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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。
U* ?! C% j3 L2 {0 K1 B& h那么,平局、主胜、客胜就有以下表达式:9 L0 X- ]9 x/ p% \, j
A(d) = {W(ij)|i=j, i∈N, j∈N}
! \, b. K8 z h- |, \+ GA(h) = {W(ij)|i>j, i∈N, j∈N}
7 J" ?0 V3 u6 y$ ]- c- lA(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]:
- ~! B+ a! h0 U- K* f2 U* {P(i)=P(Ai), i∈{0, 1, 2}& u' R9 v9 `4 J3 U8 r- m
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)
g) C1 |7 D4 K7 k5 ^, A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:
& M* G, K: U- d3 \{b(h) , 即上面所述的A(d)结果发生! w7 q$ \( I* N- M
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
! Y9 x/ V: ?2 i% b: v$ U3 {% ~{0 , 即上面所述的A(a)结果发生
2 Z$ _. `1 v1 k. ]- K2 ^以及. S; H9 p( H; b
{b(a) , 即上面所述的A(d)结果发生) A( n9 R5 ?( Q: N3 s' e
R(2)={0, 即上面所述的A(h)结果发生2 M; J9 [4 J7 ?( Q D' p
{O(a)*b(a),即上面所述的A(a)结果发生
7 ~# x6 _- F9 P: w8 s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2 t5 e/ t+ V- Z2 C
那么投注主客的期望回报总数分别为, x% g4 U# |9 M/ p7 j
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]/ ^, N. v, F- A+ ?# Y6 {0 d
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
5 [1 \# y( F+ P: t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
$ t5 }; z5 N, r! n( BE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
- ^: N/ V/ X8 e& Y2 zP(d)+p(h)O(h)=1
" W" j2 P" w, i8 g0 C0 [+ jO(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式. p. F( Q+ i& N* p6 d# L+ ^; ]
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)0 k3 J5 j& l* C; L9 U1 T
P(d)+p(a)O(a)=1
- P& X. n: n) z8 X+ |( V$ {* cO(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式
, w7 t) F1 R5 Y7 j5 X5 {; t' v/ \( a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2 d: F/ w. x) o6 ?4 Q
三、半球盘的计算描述
1 T8 q' s- x, c; a$ H$ q接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
! d& V: ^) ~- y5 q u4 h0 o7 k& h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:
7 X3 z4 ?! \ L7 R( [; C! v5 F{O(h)*b(h),即上面所述的A(d)结果发生. D% a0 q7 a. [9 h" B, D
R(1)={O(h)*b(h),即上面所述的A(h)结果发生' G2 P/ S1 Z0 @, z1 `4 |9 w8 w P8 M
{0 , 即上面所述的A(a)结果发生% v u5 }/ ?! g0 H& z
以及" ]0 q% F X6 u6 B
{0 , 即上面所述的A(d)结果发生6 x7 o2 l) q. G) j
R(2)={0, 即上面所述的A(h)结果发生& x, M5 j# z( J- N7 X' R
{O(a)*b(a),即上面所述的A(a)结果发生# a' K- ^" Q- V9 I
如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率; C& V' Z: c9 G% O8 J
投注主客的期望回报总数分别为
+ S' ]; u, q6 g) Q; R+ fE[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]5 E9 S: j$ H+ ?9 v5 U! w" _
E[R(2)]=P(a)*O(a)*b(a)9 O6 B) R( t9 U3 z6 s0 X9 r
假设实际投注回报与期望投注回报相等
0 \( g$ H& t8 P3 @* ME[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
, h7 K" B3 a. X ?O(h)*[P(d)+p(h)]=1
( W9 `" G1 ~' z' Q2 w. R+ kO(h)=1/[P(d)+p(h)]" l; E" T: z, R. {' A/ O
E[R(2)]=P(a)*O(a)*b(a)=b(a)
9 u x6 e3 _! F# h _P(a)*O(a)=1! Q2 W1 T; u) M
O(a)=1/P(a)' t- J5 k! A/ D) J4 ~
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率
7 i8 z9 P) Q7 f0 C |O(h)=1/p(h)
+ M8 A- _8 g& x* AO(a)=1/[P(d)+p(a)]- _# O5 a6 e! Z* _: j! m6 r1 y
四、平半球盘的计算描述5 [8 P( y1 T' J! p* ^7 N
这个稍复杂一点
