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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。
/ H6 {5 |, D: r b. S% u4 `那么,平局、主胜、客胜就有以下表达式:% \6 X9 b+ h, F5 T: \2 T, u
A(d) = {W(ij)|i=j, i∈N, j∈N}
; V* q9 g) B9 R& m$ GA(h) = {W(ij)|i>j, i∈N, j∈N}
- [% W/ g9 m# c8 w4 G" c0 p/ D, V# u/ tA(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]:
) }( r/ F* a% g2 J4 q& I* XP(i)=P(Ai), i∈{0, 1, 2}: @4 Q; e2 K' m+ ?9 }" I
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)
; L9 y; Y( N& H4 P8 R3 J, Y3 e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:
4 N* N% H+ H" b) n; F{b(h) , 即上面所述的A(d)结果发生* H% a& D# W4 B
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
4 H {! b. i: V. I' H) i{0 , 即上面所述的A(a)结果发生
/ e$ u# ?6 v6 p; z9 a以及
: f# @$ O8 [) ?" D{b(a) , 即上面所述的A(d)结果发生' r7 r/ p8 l" N7 t1 ? ^; f0 E
R(2)={0, 即上面所述的A(h)结果发生
- D4 I- c; A8 R{O(a)*b(a),即上面所述的A(a)结果发生8 ~* c7 ?9 U8 Q6 M
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6 v2 y. M$ W! A! {& V* G
那么投注主客的期望回报总数分别为# h" v! X. L0 |$ |
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]8 O ^0 R$ c# ~& N* r
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
3 ]& ~. }0 e( C$ m, G& 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- }8 N4 C( I5 J- P+ Y
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
" |$ h5 H* J! b) y8 kP(d)+p(h)O(h)=1
4 ~# ?4 c9 g! R3 B. W& c! LO(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式. Z, y/ W+ o7 R: }4 \7 } M
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)8 A3 Z! K- J E C' x {
P(d)+p(a)O(a)=1
# y0 j$ ]; `2 M- W0 @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
$ g2 i1 Q. f( q; @' J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 S N; U5 U* l- @+ e8 R0 g* N3 k6 s
三、半球盘的计算描述
# Z' e" l w# S接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)2 E2 s5 A: j* y, n( N% |
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:
+ G6 z6 O7 `# u* m{O(h)*b(h),即上面所述的A(d)结果发生: I( V" ~6 U9 V0 T* c
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
# w7 `; N* y6 S. C' C1 j: o! H* j& s{0 , 即上面所述的A(a)结果发生9 n3 B2 B! j( T' H" E; J! c' q9 V: j
以及 L" Y1 M s2 C" U$ D
{0 , 即上面所述的A(d)结果发生
! E% U3 ^8 R) QR(2)={0, 即上面所述的A(h)结果发生0 D6 F# J8 \% g# b$ T L; l: j
{O(a)*b(a),即上面所述的A(a)结果发生0 |; f- g) ^8 B6 n: I8 V5 b
如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率1 T0 K7 p6 n" M' B" D- P b0 t
投注主客的期望回报总数分别为) V A# l+ n7 F+ u! A
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]0 o8 Y/ l- h* U5 X; n, X4 f
E[R(2)]=P(a)*O(a)*b(a)/ N# v( k" }4 Q2 D6 o
假设实际投注回报与期望投注回报相等7 B+ G+ m: X. o- t6 a! M
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)" E: s M8 R4 Y5 J# q: r6 x. u
O(h)*[P(d)+p(h)]=1) i9 Q9 a7 O. Q; q4 X0 b& Q
O(h)=1/[P(d)+p(h)]
; B$ n" g3 d$ F8 t: I0 GE[R(2)]=P(a)*O(a)*b(a)=b(a)0 q8 L! `" Q. i) A* X
P(a)*O(a)=1 G' K, q- J2 x
O(a)=1/P(a)& B6 j8 {5 |2 \' ~
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率
+ Q6 ^4 d4 Z& a% X+ |O(h)=1/p(h)
3 ]4 N5 }. f6 V1 w3 ?/ |O(a)=1/[P(d)+p(a)]
( B8 Y. G' L' L8 p3 I/ N5 e- F/ R+ E四、平半球盘的计算描述
- t* L4 {1 Y" y) i2 n8 W, j" c9 m这个稍复杂一点% V# e7 p# g7 Q) R$ K
