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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。
8 @% h, i3 j0 g' W% C; _那么,平局、主胜、客胜就有以下表达式:; j" i0 i2 b. {: T! ?4 ^- R
A(d) = {W(ij)|i=j, i∈N, j∈N}
$ p1 ~' u3 }3 B3 o: U* IA(h) = {W(ij)|i>j, i∈N, j∈N}9 A* }( | O r o
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]:
- y8 j% w* `- x: u& mP(i)=P(Ai), i∈{0, 1, 2}
# b* U7 p1 y" s, m7 i! y; F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)
: m6 E1 X& B' U) D( `; f2 Y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:: u& @" m, @9 l$ ~9 l( r$ T& Y
{b(h) , 即上面所述的A(d)结果发生/ {0 Z5 M+ z( ^- d. f+ ^
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
6 p: ~, P$ H3 l7 k0 d{0 , 即上面所述的A(a)结果发生
. e8 f. D' X" }$ ^3 Y+ |以及5 N. I. |% ^8 R$ X$ {2 J
{b(a) , 即上面所述的A(d)结果发生
: [) S9 m% s: u7 F- G. F3 E' fR(2)={0, 即上面所述的A(h)结果发生" i8 v) P+ l5 J* ^- R" t, t
{O(a)*b(a),即上面所述的A(a)结果发生: E- u( c) O- @, g b: V& 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
. R4 d$ P( n" L$ g那么投注主客的期望回报总数分别为
: {- q( s# T* ?E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]
# ^: [; f m: m# u' lE[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
3 P- r2 v; d8 u, R! g2 M; s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
' x" t- p5 h0 ?& d; O5 xE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)2 ?0 C$ h& Q3 s: j f
P(d)+p(h)O(h)=1
' e* k2 _6 ~# U4 i. |0 H0 eO(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式& V0 E: O! f3 A
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a) }, H) t2 E7 N* X9 J! J1 v
P(d)+p(a)O(a)=17 F7 |9 |7 G+ p( |; t" X7 y
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" H+ u5 ?& S. m4 k+ y5 K, |
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! j% W8 z/ o" l" h. s
三、半球盘的计算描述
. E9 M% z- R4 Z# F; Q5 _8 b接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
8 D1 o2 b( }- s# B( U' [: |+ G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:
6 [% U6 _" D6 `8 Z2 ^+ \2 o( @{O(h)*b(h),即上面所述的A(d)结果发生
: ]5 @! b* K3 _" A4 N1 QR(1)={O(h)*b(h),即上面所述的A(h)结果发生6 g% f+ l+ v4 l: b" j# w0 y
{0 , 即上面所述的A(a)结果发生3 i& j/ b) I) W) J( B$ W9 b/ R
以及8 r/ x* F0 t3 n6 R8 c* C' c. J% I5 ^
{0 , 即上面所述的A(d)结果发生
6 z* J" s8 a' X1 z" CR(2)={0, 即上面所述的A(h)结果发生
( P0 m& H. M* E{O(a)*b(a),即上面所述的A(a)结果发生
6 H5 x2 E) s {9 y! B9 u如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率: A f4 V2 ^6 y9 y8 _
投注主客的期望回报总数分别为
$ s- j7 }: V( A V: n, WE[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]
) p! A& t Y" Z+ @E[R(2)]=P(a)*O(a)*b(a)
' z% x" ?- j' d, `+ N, i% F) T假设实际投注回报与期望投注回报相等
2 r/ X- E1 H1 DE[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h), Q6 }, g7 d7 R& e% K P5 T# R
O(h)*[P(d)+p(h)]=1
v9 n# C0 Q; ?+ [; u4 fO(h)=1/[P(d)+p(h)]
7 L0 d- ~# {' d6 J: Y3 BE[R(2)]=P(a)*O(a)*b(a)=b(a)
* J6 k! R3 \8 v0 H! QP(a)*O(a)=19 U/ N6 e" h$ N' ?' ]
O(a)=1/P(a)$ F' v& ?+ {* I# _) h6 V
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率
/ A7 }: ^, a8 q' j# XO(h)=1/p(h)
4 ]3 w( t, r* F9 I5 c0 I- |O(a)=1/[P(d)+p(a)]* f% ~1 I6 d3 |7 w
四、平半球盘的计算描述, J4 Z7 a. c# N& X" s0 Z
这个稍复杂一点0 _: |* o) V4 {8 ^( Q/ r8 X
