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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。2 b3 S" u8 G4 m3 d# H6 T
那么,平局、主胜、客胜就有以下表达式:( e. u/ Z% s9 }) e/ o3 e0 P2 k( T
A(d) = {W(ij)|i=j, i∈N, j∈N}* T% p2 N) t# |! W. U1 T7 G9 F
A(h) = {W(ij)|i>j, i∈N, j∈N}
8 r( i: v+ y, r) s' G, v( o4 mA(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]:
& n1 l5 I' {& s: r8 CP(i)=P(Ai), i∈{0, 1, 2}
6 P' G: d2 o, W* | X% R0 s$ s( w8 G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)6 y6 P" M" g* t2 ]4 d4 D
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:
! c: P9 I: Q. R4 ?1 D$ k{b(h) , 即上面所述的A(d)结果发生
" ^4 ~+ c, Z$ vR(1)={O(h)*b(h),即上面所述的A(h)结果发生; Z5 B3 ~" j/ }8 x p, R- c n$ h
{0 , 即上面所述的A(a)结果发生* U" }% o: H. [3 U
以及) Q, W! U; b, v5 K8 O3 L
{b(a) , 即上面所述的A(d)结果发生
6 x- V \1 p5 N) b5 TR(2)={0, 即上面所述的A(h)结果发生
- v* f9 J" b1 f2 A{O(a)*b(a),即上面所述的A(a)结果发生: A/ \3 f6 e+ E- J
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: `9 t7 D- `7 }5 y' }
那么投注主客的期望回报总数分别为( r# F. p* e! _% l; M6 G
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]( s( x, ~( _# L/ H) E
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
6 m. M8 C, s0 j2 d6 R7 o9 Z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
4 k s# U# d/ ~5 {) SE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
( o6 S5 Y- m; @( ^" i8 U4 u& |P(d)+p(h)O(h)=1( F) m, c( v. F1 P* {
O(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式
5 U$ Y6 ?/ m1 ^, Z' N& Z( t. _* iE[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)* ^9 q: @9 B3 x
P(d)+p(a)O(a)=1
% D" s& l: ^ F0 }) N1 S* MO(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式7 n8 A5 l% l' p/ V. h- k8 y
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 y9 H6 N7 Y4 L1 O9 F [三、半球盘的计算描述. N0 W$ d" K2 |# e7 J
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
& |; K: N/ l7 \6 i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:" x8 t' W& R5 O
{O(h)*b(h),即上面所述的A(d)结果发生
, n) I) _* w7 I! HR(1)={O(h)*b(h),即上面所述的A(h)结果发生: X/ S/ k' [0 ^# b* d8 H
{0 , 即上面所述的A(a)结果发生; U* }" N) ^4 R
以及
! K" s, U3 A! a+ {/ ?2 S2 X2 D{0 , 即上面所述的A(d)结果发生
+ d: b6 s( ~& s0 p2 a4 ^$ CR(2)={0, 即上面所述的A(h)结果发生 Y# F1 R. M' f+ Z* h
{O(a)*b(a),即上面所述的A(a)结果发生6 O$ B( G1 D& [! L% D7 L
如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率8 w2 ^; i* E5 f$ J* i& r4 [
投注主客的期望回报总数分别为9 s/ _$ i. G; a) P8 v ?' c% S
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]
4 _* Z5 n9 u; @% j+ g, g8 `: O. X1 bE[R(2)]=P(a)*O(a)*b(a)
5 T5 I3 x/ P9 n {& ]+ p3 m假设实际投注回报与期望投注回报相等
1 J" C5 L$ n- U5 o1 P7 ME[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
, s' j9 o" W4 F- }# S$ GO(h)*[P(d)+p(h)]=16 R; @/ e" g. _1 G
O(h)=1/[P(d)+p(h)]
) p3 q( Z& m4 W; vE[R(2)]=P(a)*O(a)*b(a)=b(a)
% [" r+ K) M" ]/ A; Z: r7 jP(a)*O(a)=1
: d9 X' Y( S# ?' A2 s( sO(a)=1/P(a)
, | O4 L- W n$ C' M* l* p同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率1 N4 T8 W) O8 _, _
O(h)=1/p(h)9 U8 o* R, Z O
O(a)=1/[P(d)+p(a)]
' P( r5 Y: H/ G2 ]四、平半球盘的计算描述9 w5 w2 z( F1 w, x0 z) d" y
这个稍复杂一点
