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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。' W$ v" I8 ^8 e; I8 V; e% p
那么,平局、主胜、客胜就有以下表达式:7 N, W1 I7 y* V* F e
A(d) = {W(ij)|i=j, i∈N, j∈N}( m+ H" ]. `# H* A. N r) j
A(h) = {W(ij)|i>j, i∈N, j∈N}
" _6 e, Q/ G# w( X9 d: fA(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]:- F/ U6 |9 q ? `1 \/ Q/ z# f
P(i)=P(Ai), i∈{0, 1, 2}6 P/ u- Z& `8 F! s+ s
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)
! W5 t8 k6 H7 x1 C- o) {; O8 L+ S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:
$ r1 K* s7 n0 s, ~* Q{b(h) , 即上面所述的A(d)结果发生9 g3 N+ G% Y* }
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
& C0 J8 ?4 P. J( ^. P{0 , 即上面所述的A(a)结果发生
$ C. ]$ L d) ~% d" ?2 E5 i以及
f6 r) d. v' P1 \+ m/ l: l{b(a) , 即上面所述的A(d)结果发生" J7 f; L7 r6 E" l1 g/ m, V/ q! k
R(2)={0, 即上面所述的A(h)结果发生3 W8 c6 R, V) F, l0 d9 U
{O(a)*b(a),即上面所述的A(a)结果发生* n3 v- x# M, O) ^
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
& x* x# ^; q) Q5 Z; t/ {那么投注主客的期望回报总数分别为( Z2 B- w$ ~( s* w
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]
6 k Q% e6 z3 T* `- L9 HE[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
1 f6 V2 @9 v7 y! J& L, M8 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( T' R/ I& o! X8 b4 c
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)" O' v: u: |, ~) R' g6 V6 g4 E6 s: w
P(d)+p(h)O(h)=11 p' X& v9 n1 g) y" r2 v! q: Z
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
% _. k$ y2 l/ J. f& n: E+ ~E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
! @3 l9 W1 Q: M; |8 x/ lP(d)+p(a)O(a)=1
3 S# V8 \. q+ C( r" TO(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式/ l7 V4 x4 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
* B: Z% c# G( }: e% W8 z+ o! Y三、半球盘的计算描述
5 t/ v/ u5 @8 U$ i接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
2 u: s2 x4 E, G4 a: k5 W& @: 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:5 n' @1 x6 f k3 p
{O(h)*b(h),即上面所述的A(d)结果发生
' {! K9 s" O8 k( u: g ~# BR(1)={O(h)*b(h),即上面所述的A(h)结果发生
% a5 M( ^2 G+ x* @$ Y{0 , 即上面所述的A(a)结果发生3 \) v/ T1 c+ P2 z) @( ?. s/ g$ V# {3 }
以及
; K/ X, [5 J8 n9 E: v* y{0 , 即上面所述的A(d)结果发生! g6 {8 q5 T, p1 z6 P y/ h J
R(2)={0, 即上面所述的A(h)结果发生- y# m H% M8 p
{O(a)*b(a),即上面所述的A(a)结果发生* ?3 B$ u5 |+ X }4 y
如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率" h( d8 \3 m z& Y; n
投注主客的期望回报总数分别为: t2 K0 m: o5 o5 g0 @
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]
, r' A) s* K2 p- KE[R(2)]=P(a)*O(a)*b(a)
, l; f! d$ g# [+ y假设实际投注回报与期望投注回报相等; Y3 N0 F0 |$ N7 X, `& `
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)5 B b5 @8 N7 F; Y9 [ a& O& \
O(h)*[P(d)+p(h)]=1, X8 x: w$ H% ]
O(h)=1/[P(d)+p(h)]
; \9 U8 ^; ?0 B% k+ vE[R(2)]=P(a)*O(a)*b(a)=b(a): F& B* _0 W5 }, T3 ]% \: j8 [4 c
P(a)*O(a)=1
4 k1 l! ]8 b/ K% n0 ]8 kO(a)=1/P(a), \7 C0 W: _1 _. U5 G) d
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率" @* [) v2 x0 j+ d n. }* c
O(h)=1/p(h)
0 l6 [$ ^' n! hO(a)=1/[P(d)+p(a)]
' g& ?/ T f; \3 I5 u$ d四、平半球盘的计算描述% H5 d2 x; o& Z0 X& k
这个稍复杂一点