接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)5 L# d+ `7 ~6 P! F3 E! i. Q" p7 |
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:9 G4 Y" T5 n8 ~- [4 B9 c. U$ f* Y
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
5 ?. G' A% t6 z! x' L& mR(1)={O(h)*b(h), 即上面所述的A(h)结果发生( X" q/ L. Q0 H* v+ q: M
{0, 即上面所述的A(a)结果发生
4 W( X5 J4 d* u/ z6 i) n以及
% X* J& X# {* v' u" x) C& m{1/2×b(a) , 即上面所述的A(d)结果发生
# f6 ^$ `1 D8 D5 D( j0 OR(2)={0, 即上面所述的A(h)结果发生& J; K2 Y n0 e5 [ s8 J0 T3 `
{O(a)*b(a), 即上面所述的A(a)结果发生
( L ~) D3 D6 P& T2 t投注主客的期望回报总数分别为
6 _) u7 g) T8 Q& nE[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))
2 ~. g- t7 Z& F" M" ]- g H: mE[R(2)]=1/2×b(a)×P(d)+P(a)*O(a)*b(a)=b(a)*[1/2×P(d)+P(a)*O(a)]5 g7 I7 Z2 j1 p! J. Y
和上面计算过程相似,得出:+ W: v) B5 @/ ~- C" m/ i H# g
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
V. v# `/ z! T8 N9 L" zP(d)×{[O(h)+1]/2}+P(h)×O(h)=1" L9 s3 v( I% z. `! c5 W
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
" \. \/ S; Q3 \% |O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))7 s6 |4 j# J+ Q A" H! h: }
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
4 E# m+ Z" I% N$ [1/2×P(d)+P(a)*O(a)=1- Z, @3 g3 a, x& I
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)2 g9 c1 t3 H8 v! ^5 e
同样主队让平半就分别是& D1 R7 P+ W8 A P! }/ \+ n) ^, P
O(h)=(1-P(d)/2)/P(h)
7 p- I4 x! _2 v `O(a)=(1-P(d)/2)/(P(d)/2+P(a))4 ]1 a: Z) O: J8 Q, f8 b! w
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)& H6 l4 R3 Q( y. D! m
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
9 [- P5 h0 k* i' |7 cB(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}! n. T4 J: i% N
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
( }0 N& d$ P7 V2 w- ~7 [3 WB(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数3 W8 c! H' i3 u0 {: a+ L
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:* d; U) T9 `5 n4 {% v! j
{b(h)*O(h) , 即上面所述的B(d)结果发生+ V) n, x+ o: U5 A* P. H0 X
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
0 J1 V' c( O& ?( ^+ U. f{0 , 即上面所述的B(a)结果发生, g! l2 ~9 X5 t6 c; t
以及
9 h9 i& {0 q/ L9 n, q" m$ `& u{b(a) , 即上面所述的B(d)结果发生
: b7 E5 [" c; X5 }R(2)={0, 即上面所述的B(h)结果发生
h" E+ c3 O7 n3 _{O(a)*b(a),即上面所述的B(a)结果发生. s% m" `7 _& v! s& Y: @7 m
投注主客的期望回报总数分别为
1 | D' ^5 X$ ]! g) s' f5 [' YE[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)]) E% |3 @- M$ X- P1 t# |
E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))) H* x3 a1 T, C/ V' @2 _. i, ?
假设实际投注回报与期望投注回报相等) Q5 [# `/ z7 W2 g# C( g
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)* K1 p. D# ?; z) r+ J5 e+ E$ E
P(h)*O(h)+P(h1)-P(h1)*O(h)=1: e0 S9 q2 b) E7 e, B: k% _
O(h)*(P(h)-P(h1))=1-P(h1)
6 C E: ? j6 L" F+ n; |: |O(h)=(1-P(h1))/(P(h)-P(h1))
& B& ~9 Z6 W1 i& _E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
3 n, V/ \3 s/ Q' iP(h1)+O(a)-P(h)*O(a)=1
7 ~% x8 a+ l6 _: A! J P( V; yO(a)*(1-P(h))=1-P(h1)- D" g6 S# Z/ W! D# b) Q
O(a)=(1-P(h1))/(1-P(h))0 L: q( j8 e8 p& o$ L) v
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。
/ O0 j! D- {$ T9 n" L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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