接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)7 T( m* W& g6 Q5 }
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:
, }8 M$ q$ S& [1 ^7 C: L{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生& S9 F" z6 a4 W0 K0 P# l+ t& ^
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生# J8 m1 d6 I) Z6 K' W9 D0 P5 f/ f
{0, 即上面所述的A(a)结果发生) y) o2 C$ w5 G
以及1 D. m; x0 d/ E/ ^. v
{1/2×b(a) , 即上面所述的A(d)结果发生
; B3 ]& y2 w+ \4 t3 x0 j. I( m0 DR(2)={0, 即上面所述的A(h)结果发生/ s2 p# V2 W5 k. K* M
{O(a)*b(a), 即上面所述的A(a)结果发生4 }! f& A7 A$ B* B7 J/ n
投注主客的期望回报总数分别为
, A7 Q) S/ A1 }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)): g! w4 g9 d, v- ^
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)]$ }% @1 x9 ?0 m+ x- R' G5 H
和上面计算过程相似,得出:
. ]& p; H' n* l, ], f- }E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
$ A1 E9 \6 b; ]" Y4 kP(d)×{[O(h)+1]/2}+P(h)×O(h)=1
9 _+ H- E+ @ fO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
2 i- E( w/ G& L/ N0 O. `" [- U% D8 GO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h)): H3 b3 g& W2 a) n$ E6 b# i
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)8 y8 ]' e' m. _
1/2×P(d)+P(a)*O(a)=1
6 n C! ]- P* {% ^; P% G2 fO(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
5 S2 K. B2 o9 ~9 x同样主队让平半就分别是
( E5 i+ T9 H4 D& p- b. eO(h)=(1-P(d)/2)/P(h)
7 [- O( n8 n) X8 WO(a)=(1-P(d)/2)/(P(d)/2+P(a))
% b) }. S! A o* _4 @0 I9 p+ i! ^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)
- d& [' E. _% z( M9 E' n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
, F/ d9 ~$ R/ a2 i& dB(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
0 y T1 ?, ^" Y1 w4 X% BB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}; k; V. p0 [5 v6 P: l& c( _
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 ]5 x; b/ x2 G v) _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:
5 U9 L R& l7 d M6 H{b(h)*O(h) , 即上面所述的B(d)结果发生
& F7 A- h7 {6 o# I; a6 ~! wR(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
C. q5 ]4 c4 t- c3 E{0 , 即上面所述的B(a)结果发生2 S+ m# x5 Z7 P! O1 @
以及1 j7 z0 ]% d6 `+ n+ g5 D0 p
{b(a) , 即上面所述的B(d)结果发生
4 B5 A" k% Z& t3 c1 |" q# l7 AR(2)={0, 即上面所述的B(h)结果发生7 |+ q+ h; x# a- [# e+ e$ B! ^/ e" i
{O(a)*b(a),即上面所述的B(a)结果发生+ i" C: m8 n8 n! A8 D
投注主客的期望回报总数分别为# v+ L" Q0 d) l
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)]
/ p% v2 h9 `$ H( OE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a)), I% k% ?# k* h6 {5 Q, a! u5 M. U+ T
假设实际投注回报与期望投注回报相等
0 w& P# L1 p5 g, {! w4 A$ p oE[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)/ A U2 |; p" `; s; U% E$ L
P(h)*O(h)+P(h1)-P(h1)*O(h)=1
: N+ e3 c9 q$ Y2 y8 R) B/ v1 pO(h)*(P(h)-P(h1))=1-P(h1)
# B$ T# O" Y, C% rO(h)=(1-P(h1))/(P(h)-P(h1))% D) x' ~% A. H" S9 @" i! B2 A
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
% j% y2 c% ^0 C0 f' zP(h1)+O(a)-P(h)*O(a)=1; m, K% V% [! {) t2 g0 u
O(a)*(1-P(h))=1-P(h1)
% K0 p. f) D$ ]% m/ G& t4 [, AO(a)=(1-P(h1))/(1-P(h))
1 w4 C5 a' [, n& ^! ~7 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。- m& G9 n: 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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