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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。% I- Z+ G t7 j8 C
那么,平局、主胜、客胜就有以下表达式:
1 _& w: i: [. {! [9 N7 n: AA(d) = {W(ij)|i=j, i∈N, j∈N}7 X0 u( V( X: Z1 ]0 u
A(h) = {W(ij)|i>j, i∈N, j∈N}. n* i; m/ o% }% j/ `4 n1 |
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]:+ M) F- o8 g) @) _. E& ?5 Q; M
P(i)=P(Ai), i∈{0, 1, 2}
8 k* m- Z# Y2 v: T: ?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)- Q; S- |* f* A& _+ B
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:% Y( P: J' V/ x' b
{b(h) , 即上面所述的A(d)结果发生& ^, C: I% F3 P/ I% P; u2 i
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
! W$ ]7 P+ n9 u1 _; f3 Z{0 , 即上面所述的A(a)结果发生
3 |# k7 v. q9 A3 W4 m以及
. f! r8 h& r" o, J1 e2 N{b(a) , 即上面所述的A(d)结果发生
6 l- p- |4 ?+ J6 V/ KR(2)={0, 即上面所述的A(h)结果发生
3 g$ c5 X1 v6 N0 P: A, \{O(a)*b(a),即上面所述的A(a)结果发生
7 e. ]/ L3 Q, \+ [0 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
& s- H! Z* b" J: q那么投注主客的期望回报总数分别为
* s' n& Q/ P1 l+ l3 y+ M! |4 ^E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]9 n3 ]. p2 v8 ?9 | D
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]! I' f* C: P& w4 U2 G
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
( O6 P5 k* Z! ~+ V$ F" A: ~E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
3 {7 S: @7 ^ O7 R$ GP(d)+p(h)O(h)=1
4 [( j; d, z) A: G$ `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1 l) ?) {+ `1 ^% O T# B7 d% [6 Q
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a): R- u3 U: A o) j) _2 R9 A
P(d)+p(a)O(a)=1. p" w, M1 o! |$ E$ [$ ?' E. i
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4 c( a' |- R+ f2 ~) O
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
5 W' @ E: j" ~( z3 R: U三、半球盘的计算描述5 C8 V2 T" |+ F! n" d, P4 t
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况); \* d' f. Q2 E. i. Z
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:3 v9 t' [; ?! f1 ^" u
{O(h)*b(h),即上面所述的A(d)结果发生
( o) y8 P9 U! e. eR(1)={O(h)*b(h),即上面所述的A(h)结果发生
8 A/ i! h* x% n! L# T{0 , 即上面所述的A(a)结果发生 o+ V3 n; \# p* M) s. p" U, R
以及
/ C' j$ c& n( U! W{0 , 即上面所述的A(d)结果发生/ z9 }! A3 {# G* c8 G
R(2)={0, 即上面所述的A(h)结果发生
. k* c6 R; J0 Y4 ^* X1 ]{O(a)*b(a),即上面所述的A(a)结果发生. X6 V. a x; p4 m- g# C. c
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; J- C/ j/ `" K投注主客的期望回报总数分别为
9 y8 Z6 Y( q7 l7 o) ^. z, fE[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]1 y I: r. ?+ z9 O. Q
E[R(2)]=P(a)*O(a)*b(a)
6 x8 |7 |- J+ u1 P假设实际投注回报与期望投注回报相等
) }. G( |- g6 F& `# z0 b7 ?E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)- W- I. ^; S" P4 H* _7 z. @5 J
O(h)*[P(d)+p(h)]=1
, s0 K3 B6 e* V. lO(h)=1/[P(d)+p(h)]
8 U" k; l" z a+ e2 AE[R(2)]=P(a)*O(a)*b(a)=b(a)3 I+ B2 q. [6 l7 M6 }
P(a)*O(a)=1
& U* m2 B+ e; c, o0 g' B1 ^ `; IO(a)=1/P(a)( V$ L0 ~$ w0 ^' n
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率0 |" M+ d- m# \. J
O(h)=1/p(h)
& q3 E6 y4 `9 `O(a)=1/[P(d)+p(a)]
- J: r6 ?- S2 g5 P J四、平半球盘的计算描述
/ D# m2 c" d: F# l! j1 u9 i2 `这个稍复杂一点2 B+ K7 b0 I" H7 e8 T( S d
