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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。
; s& D4 @/ |+ l8 _% b( G" S那么,平局、主胜、客胜就有以下表达式:
$ T9 _5 {) _4 E5 a6 e. E, T1 gA(d) = {W(ij)|i=j, i∈N, j∈N}
7 e- r$ I( p1 x3 V; D! t1 BA(h) = {W(ij)|i>j, i∈N, j∈N}& R# @5 p8 D$ J ]
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]:+ h8 a! M6 l0 q4 q
P(i)=P(Ai), i∈{0, 1, 2}: V) H8 P9 x4 v8 @9 B
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): E! v# y$ Q/ l+ ?! u/ Y. M
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:
$ H+ g2 m9 b; a. p{b(h) , 即上面所述的A(d)结果发生 ?5 L9 ~) N/ z/ r
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
( [/ ^8 M* X, T8 B$ ?4 U{0 , 即上面所述的A(a)结果发生6 m: k) v5 R+ {% y+ ?% v' Y3 K% ^
以及- u8 |8 q4 a( k4 m( t) r, l
{b(a) , 即上面所述的A(d)结果发生
" k9 {5 I* d8 p. e& F- rR(2)={0, 即上面所述的A(h)结果发生
6 R; r/ I: d. n: ^5 q" W{O(a)*b(a),即上面所述的A(a)结果发生
6 Z" ]# W, b( W5 [; X9 q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
7 `0 m7 A. u4 c' p5 _那么投注主客的期望回报总数分别为
# C8 ^2 r. ^ E7 zE[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]
) c, d) k# M: Q, H( hE[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]' U! z2 C0 D& q" O4 \# F5 }" l
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
, P7 {. t9 H$ N& BE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)1 C* K0 r% |2 s5 v9 Z
P(d)+p(h)O(h)=1
/ s" Z2 w9 ^0 h; E: R; _4 v+ j& RO(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式) I8 x8 M: m& Q2 Z) g
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
9 X" }9 X9 \. ]' P5 T LP(d)+p(a)O(a)=1
0 I5 L1 I% \- @2 k0 a+ VO(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式' e5 x. _) L8 O" K3 F& ^
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+ y% ~* p/ Y- ~
三、半球盘的计算描述
7 D6 w4 N9 U: B9 }4 ]: i$ W接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)5 [5 @. i$ k+ v; J0 d
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: U9 \" u3 a: r! J# Z8 l9 N3 Z4 n
{O(h)*b(h),即上面所述的A(d)结果发生" ~" p1 S' P; L1 @8 b; Y
R(1)={O(h)*b(h),即上面所述的A(h)结果发生9 m0 \( G0 Z# S0 i8 I ~7 O
{0 , 即上面所述的A(a)结果发生
( X9 x# B9 E- o+ O/ Z8 O以及
" o' D' n+ ?. a: [& A{0 , 即上面所述的A(d)结果发生
) f# u$ x7 }. |' QR(2)={0, 即上面所述的A(h)结果发生
1 v K y$ c, R/ y" u{O(a)*b(a),即上面所述的A(a)结果发生
# y" z# ]* f+ L$ V如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率7 k: ?7 m! r% b/ h) d
投注主客的期望回报总数分别为3 k( K* u5 E( a% V% p& e
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]
9 }: m0 m* S5 @6 PE[R(2)]=P(a)*O(a)*b(a)0 s8 i: D4 w: x/ a9 d. d
假设实际投注回报与期望投注回报相等
4 @. D, |- \8 W( ~( S% D; _E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
$ L4 W$ y" A& w; V6 D" W3 [: rO(h)*[P(d)+p(h)]=1" Z0 c/ D% `. b4 f$ i# n1 u
O(h)=1/[P(d)+p(h)]
* g& a, Y& Z+ ]; f# D$ kE[R(2)]=P(a)*O(a)*b(a)=b(a)
2 k; o* ^# W3 i# t% `P(a)*O(a)=1
' U7 Z2 z$ g2 p5 }O(a)=1/P(a)1 t' p8 K, v8 p; Q$ J# p" S' g- X
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率! a4 Q7 H4 U& q9 E
O(h)=1/p(h)
b2 x J5 f4 n! s$ P7 A5 K3 vO(a)=1/[P(d)+p(a)]! c+ W& i" K! S
四、平半球盘的计算描述
$ p; j' x) O! o- c; O这个稍复杂一点
+ f& O7 H7 o( @! p接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
