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[体育菠菜心得方法] 亚洲让球盘的数学描述
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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。
2 f! j' O- k' Y那么,平局、主胜、客胜就有以下表达式:
8 F& g7 Y" T5 y1 LA(d) = {W(ij)|i=j, i∈N, j∈N}
' i& C1 }( J& QA(h) = {W(ij)|i>j, i∈N, j∈N}
# P# ^) y! \: n" [4 @. Z) v) w" `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]:
5 j2 L2 S( ^- E' eP(i)=P(Ai), i∈{0, 1, 2}+ [# a0 i3 J9 Z" t& h+ V; L* o
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)
7 F* t& O2 z- [" I9 U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:
' O8 v- u$ t, w! m- _0 Z! _( U{b(h) , 即上面所述的A(d)结果发生( J4 D$ K$ \- M( t# _0 p
R(1)={O(h)*b(h),即上面所述的A(h)结果发生. \& r% A$ Q! S! y, O! x
{0 , 即上面所述的A(a)结果发生
$ k- p5 H  k5 n" p* E, _% z以及0 g' ~4 b8 B# ~) m$ Y
{b(a) , 即上面所述的A(d)结果发生  I3 R6 P5 {+ w! c" t; e
R(2)={0, 即上面所述的A(h)结果发生
) j- _3 I+ |1 O1 A8 f; j& F: s{O(a)*b(a),即上面所述的A(a)结果发生% Y+ q3 f! b! ~) c
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
$ i6 z7 g. I8 \! R那么投注主客的期望回报总数分别为! G3 D3 A! d2 O) p; o
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]
3 l& }' j0 y; M8 H  W1 HE[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]$ n  x5 S, ^9 p, h, A2 H
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3 s4 X& Y" {: f  a- e
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)) @/ Y( ?2 L4 N! J
P(d)+p(h)O(h)=1! J$ z) @  R7 m0 g* 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
- X. ^% k4 L& @( Y3 f# i. w3 XE[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
) I8 q7 U0 J6 }! _P(d)+p(a)O(a)=1. I9 Q) p" d& P) V' }9 B4 `
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$ Y: l* b, M# }% o) Y. u
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
4 o' K; s+ p0 e7 D6 y三、半球盘的计算描述0 j# B% ?" a& L0 v
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)7 ?3 b+ T/ o6 T: Y8 h9 h2 O2 B
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:
# t/ T& U+ P3 c( D3 _3 D{O(h)*b(h),即上面所述的A(d)结果发生7 c9 P4 K& q+ n! H3 _2 m% P
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
, b' M3 e7 d/ k& r5 s{0 , 即上面所述的A(a)结果发生
4 P, z+ I$ |0 G- `  r8 k, \以及
$ D4 u2 V7 U) Q) n4 X0 w4 w{0 , 即上面所述的A(d)结果发生5 q& H1 M! {5 P/ W
R(2)={0, 即上面所述的A(h)结果发生9 n0 p* i* b8 }* B2 H
{O(a)*b(a),即上面所述的A(a)结果发生" _7 }- u5 `* _- M9 t
如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
( z9 i- ~5 ~* ]+ Q$ G6 [投注主客的期望回报总数分别为8 E6 z9 x& B7 {0 |6 B
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]
9 B( S' X% J1 }  |: E) TE[R(2)]=P(a)*O(a)*b(a)
$ a2 T" r2 U  ?" M, c% U假设实际投注回报与期望投注回报相等
' a. I# g& M, T; y% Q5 m# w4 Z+ LE[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h), f" p. H3 O. M. ?
O(h)*[P(d)+p(h)]=1& t: f3 P/ g7 ]2 u- i: Q* o5 O# |
O(h)=1/[P(d)+p(h)]' K2 H: q5 ~: j8 U# s! ~! ~
E[R(2)]=P(a)*O(a)*b(a)=b(a)
+ o% o* F  a7 G( {, W( H( XP(a)*O(a)=1. K/ C. W6 u9 X; F: X
O(a)=1/P(a)& n% }3 S+ [: c" M; J
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率; t+ [) I- y8 d
O(h)=1/p(h)9 `- [* L" e8 t6 r, M7 L+ t7 U
O(a)=1/[P(d)+p(a)]6 U: c; V$ e/ S" L$ I; s( W
四、平半球盘的计算描述
' b( H9 e% B/ I( w$ W7 |/ c这个稍复杂一点
* C0 P; A! Y( N' T5 P: n, N接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)2 Y/ g/ l6 W: S, u4 L, q5 H
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:# X9 U5 ~! g$ d5 q( s
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
* M8 H% ^8 n- ]& \+ ?# F5 ZR(1)={O(h)*b(h), 即上面所述的A(h)结果发生
- @, ]$ i1 D& H6 [+ x' t. _/ a{0, 即上面所述的A(a)结果发生
+ X: K  J& J+ [, t0 B7 P以及. C1 q3 F) q  e
{1/2×b(a) , 即上面所述的A(d)结果发生5 d; a$ @3 i8 E2 v
R(2)={0, 即上面所述的A(h)结果发生
4 N5 r* q! Q8 C{O(a)*b(a), 即上面所述的A(a)结果发生! r# |, k! I# I' }! U* }7 v
投注主客的期望回报总数分别为
# D2 C; [. _- J! D4 J+ F3 cE[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 G4 i1 T8 J3 e  n: c
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)]9 y9 R& t0 V8 X  g
和上面计算过程相似,得出:
3 }% N# ^& b6 o0 R) zE[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
