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一、我们先假设一个抽样数W={W(ij)|i,j∈N}, W(ij)就是比赛的进球结果,i,j分别表示主客队的进球数。: v6 C) C* x" W/ D" U
那么,平局、主胜、客胜就有以下表达式:6 p) E x) t7 ^9 P! @% X5 q6 A6 j
A(d) = {W(ij)|i=j, i∈N, j∈N}4 G4 J+ |2 e c7 R
A(h) = {W(ij)|i>j, i∈N, j∈N}9 [4 [" f+ T3 H% c4 ~. }
A(a) = {W(ij)|i 接着我们引入一个符号P(i)表示平胜负的概率,P(Ai)∈[0,1]:3 p. I6 _. ]7 ^: G' \1 [* o/ p
P(i)=P(Ai), i∈{0, 1, 2}& D' ]- | j4 a) U) f: `7 ` _
二、首先来说说平手盘(即0:0Handicaps或我们经常在国外上看到的(Moneyline)
; l% G% }" C6 V1 N1 x- g假设b(h)表示主队的投注总数,b(a)表示客队的投注总数,那么投注主客队的回报总数额为:2 v8 c5 {) ]4 e3 X" `" f" t6 c
{b(h) , 即上面所述的A(d)结果发生
3 }$ {. Y" y1 ]% \R(1)={O(h)*b(h),即上面所述的A(h)结果发生
* m% {* D4 S6 j! m; Z: b: x{0 , 即上面所述的A(a)结果发生
# C D) B$ m5 P. q以及
# k9 O4 c- M! k E+ |. |4 Y0 `{b(a) , 即上面所述的A(d)结果发生7 |; p0 F6 J1 T) j$ h( n) j
R(2)={0, 即上面所述的A(h)结果发生
- y" U( b6 A) b; F M7 j O9 z{O(a)*b(a),即上面所述的A(a)结果发生
3 o! Z: X: r; a4 K( e% G) y如果O(h)表示平手盘下的主队赔率,O(a)表示平手盘下的客队赔率
; \) J: \ ^$ A* B! K6 f! U那么投注主客的期望回报总数分别为
! P0 m7 A3 y5 jE[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]
1 a9 y% E4 h2 ~ lE[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]- G+ K. F h; R/ B9 c+ h
按照真实赔率(暂不包含庄家优势),我们可以认为实际投注回报与期望投注回报相等 T- l w: A9 O+ U
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)* B# A( d9 Z- }/ n z1 _
P(d)+p(h)O(h)=1
: E3 {2 e8 B0 {9 fO(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式$ L% ?! j* H. | |; k
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a). l1 M! A6 N Q5 X; J5 e2 x
P(d)+p(a)O(a)=1# Y3 u X# S* u7 r2 V. Z
O(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式
# r& y+ n5 x4 ?: y; Z" D2 v在极端情况下,可以认为平手盘亚洲赔率(或moneyline),就是在不发生平局结果条件下(就是公式中P(d)=0),主胜客胜概率的倒数$ T: u% t" T0 f7 d. R) y
三、半球盘的计算描述
+ r& ^5 K5 m* _8 O) b z* V接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)% x. L* s# Z* ?7 m- }9 L
还是假设b(h)表示主队的投注总数,b(a)表示客队的投注总数,那么投注主客队的回报总数额为:# l2 a. ~7 p9 z5 x
{O(h)*b(h),即上面所述的A(d)结果发生: T3 I6 _3 x& Q" i
R(1)={O(h)*b(h),即上面所述的A(h)结果发生. n) u) t- S- B, W
{0 , 即上面所述的A(a)结果发生
W# p1 s) G+ _9 ^) b. z0 D以及) w7 r5 r4 C- m/ @
{0 , 即上面所述的A(d)结果发生# ]8 d8 a2 I$ I, \! C7 C8 h. `
R(2)={0, 即上面所述的A(h)结果发生
1 u! U9 O# W! A8 ^1 {; I{O(a)*b(a),即上面所述的A(a)结果发生
, P& u) H4 B, ]如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
* ^5 m" ^1 R) d# `( f, ?投注主客的期望回报总数分别为
9 F, l9 K( C0 x7 e bE[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]. n1 L& c: V- S" S% H
E[R(2)]=P(a)*O(a)*b(a)) s$ Z+ o7 E) w9 e
假设实际投注回报与期望投注回报相等7 Q# L/ b0 X8 y. ~
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
/ N P* c2 S, S- K/ Y3 DO(h)*[P(d)+p(h)]=1
6 A* N/ X+ [* u+ T% jO(h)=1/[P(d)+p(h)]( j4 T* r& K* D: W& v; e
E[R(2)]=P(a)*O(a)*b(a)=b(a)3 s$ ]$ Q( A- @
P(a)*O(a)=1. F( P$ e- F/ L) c2 O
O(a)=1/P(a)
! i2 \1 ?+ L2 _) A* V' f& W9 R d2 L同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率- M) b, h0 u0 H3 U
O(h)=1/p(h)# u/ g9 b6 V* g$ z9 ^
O(a)=1/[P(d)+p(a)]) g7 V; n6 B; Q! U
四、平半球盘的计算描述
4 k4 p% c9 L0 t+ C5 A0 c这个稍复杂一点
7 \ e5 {* G/ _6 U+ o接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
. @& X" _3 l- V% R, t还是假设b(h)表示主队的投注总数,b(a)表示客队的投注总数,那么投注主客队的回报总数额计算:
- B- u e6 \0 K8 P) \0 a: M" B{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