3 t4 m5 t: ~, C; T# i接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)' ^0 w) j" s3 g) w2 ]/ K% M3 `/ 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:
: K- K- Y8 A+ s; Z: N{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生4 m4 [1 l0 \+ U4 J! o
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生
5 A3 r- n8 V( t# n3 [& _. M{0, 即上面所述的A(a)结果发生9 B5 X; U8 w1 g$ Q0 ?" n
以及
" S2 p) Y5 g; Z+ K7 _{1/2×b(a) , 即上面所述的A(d)结果发生
. F5 X8 x3 Y ^8 o: n: G9 UR(2)={0, 即上面所述的A(h)结果发生6 Y4 Q0 P k4 U6 U
{O(a)*b(a), 即上面所述的A(a)结果发生& i7 ?+ ?" l9 ?5 K
投注主客的期望回报总数分别为- F' v! F+ o0 O# l
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 R) h' O3 f. Y2 bE[R(2)]=1/2×b(a)×P(d)+P(a)*O(a)*b(a)=b(a)*[1/2×P(d)+P(a)*O(a)]
! b$ C5 Y. B6 C) ^和上面计算过程相似,得出:& G0 n. f( }# x- C
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)$ x: w0 q# P$ {
P(d)×{[O(h)+1]/2}+P(h)×O(h)=19 F* w( i* Y9 Q) b6 T: [
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1; @: |' O2 G& p% u/ q" G/ J
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))) x. W1 N7 z _/ G/ C2 V
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)* _2 R, E- C# A0 w
1/2×P(d)+P(a)*O(a)=18 S8 ^( X6 P( C* B
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)+ |3 @. y( ]/ y# y
同样主队让平半就分别是 q: T3 i1 ]( H6 E
O(h)=(1-P(d)/2)/P(h)1 \: w2 V! e2 C5 g" g/ e4 u: _
O(a)=(1-P(d)/2)/(P(d)/2+P(a))
0 G. L4 H1 F j- m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)0 \2 k9 X/ W8 v+ {4 k: m( v& 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2 j2 D4 c, Z" J0 o
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}5 o ~* ~& L! p6 j5 ?: Z3 f$ N
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
! \1 j( R; m( H+ A0 UB(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数 K' o7 _" ^ R; X
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:
H5 N9 U1 o: ?2 j3 h{b(h)*O(h) , 即上面所述的B(d)结果发生; I9 s0 R( V r0 J- b
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生4 [4 Z% Z' f9 G$ H. E5 {+ B
{0 , 即上面所述的B(a)结果发生! A% n; W6 D. q
以及" L" s8 W I* P! i5 [. ~3 S
{b(a) , 即上面所述的B(d)结果发生
0 m6 f0 W. r+ ?) rR(2)={0, 即上面所述的B(h)结果发生
( W: s: L* Z2 ^. N{O(a)*b(a),即上面所述的B(a)结果发生$ m& `; }( R8 l8 `! x) T0 P
投注主客的期望回报总数分别为8 d* O% Z* _6 W4 N0 x
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)]$ D7 z K9 q# u* n* H* e5 C6 s8 M
E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))+ y ?( w1 V$ H5 g6 L6 l Q
假设实际投注回报与期望投注回报相等2 ~; _: D. u, i
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
' v% [' v0 F b3 `* }P(h)*O(h)+P(h1)-P(h1)*O(h)=1
$ d7 A4 n0 M; P# M7 X4 D$ Y, qO(h)*(P(h)-P(h1))=1-P(h1)
. k* y7 ?0 ^2 X! q" \- y1 rO(h)=(1-P(h1))/(P(h)-P(h1))% ^& z- ]# d( d
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)2 O4 X- f" G* w: _2 s& z
P(h1)+O(a)-P(h)*O(a)=1# ?. \8 B/ o/ j5 W' _8 E' a
O(a)*(1-P(h))=1-P(h1)
3 K5 W& O5 W" d, T7 gO(a)=(1-P(h1))/(1-P(h)); K- d) N# O1 ?& G+ _
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。
* B! N; u1 |; F0 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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