 0 =>> B(b-1) ≥ A + C
如果平局:
③ Cc - A - B - C ≥ 0 =>> C(c-1) ≥ A + B
总预算:
④ A + B + C = M
将 ① - ② 得:
⑤ Aa ≥ Bb =>> A ≥ Bb/a =>> Aa/b ≥ B
将 ② - ③ 得:
⑥ Bb ≥ Cc =>> B ≥ Cc/b =>> Bb/c ≥ C
将 ③ - ① 得:
⑦ Cc ≥ Aa =>> C ≥ Aa/c =>> Cc/a ≥ A
将 ⑤ 与 ⑥ 组合得:
⑧ Aa ≥ Bb ≥ Cc
将 ⑤ 与 ⑦ 组合得:
⑨ Cc ≥ Aa ≥ Bb
将 ⑥ 与 ⑦ 组合得:
⑩ Bb ≥ Cc ≥ Aa
A + Aa/b + Aa/c = M
Bb/a + B + Bb/c = M
Cc/a + Cc/b + C = M
A = M/(1 + a/b + a/c)
B = M/(b/a + 1 + b/c)
C = M/(c/a + c/b + 1)
M = A + B
确保无论下注哪个,都不会亏本
Aa - A - B ≥ 0 =>> Aa - M ≥ 0 =>> Aa ≥ M
Bb - B - A ≥ 0 =>> Bb - M ≥ 0 =>> Bb ≥ M
得:
M ≥ A ≥ M/a
M ≥ B ≥ M/b
设:a ≥ b
则 M/a ≤ M/b
所以 A ≤ B
结果:
M/a ≤ M/b ≤ A ≤ B
M/a ≤ M/b ≤ B ≤ M