; I9 U- \6 j5 ~& o接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)( ]; t q$ k. r X- |) u3 ?6 W
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:
* k% `, ~4 _+ G{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生0 q; p8 N8 @/ M/ P! [( @
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生; ]+ L& W% l9 L
{0, 即上面所述的A(a)结果发生/ ?+ s- I' p& x
以及
0 S: C' Z2 E2 U# q8 c+ L2 k{1/2×b(a) , 即上面所述的A(d)结果发生8 V3 Q m3 n+ Y5 K
R(2)={0, 即上面所述的A(h)结果发生
8 M: Z( p; M: q* _3 h+ x{O(a)*b(a), 即上面所述的A(a)结果发生
8 Y9 y& \/ P/ Y7 h! L投注主客的期望回报总数分别为# ~7 P3 H# ?; t$ B/ f2 {
E[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))
0 T: z4 p, @/ yE[R(2)]=1/2×b(a)×P(d)+P(a)*O(a)*b(a)=b(a)*[1/2×P(d)+P(a)*O(a)]! M0 d( t1 b% L2 U3 H. m. e) `
和上面计算过程相似,得出:& e' i) i& ^, v, y" `$ Z' R
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
. L/ Q+ [& n1 x! s/ v+ E# v, YP(d)×{[O(h)+1]/2}+P(h)×O(h)=1. z8 O9 Q. t g M2 \$ ?$ H
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
3 ?2 M9 [: M: i0 k `O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
3 d$ U# x }5 P! x K& V5 e8 ZE[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)& g2 H, _$ u5 G4 r" B |: \( ?4 t! m
1/2×P(d)+P(a)*O(a)=18 s/ Y8 e8 ~- u5 h5 f8 F. s
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)) Q, h; L/ J9 Z# n" P" V# F4 A
同样主队让平半就分别是+ x6 ~, W L: { D9 F1 f/ J% Q- V
O(h)=(1-P(d)/2)/P(h)6 g N8 V; P9 w3 X
O(a)=(1-P(d)/2)/(P(d)/2+P(a))2 c9 g( w8 x- H8 }0 P
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)! f* L9 @- j- S8 `2 U1 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
" \ D- E$ ~9 ~4 h5 `B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
: g2 U; G% a- z' ]4 S' U+ rB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}$ |* x, }2 c5 V
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数$ {2 T1 W: Y) g! y% \
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:
& r6 h2 Y) E( y+ k n& m) M{b(h)*O(h) , 即上面所述的B(d)结果发生
) t& ?2 {. Q# B0 ]$ B/ ?6 E7 q: vR(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生7 S2 e- n9 q- d5 y
{0 , 即上面所述的B(a)结果发生, m R1 M3 U$ @' V5 N+ [! ~
以及! @4 k! d/ a* q$ a
{b(a) , 即上面所述的B(d)结果发生& u1 x) @/ g6 O7 z! w- r& h" d
R(2)={0, 即上面所述的B(h)结果发生" C1 z2 `; K2 O' P- Z
{O(a)*b(a),即上面所述的B(a)结果发生
4 p( |* O5 I# {1 |- X q投注主客的期望回报总数分别为* l; x# \# H3 C- Q& P
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)]
7 @7 x2 h% [; s0 ?3 bE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
+ }# E- P1 Y. X! @假设实际投注回报与期望投注回报相等
# s3 x/ {! l' x# h' YE[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)6 Y" |5 T* `! K/ f* @' [
P(h)*O(h)+P(h1)-P(h1)*O(h)=11 S" e: g, V. V6 L8 O6 f' I d0 G
O(h)*(P(h)-P(h1))=1-P(h1)( r* j8 O J' T1 P% C' O1 j/ \
O(h)=(1-P(h1))/(P(h)-P(h1))! a ]/ d0 Q" |
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
& Z' w, n: a9 c5 HP(h1)+O(a)-P(h)*O(a)=1! }$ v# d& M; m
O(a)*(1-P(h))=1-P(h1)
1 j8 K' D- R4 E% [5 aO(a)=(1-P(h1))/(1-P(h))
" c" A. R( B7 X+ _/ |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。# p1 k! |8 ]* k0 n
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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