接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)& `5 }* r4 W3 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计算:
! r6 R2 i8 k/ a# ~# H' b9 }{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生; y6 e8 `1 ~% v! b& k O" C
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生4 r( l% c! E. M0 d5 |
{0, 即上面所述的A(a)结果发生 p' {9 {$ t' e
以及; t( c1 n* Q# m V0 N. S1 F# I
{1/2×b(a) , 即上面所述的A(d)结果发生
0 ]! }3 K9 C; i2 O7 [$ hR(2)={0, 即上面所述的A(h)结果发生
) j+ G; Z( N9 ?8 Y" _/ y+ {{O(a)*b(a), 即上面所述的A(a)结果发生% g3 r. D% w2 ?' A6 ?, f! @
投注主客的期望回报总数分别为
0 b2 o& q8 f, F" U0 { wE[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))
) o& ^( Z/ V8 x* D2 J7 LE[R(2)]=1/2×b(a)×P(d)+P(a)*O(a)*b(a)=b(a)*[1/2×P(d)+P(a)*O(a)]
+ T' u8 ?. X4 E9 |4 _和上面计算过程相似,得出:
" I: c8 G! M% x Q& N8 j$ Z: FE[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)1 ^5 A$ d: f0 a
P(d)×{[O(h)+1]/2}+P(h)×O(h)=16 T" X( E: j3 ? R4 M$ q) X* W
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
3 I8 n- k9 N$ M- gO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))$ y1 ]- N% x" Y( Y
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
; U' J9 I) c/ P# |1/2×P(d)+P(a)*O(a)=1
/ V- @8 v8 J. p1 v; F& a Q6 J1 [O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)9 y: ^( G" M1 O4 x3 v: l1 D* T2 G
同样主队让平半就分别是
# k8 ^. H: U9 W0 jO(h)=(1-P(d)/2)/P(h)2 {, X& e! f3 [- X8 a
O(a)=(1-P(d)/2)/(P(d)/2+P(a))5 E8 w5 z* U6 v6 i6 _1 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)
* ^& i' ]3 \5 v8 B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
" v4 G+ L# O T: `8 `B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
! x8 L7 u. Y9 E) ?" |B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}! \; |9 Q& B9 _; \5 E
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
/ O8 b1 L3 V% z7 O1 H$ w: [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:/ A4 }. g6 T: n* c. J$ ?5 B; F
{b(h)*O(h) , 即上面所述的B(d)结果发生
' |/ f3 D& e% X# r, h7 OR(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
- D4 K7 ~. K) D. {% o& @+ n* X{0 , 即上面所述的B(a)结果发生7 P R3 c* m8 e
以及
+ T$ w9 s4 @6 T" N7 n! @' [{b(a) , 即上面所述的B(d)结果发生: T% M S% X2 B+ V" X
R(2)={0, 即上面所述的B(h)结果发生
5 Y( o% ~! h8 Q& |" \2 c{O(a)*b(a),即上面所述的B(a)结果发生$ B& t6 k( T. |- P6 [
投注主客的期望回报总数分别为
5 C' x) D8 x& F& X4 j$ u4 SE[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)]! G9 F2 Z7 z* b
E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
( A! R7 V- o j6 F* j假设实际投注回报与期望投注回报相等
- f8 m3 p3 l/ ^+ [- BE[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)9 J j. G# i" r) d/ X7 H
P(h)*O(h)+P(h1)-P(h1)*O(h)=1
/ G( S ]. \6 q- r% FO(h)*(P(h)-P(h1))=1-P(h1), o: _" }$ Q% c$ c* }
O(h)=(1-P(h1))/(P(h)-P(h1))* O4 A. M9 Q, l- c" _
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
6 e3 l! V( ?; J0 O- WP(h1)+O(a)-P(h)*O(a)=1
% k1 e, v/ J8 b0 O: J. `1 n3 {# h! BO(a)*(1-P(h))=1-P(h1)
$ z: Q; H3 I" q9 ^% X% uO(a)=(1-P(h1))/(1-P(h))
) ~) R' Y5 j2 J# o8 l. T. 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。
3 m% I$ L4 E( J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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