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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。. b ?7 x6 e$ C* F s. I
那么,平局、主胜、客胜就有以下表达式:
5 u5 h2 f6 b4 S* F4 GA(d) = {W(ij)|i=j, i∈N, j∈N}
+ h( j) g& _1 }2 {' ]A(h) = {W(ij)|i>j, i∈N, j∈N}2 N$ t& z M8 T; o/ N
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]:
( \$ r1 B' `% C* t/ v pP(i)=P(Ai), i∈{0, 1, 2}
7 b1 T: i" o0 I) X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)
5 j$ z3 ^7 }/ D a) e x$ `: \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:
( O( W. q9 Y1 i5 A2 a: m{b(h) , 即上面所述的A(d)结果发生5 ~0 e7 }2 x2 H. H) M6 N% t0 [
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
, K3 X- s' M% Q{0 , 即上面所述的A(a)结果发生
; h+ Q4 f* C% `以及: h+ V6 Y2 O' J- ]# K$ |, M9 ^# C# t
{b(a) , 即上面所述的A(d)结果发生/ I* p# n1 G C1 Q6 }- S* o
R(2)={0, 即上面所述的A(h)结果发生
* ~. k5 o5 C6 K Y2 }8 H{O(a)*b(a),即上面所述的A(a)结果发生0 q6 ]- {& L) c" z0 p0 i9 z* 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" y9 k2 Q- d. g$ k
那么投注主客的期望回报总数分别为
" R& }* }5 p' CE[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]4 H* \2 u3 E1 F+ b
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
, n" ^( ^" ^, C' I6 J3 C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! B* j, \. u% t" r
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
* z' x0 f8 _9 k! S' {8 ~0 uP(d)+p(h)O(h)=1
$ @/ \+ N6 e% X4 yO(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式
/ I" m0 p* v/ s, _2 i5 Z3 FE[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a) n$ y; T4 F( `% G# [
P(d)+p(a)O(a)=10 v t) W: f* |, u2 n
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; z$ M- [3 a5 A0 t# N0 | A
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
. P0 d( f" |" ^; A; }7 U9 k4 I三、半球盘的计算描述
V: J0 k+ L. k7 [! a% G接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
8 ^- d8 ^: V, [2 S9 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:2 N# |9 n4 u# x5 `! I8 |
{O(h)*b(h),即上面所述的A(d)结果发生
# Q* ]. ~, O2 o. ?0 [+ t+ M* fR(1)={O(h)*b(h),即上面所述的A(h)结果发生
* s* d$ ]5 R+ x{0 , 即上面所述的A(a)结果发生
1 F, u# ~1 b4 r: ?1 A7 ~( ?' m以及
1 J* v* o% v! I/ e{0 , 即上面所述的A(d)结果发生
) w* [, R+ q4 [8 ]% X1 GR(2)={0, 即上面所述的A(h)结果发生
0 J V$ | Z" b5 w3 j( V- Q{O(a)*b(a),即上面所述的A(a)结果发生
+ L0 l! [! o& A$ R) d如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
: [2 V$ H" q! a投注主客的期望回报总数分别为% }( n3 x0 ~. q- y
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]
$ j) Q; O3 @' ]E[R(2)]=P(a)*O(a)*b(a)6 l) i+ T7 G' E6 ~
假设实际投注回报与期望投注回报相等7 S3 K7 W( t" O( l, v
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
7 A0 k( v( _, ?O(h)*[P(d)+p(h)]=1' o9 j) c) B% c
O(h)=1/[P(d)+p(h)]1 ^2 Q! ^1 J: ~! t: ^+ z
E[R(2)]=P(a)*O(a)*b(a)=b(a)% z, ?5 L- s4 s7 j7 q: v8 f
P(a)*O(a)=1
, C4 Q8 x/ D8 H6 ^9 lO(a)=1/P(a)
" X" F6 U/ R' T, C7 H! t) l同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率3 a2 y. q0 \4 t
O(h)=1/p(h)+ N4 d4 B$ e( t4 k) T) o' E
O(a)=1/[P(d)+p(a)]7 ~/ R8 e" h1 m
四、平半球盘的计算描述5 ^, U b% v# E/ f) [
这个稍复杂一点7 _7 z: N8 y: d- ?0 i+ @- u
接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)$ H- @, L: u+ D7 j; w! {