9 H; L7 u \: U接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
+ w' l1 u8 N" Y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:
$ m# M7 o, [/ Z4 z4 D/ `# p{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生, X) h ?7 c, w+ {( E
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生( p9 J, ]' d/ P
{0, 即上面所述的A(a)结果发生
7 S2 ~, q# T+ @3 _& [# h以及0 e6 L: o2 s1 y6 k3 k
{1/2×b(a) , 即上面所述的A(d)结果发生
7 ]6 v% P0 m( L3 ]R(2)={0, 即上面所述的A(h)结果发生
- ]9 r [6 b; ~! h6 J{O(a)*b(a), 即上面所述的A(a)结果发生# ?4 Z4 a9 Z6 N+ o
投注主客的期望回报总数分别为
" |5 ?7 \/ v% P& o# aE[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))
6 t5 s4 F% ?- [9 K; \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)]
6 n9 i/ T& e' j和上面计算过程相似,得出:9 T* Y% c7 [. K, J3 O; {$ e3 P. I
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
4 J) y1 ^2 f6 c/ w# X7 c) x" vP(d)×{[O(h)+1]/2}+P(h)×O(h)=1
+ x2 L- v" Q7 b) yO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=11 W3 q" B# X% ^1 a4 ^9 I( H
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))* l4 }4 Q) D2 h. ^
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)) R3 v9 ?2 U9 q3 t, o3 T
1/2×P(d)+P(a)*O(a)=1 C; P4 E8 v* h* E- h
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)2 ^2 V( N: q" O$ y
同样主队让平半就分别是& v. n& q$ N, o. [/ X
O(h)=(1-P(d)/2)/P(h)
Y! l" O U. q* [O(a)=(1-P(d)/2)/(P(d)/2+P(a))7 u z4 C% S& H
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)! j9 R' x5 j7 h) x3 H
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
: U# p; }) x8 n" `5 ^; ?B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
0 b* X* V+ f. y9 d; Z9 y( E KB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}, {( g2 W1 u* b$ d A
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数$ l- ]# \3 N- K2 l J
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. w; b( i- p0 {: ^2 I
{b(h)*O(h) , 即上面所述的B(d)结果发生0 n2 M) C. e G
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生' ]% f0 B% t2 o
{0 , 即上面所述的B(a)结果发生/ F4 H4 N6 ]: F. H0 Y/ @. D& S# A+ f
以及
2 m7 o7 t$ t U' X4 O{b(a) , 即上面所述的B(d)结果发生# s0 y4 _$ [ y( b( M, j. X
R(2)={0, 即上面所述的B(h)结果发生
& T( \& ^. b$ F$ ^9 b3 z9 l K/ v{O(a)*b(a),即上面所述的B(a)结果发生, z! N0 Y" h6 u+ ?* q
投注主客的期望回报总数分别为- {( ]9 n" T8 v/ B
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)]
3 V5 _2 v4 d5 N2 S4 z9 OE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a)): N/ m$ o" n& B" j! h
假设实际投注回报与期望投注回报相等
1 C: r: \: E3 H* T, JE[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
; \" z2 K4 g3 F4 |3 PP(h)*O(h)+P(h1)-P(h1)*O(h)=1& [$ R7 G& N. ^( K( z2 O
O(h)*(P(h)-P(h1))=1-P(h1)" R2 ?2 z: C5 r- J8 Q' o2 J' n6 a5 o$ O
O(h)=(1-P(h1))/(P(h)-P(h1))
+ f' W8 w# v1 O* J3 [) [( \8 T) mE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
* T1 F. S$ ?( r- s dP(h1)+O(a)-P(h)*O(a)=19 q# W; s& J/ d# c6 h8 m
O(a)*(1-P(h))=1-P(h1)8 M1 }+ l M% u# R, X p% G0 m
O(a)=(1-P(h1))/(1-P(h))+ Q s# E8 F4 x! D0 i
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。( I; `' {, |- H( m. X* v- ]
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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