  B+ d/ N. z: }# w1 x  H. dP(d)×{[O(h)+1]/2}+P(h)×O(h)=1
, d1 n. `; e- n: @! E# dO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1. \( l  q4 g& q+ ?8 ]5 J3 `
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))9 n5 l6 i/ _" U9 S: B, T9 v
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
' Q$ J$ m/ b/ U6 y5 L3 }1/2×P(d)+P(a)*O(a)=11 k6 \( {2 [' M+ _0 z( a
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)+ M4 |& ~# P# C' a% ^
同样主队让平半就分别是
  M" i# e9 J7 \" QO(h)=(1-P(d)/2)/P(h)
) Q! Z! {4 ], T4 C5 L. j  b$ [$ ]O(a)=(1-P(d)/2)/(P(d)/2+P(a))
% I% C! N  u: a" \8 x& o五、一球、两球等整数盘(这里先暂时说主队让1球的情况,0:1,Handicaps,其它可以类推的)
% `( m# i+ j+ z6 X) y0 a2 ?可以采用类似公式,在(一)中我们分别用A(d)、A(h)、A(a)描述平局、主胜、客胜事件的发生。现在改用另外的符号代替,如B(d)、B(h)、B(a),同时除了平、胜、负概率P(i)(i=d,h,a)外,还需要引入一个一个概率值P(hX)来代表主队赢一球(X=1)、二球(X=2)...的概率,下面来进行演算
! S& G4 i: q: L) ~6 M" t; KB(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
/ z+ M" U, B, R6 E/ q/ O% B, NB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}+ h0 ]& q1 F& h4 U3 h1 x
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
/ Q" n% v, x" c+ b, @接着,假设b(h)表示主队的投注总数,b(a)表示客队的投注总数,那么投注主客队的回报总数额为:8 I/ u: G6 V/ R: z; M$ m/ X# I
{b(h)*O(h) , 即上面所述的B(d)结果发生
' P/ R) b# Y) b+ P2 {! ZR(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生9 w3 }+ x& y# V# W  A/ I
{0 , 即上面所述的B(a)结果发生
0 f# w+ i9 K2 O# V. N' d! e# m3 i) {以及' _8 {7 }: u1 b' J2 e) @
{b(a) , 即上面所述的B(d)结果发生& h  h2 O* r" ]% H
R(2)={0, 即上面所述的B(h)结果发生
5 P. U5 i9 @  E0 q; H0 D{O(a)*b(a),即上面所述的B(a)结果发生5 ]' w' }3 O. f
投注主客的期望回报总数分别为, P$ s* [5 w' r
E[R(1)]=P(h)*b(h)*O(h)+P(h1)*(b(h)-O(h)*b(h))=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]
3 G+ q* a' d5 g2 W+ FE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))% w/ |( N$ S6 n7 F$ a! y
假设实际投注回报与期望投注回报相等% R% H( K. l: {' w7 n
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h). S6 x: {& J' T1 m8 G8 ?/ N
P(h)*O(h)+P(h1)-P(h1)*O(h)=1
" f/ X) C/ @1 w; VO(h)*(P(h)-P(h1))=1-P(h1)
6 i1 B7 {* y" kO(h)=(1-P(h1))/(P(h)-P(h1))
+ q7 ~4 ]- o4 \& V& b5 y* wE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
% p- v4 V* D/ }3 u; Z4 Z6 ^% a" x1 NP(h1)+O(a)-P(h)*O(a)=1+ h3 z0 U7 W& B) K% s8 V) i( k
O(a)*(1-P(h))=1-P(h1)# q/ b, g7 R0 ?
O(a)=(1-P(h1))/(1-P(h))
, \) `0 e. M" w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。
4 w- M- |4 d5 ?3 w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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2#
好象不是很明白
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在极端情况下,可以认为平手盘亚洲赔率
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太复杂,有没有简单易懂的??
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5#
主题回复处广告图案-天策传媒
好复杂啊!!!!!
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6#
谁看的懂啊。就是你们这些家伙把简单的事复杂化
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7#
谢谢楼主的分享
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8#
徐曹操曹操双方的首发参赛
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9#
新人来学习下,谢谢楼主。
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10#
楼主的经验不错啊
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这个·好复杂的
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12#
这个看起来真有点复杂。
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:) :( :D :'( :@ :o
:P :$ ;P :L :Q :lol
:loveliness: :funk: :curse: :dizzy: :shutup: :sleepy:
:hug: :victory: :time: :kiss: :handshake: :call:
:) :( :D :'( :@ :o
:P :$ ;P :L :Q :lol
:loveliness: :funk: :curse: :dizzy: :shutup: :sleepy:
:hug: :victory: :time: :kiss: :handshake: :call:
:hug: :victory:
:) :( :D :'( :@ :o
:P :$ ;P :L :Q :lol
:loveliness: :funk: :curse: :dizzy: :shutup: :sleepy:
:hug: :victory: :time: :kiss: :handshake: :call:
:hug: :victory: :time: :kiss: :handshake: :call:
:hug: :victory: :time: :kiss: :handshake: :call:
:hug: :victory: :time: :kiss: :handshake: :call:
:hug: :victory: :time: :kiss: :handshake: :call:
:hug: :victory: :time: :kiss: :handshake:
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