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:! i/ \: r9 f( g" }$ j4 `( A
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生4 H2 V6 @; S3 V: d8 `% @/ f
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生( g4 A1 U# I: @1 S4 K
{0, 即上面所述的A(a)结果发生# ~* ] H" m t# c% C: D+ o7 h0 I: Z
以及1 i9 I. ~& r. p2 c/ M' N( f
{1/2×b(a) , 即上面所述的A(d)结果发生: t, _( ~* ~9 {8 t6 F. h: {: C
R(2)={0, 即上面所述的A(h)结果发生
2 P6 M: z# I/ {! K/ I! r{O(a)*b(a), 即上面所述的A(a)结果发生
0 N b- h! U9 e6 q% u, t投注主客的期望回报总数分别为2 g4 \ q1 m) {! b* `9 Z
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))6 V' w" F, l8 A+ J
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)]
7 f: A# t" g7 o* K# [6 j和上面计算过程相似,得出:
@5 R5 ?; p$ z: P4 ME[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)- ~9 ~3 s/ J, e9 c* W
P(d)×{[O(h)+1]/2}+P(h)×O(h)=1
6 m' K% s) J; gO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
" `5 @+ Z0 |" Y; V. B, Q4 ]O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
1 G q; ~% w: xE[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
7 Y3 [# T! R7 x# o1/2×P(d)+P(a)*O(a)=12 B8 j, w. U/ e3 s
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
' R: m# x' {, Q I P/ Q+ y5 k同样主队让平半就分别是
0 J s4 ~& x$ `( o! lO(h)=(1-P(d)/2)/P(h)
( V! C y2 @ z. w) n" nO(a)=(1-P(d)/2)/(P(d)/2+P(a))
8 o$ y: P" u; q% C& n 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)( w' S2 m1 x8 O. y) R$ M6 T& @
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, k- }# M8 p* |! I
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}0 r, w# i' c# m3 T+ `
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
1 e8 h" f# z1 t, |: eB(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数 d2 }) u6 \ 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:
, O7 ]8 W% |. R1 @5 ]9 i- ]( u. X" H{b(h)*O(h) , 即上面所述的B(d)结果发生0 M% Q* ]; X P- l6 k) M/ T9 u
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生( R8 [, a( r8 W* m7 P4 q
{0 , 即上面所述的B(a)结果发生6 j2 K2 R3 y: W3 Q# T# q
以及
: S3 V* ]% b4 ~5 B o{b(a) , 即上面所述的B(d)结果发生
! u' ?# Q, N8 r, Z3 [& WR(2)={0, 即上面所述的B(h)结果发生
5 X$ ?- R4 V: e! ?/ e! |{O(a)*b(a),即上面所述的B(a)结果发生" u( P$ I; X( u8 B
投注主客的期望回报总数分别为, o8 O( L5 u4 f. A
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)]
4 b. r' q. {2 r3 P, h. X9 |E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
; T4 i$ H& A! K" r. H3 g5 p假设实际投注回报与期望投注回报相等$ D$ f+ S& A& ~7 J, z3 X. x; M" U
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
; X: k9 a- N9 L! |& o" O, {5 bP(h)*O(h)+P(h1)-P(h1)*O(h)=1: e7 Y2 U, G- J, F
O(h)*(P(h)-P(h1))=1-P(h1)7 K2 E' s3 U/ z( Z$ i0 Q' A) a
O(h)=(1-P(h1))/(P(h)-P(h1))
# y5 e1 ~! M/ h9 ^; t& M4 \! WE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)9 h# ?, y# x- O& d/ q4 ]( [
P(h1)+O(a)-P(h)*O(a)=12 ]7 ~, X" _5 K: u5 P( v9 R1 _/ c
O(a)*(1-P(h))=1-P(h1)
& o. @; j8 R$ c1 M( [$ BO(a)=(1-P(h1))/(1-P(h))
: a4 H6 {' _! W3 h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。; G$ T4 a8 }8 D# e
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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