: u M- E: `2 ?$ N2 c8 i1 `! iR(1)={O(h)*b(h), 即上面所述的A(h)结果发生
- N% K* Q8 \: E: m- V; o# _& t{0, 即上面所述的A(a)结果发生0 x F. i. X% H' {3 y$ J9 \( P7 a) l
以及7 T3 E; n0 b. g" k+ H! k; r4 v
{1/2×b(a) , 即上面所述的A(d)结果发生7 @6 a/ g D* s$ C9 R N$ e
R(2)={0, 即上面所述的A(h)结果发生3 q# H8 w: t* E5 i+ ?5 n. s
{O(a)*b(a), 即上面所述的A(a)结果发生, x. J0 o" h" a- A+ P8 W: \
投注主客的期望回报总数分别为
. N9 d" q( d5 x" w* OE[R(1)]=P(d)×{[O(h)+1]/2}×b(h)+P(h)×O(h)×b(h)=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))* X; F1 S' |" o
E[R(2)]=1/2×b(a)×P(d)+P(a)*O(a)*b(a)=b(a)*[1/2×P(d)+P(a)*O(a)]
0 X6 w& ^9 ~! @+ ~ v6 x和上面计算过程相似,得出:! n; V% W5 c. I% L! T
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)* n+ |% U* |% |! f
P(d)×{[O(h)+1]/2}+P(h)×O(h)=1/ ]* f/ j2 h5 e4 l" C/ y3 E
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
. q# g7 ?3 ?% D* x- z) A9 F, V7 |( v VO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
# a4 N! a: n3 ?+ T( h& qE[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
+ S2 N! J6 I- X1/2×P(d)+P(a)*O(a)=1
& i! W" W5 ~8 p9 ?6 r5 zO(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)" o: O8 m% T# L! \) e$ P- C
同样主队让平半就分别是
5 |- J' ?8 L$ }5 KO(h)=(1-P(d)/2)/P(h)' b [! Z7 |( T
O(a)=(1-P(d)/2)/(P(d)/2+P(a))$ R( [% u: Z: h2 {& d
五、一球、两球等整数盘(这里先暂时说主队让1球的情况,0:1,Handicaps,其它可以类推的)
- ], A: c c( _可以采用类似公式,在(一)中我们分别用A(d)、A(h)、A(a)描述平局、主胜、客胜事件的发生。现在改用另外的符号代替,如B(d)、B(h)、B(a),同时除了平、胜、负概率P(i)(i=d,h,a)外,还需要引入一个一个概率值P(hX)来代表主队赢一球(X=1)、二球(X=2)...的概率,下面来进行演算2 b% q/ [2 a6 x! g
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}/ L/ u7 R6 Q) @6 S
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
8 f% Q$ M$ C$ z( W QB(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数1 I- V' d! J/ b/ @5 M
接着,假设b(h)表示主队的投注总数,b(a)表示客队的投注总数,那么投注主客队的回报总数额为:
{ f( D q: ]# e, ?- P{b(h)*O(h) , 即上面所述的B(d)结果发生3 U# x! i6 K& x3 R5 y) P# f
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
4 A; [9 f3 f- y9 i1 v{0 , 即上面所述的B(a)结果发生. I4 G" z# r% q2 e$ i4 G
以及0 w; W8 o" S0 r. `" N+ a
{b(a) , 即上面所述的B(d)结果发生6 M' n4 k8 S- N- J4 q9 L1 c
R(2)={0, 即上面所述的B(h)结果发生% N0 c. \6 d7 m, G# R
{O(a)*b(a),即上面所述的B(a)结果发生' T8 t( }0 {$ W$ V* s
投注主客的期望回报总数分别为# B% ]! V9 X4 ?! T9 e0 G% W
E[R(1)]=P(h)*b(h)*O(h)+P(h1)*(b(h)-O(h)*b(h))=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]
; H; }$ ?3 c$ f+ Z& hE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
0 q5 v0 Z8 o T$ ]3 y2 S5 ]假设实际投注回报与期望投注回报相等! s- N. E: ?& @" h% ]
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)2 @* ?5 k$ K& O1 a$ l4 m
P(h)*O(h)+P(h1)-P(h1)*O(h)=15 m- ?5 A5 m+ m$ C! V' X
O(h)*(P(h)-P(h1))=1-P(h1)
U @" @) U7 {' q |0 K3 oO(h)=(1-P(h1))/(P(h)-P(h1))
0 z9 b1 S3 s" [+ u" c; FE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
z9 m' K- R' N# sP(h1)+O(a)-P(h)*O(a)=11 \9 f T8 c3 _2 F' a/ H2 ]
O(a)*(1-P(h))=1-P(h1)
9 ] C+ o% q4 Y2 o% ^O(a)=(1-P(h1))/(1-P(h))8 N, L1 w) K( _ @; p& a
以上(五)部分是让一球的情况,让两球以上整数盘和反过来受让整数盘是可以同样演算的。9 ]' [9 `) J ^8 H
简单小结一球或整数盘,其实理论的演算过程不难,但是如何准确计算赢整数球的概率(P(hi)就是其中的难点,这已经涉及到如何用相对动态实力差或球差来计算各种赢球概率(是指赢1、2、3...球的概率,也可以说是赢球比分概率)的问题,使用自己数据模型里的数据来计算。 |
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