8 m9 m! S0 W D/ v# m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:
6 @& {& ~3 ?& i/ m& f8 d{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生! M4 k% [) t s
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生+ [3 g7 b, Y: I) A: X
{0, 即上面所述的A(a)结果发生: g/ R' n* ^( l$ u5 n9 U
以及 I5 A% f9 n, w4 d' ?7 g
{1/2×b(a) , 即上面所述的A(d)结果发生
' k$ u' B+ S5 ~1 \7 _R(2)={0, 即上面所述的A(h)结果发生
* g+ o9 m F- U. `" U" Y [{O(a)*b(a), 即上面所述的A(a)结果发生
' a9 a: y, [5 ^$ z" a投注主客的期望回报总数分别为. t- Z$ J; z+ v- j* [5 R
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))
5 e; q) Q/ r1 e/ {0 V; {9 ]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)]. J) y4 n" J% V$ Q
和上面计算过程相似,得出:# s! K0 I9 x0 A
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)0 {0 W, X. j g0 w* Y+ x; O% N/ d
P(d)×{[O(h)+1]/2}+P(h)×O(h)=1( O& A1 G8 ~3 `% S
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1# T4 z5 o2 b; n' m( i- l
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
& U/ `1 i6 q$ R& Z1 a# S3 ~( t7 AE[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)3 A6 u4 N$ i1 Z7 d0 z4 k
1/2×P(d)+P(a)*O(a)=1
4 ]. T; c( P+ D, SO(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
% O4 V9 u' w& `6 {( y* \同样主队让平半就分别是
" W+ i) b. B: _; d# Z: ^9 CO(h)=(1-P(d)/2)/P(h)
. i, r; h% r1 M, f8 XO(a)=(1-P(d)/2)/(P(d)/2+P(a))
' @% [4 C* A+ \% t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). Y b1 l$ 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- X5 |% S9 F2 f! D" ` r
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
6 q/ {5 G4 O0 x8 Q7 ]4 }' oB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}/ Z R0 ^, F! T% S( c- w+ Y
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
/ L2 l2 S% W1 R7 L8 r) j4 C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:6 e! D, v: }6 u& ?! Z3 j
{b(h)*O(h) , 即上面所述的B(d)结果发生
3 c4 B# w; ~& ^3 n7 v1 qR(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
$ o6 |5 a' D/ t2 l, }, ^2 c{0 , 即上面所述的B(a)结果发生6 T& L6 `+ Y& o* A u
以及! ?% p( q4 g6 L0 V* F6 j4 u
{b(a) , 即上面所述的B(d)结果发生
5 w% X# y4 ]" A0 M, jR(2)={0, 即上面所述的B(h)结果发生
. |# H; P1 n* c* K8 p1 u{O(a)*b(a),即上面所述的B(a)结果发生
0 N5 c3 I1 [ U6 ]8 X投注主客的期望回报总数分别为& \' }& R- c- ?+ [$ _
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)]
" f2 \$ l. d: r8 T4 L+ @E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))6 ^! K4 b; ~! G/ d
假设实际投注回报与期望投注回报相等" P/ C& `& \1 e |1 b5 S0 p
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
7 I5 V8 S7 Y5 C, C; dP(h)*O(h)+P(h1)-P(h1)*O(h)=1! D$ F" T* u8 {( A
O(h)*(P(h)-P(h1))=1-P(h1)" V5 v/ ]- Y0 C
O(h)=(1-P(h1))/(P(h)-P(h1))
3 C" Y- ~* {4 |, o& c3 ]) xE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
" D- o6 i9 x& z% v. H! b* MP(h1)+O(a)-P(h)*O(a)=17 y$ }* e( _5 y
O(a)*(1-P(h))=1-P(h1)4 M0 B7 v3 j8 d& A% E7 c1 C9 Q5 S
O(a)=(1-P(h1))/(1-P(h))) g' }1 d( e/ z) n5 T/ y, E: ]2 u
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。' T2 @. g- o5 A1 y* K% P% ]
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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