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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。
5 V# I) y3 J( K- x* u那么,平局、主胜、客胜就有以下表达式:
5 Z: q. _0 K  W" m# b# Q/ `7 MA(d) = {W(ij)|i=j, i∈N, j∈N}
& z: |- m0 S9 @A(h) = {W(ij)|i>j, i∈N, j∈N}
" R( k7 f; j, Q( \' ?5 ^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]:0 ^) N; J/ B2 z5 j* [. X
P(i)=P(Ai), i∈{0, 1, 2}
' _$ r; {) d7 F: s2 k) W. |9 w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)9 k" N) k5 M4 }/ g# R( ^7 t
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 R' d# b& K" N5 r
{b(h) , 即上面所述的A(d)结果发生! U8 l8 m  B* z. x3 S' n4 Q3 q
R(1)={O(h)*b(h),即上面所述的A(h)结果发生8 [$ N- @. f! x" r
{0 , 即上面所述的A(a)结果发生7 X0 x; m8 d, f, S
以及, `- x% t( ^" n4 P+ E  u
{b(a) , 即上面所述的A(d)结果发生
' B; {9 f- G/ `% H/ [: E$ qR(2)={0, 即上面所述的A(h)结果发生3 K5 i; g8 [$ ~, \
{O(a)*b(a),即上面所述的A(a)结果发生
, s% Q0 U: F+ Q2 f5 k1 I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
7 a; _9 c- \1 G- K1 r* r那么投注主客的期望回报总数分别为' _/ q% d% e" }# `- p
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]
* o2 ~) W$ L  L$ }- b1 nE[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
+ U& b9 o5 T) v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
' j- m7 i6 V  x+ U! UE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)) d9 i  s) w& d; x
P(d)+p(h)O(h)=1
5 f: i# f) H, E! u1 o9 \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9 j) x: p5 ^& ]8 P' M
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
7 _4 h3 x4 G* a0 i+ `P(d)+p(a)O(a)=1
. x  N# Z% y. l- o. jO(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式
2 L1 i9 L8 N; o  c; ~9 B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& ~( h* {/ _$ t/ \3 J
三、半球盘的计算描述
- _! x  g/ h6 k, _6 E接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)9 u; U' s4 H( \7 d  u3 n6 v* ]
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:
$ G1 h! }+ V5 r) C, T% a1 `8 B% p{O(h)*b(h),即上面所述的A(d)结果发生4 }' o& \! `+ d, l, L! t
R(1)={O(h)*b(h),即上面所述的A(h)结果发生0 P& m+ G5 y( X2 _  P
{0 , 即上面所述的A(a)结果发生
7 p6 x4 v8 x: N& |4 m$ @以及
6 K- ^2 H, Z3 I8 p& j! i& T{0 , 即上面所述的A(d)结果发生
! j' Q/ t% c9 j3 {R(2)={0, 即上面所述的A(h)结果发生
, E) k  b% I! h4 D! S: I7 R{O(a)*b(a),即上面所述的A(a)结果发生
9 F; d1 g3 C: P4 S# P, e" ^! k如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率' w9 b5 S- K; E; ?
投注主客的期望回报总数分别为
" e- K' X1 E& e( xE[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]
8 L# e7 X/ C0 N) R, AE[R(2)]=P(a)*O(a)*b(a). y5 D. x- D; _% y  `; h
假设实际投注回报与期望投注回报相等
8 s0 `7 _; G7 I- KE[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
9 R0 Z6 N% D' i- P. I/ LO(h)*[P(d)+p(h)]=1
' q  Z3 d0 T+ `; j* ^. t4 HO(h)=1/[P(d)+p(h)]+ s' u0 h+ ]1 u; L
E[R(2)]=P(a)*O(a)*b(a)=b(a)$ U& b6 v  |( h  \& c3 z% F4 t9 x
P(a)*O(a)=1
3 K" L' j2 K3 m& v0 wO(a)=1/P(a)
7 `! Q' Q) z( T# U# X* e, U同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率( }4 D3 {! q# i: s- H" E
O(h)=1/p(h)4 P- t$ x8 A; x! K1 `' ]2 ]
O(a)=1/[P(d)+p(a)]
  W+ b, [5 p7 l  i四、平半球盘的计算描述- x8 t8 {; H2 s, F& u7 \
这个稍复杂一点
& ]; R; Y- D% U8 Y4 N5 P接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
- r, w& ]0 ?. E, B# R% n' Z( \$ s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:$ s6 |: S& K; K7 b( {
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生6 w( S1 w5 G  t% a6 ~
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生* b3 L* O4 A3 |8 Z
{0, 即上面所述的A(a)结果发生
6 n* X" E/ K8 I以及
7 a6 j1 X6 T- ?& f0 O{1/2×b(a) , 即上面所述的A(d)结果发生
* j1 [+ d* G; m. u  BR(2)={0, 即上面所述的A(h)结果发生
, h$ F! ?# H, o: h8 ?% f; u0 G{O(a)*b(a), 即上面所述的A(a)结果发生' d- E6 m& ]' D! k2 T
投注主客的期望回报总数分别为
" G8 e( F$ A  f* Y6 S: i" W8 r4 ^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 R' h" V% }& 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)]6 b; z8 X/ ^$ l! g0 d5 {$ @
和上面计算过程相似,得出:( ~8 a8 F8 y- E0 J8 p; K
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)" `: n7 p0 Z2 u0 t5 w
P(d)×{[O(h)+1]/2}+P(h)×O(h)=1/ L, X; x$ V  M* U, g/ [. \
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=13 T1 A6 P9 C1 ]
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
. J! K8 ~- c& [0 nE[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)2 x  S4 H: S0 R% S
1/2×P(d)+P(a)*O(a)=1
* G9 k5 _' T7 I, ]( Z7 k1 UO(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
5 Q- k* M* o) {8 x$ Z同样主队让平半就分别是
, @+ R+ c0 U8 _$ MO(h)=(1-P(d)/2)/P(h)( z8 E0 f' q5 x
O(a)=(1-P(d)/2)/(P(d)/2+P(a))$ ], y4 b' }4 n, b
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)
3 G3 g$ R* B# q# d, @1 b1 r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 S+ Y7 K4 H/ e2 o/ c. q4 V7 Z$ zB(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}5 t/ l" a- M2 L, O+ j, q8 ~
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}) M& s) B5 z3 ?
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
  {' A; \1 w- \8 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:
7 H  t$ V/ ]! L2 h0 I{b(h)*O(h) , 即上面所述的B(d)结果发生( {5 r# k. n. |2 d; e4 J5 `
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
- N  n4 \& V; ~{0 , 即上面所述的B(a)结果发生
0 }2 G: Y9 A1 T以及
1 _* _3 y; o3 ~: H! c{b(a) , 即上面所述的B(d)结果发生  T, f- O, ?  `3 }# }  ]- z
R(2)={0, 即上面所述的B(h)结果发生4 I; l! T" `9 N& _( b" i# T
{O(a)*b(a),即上面所述的B(a)结果发生
+ c3 Q/ z4 A5 n1 ~" _1 j投注主客的期望回报总数分别为
. w* ]6 M( U" `# m. 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)]
* @8 N1 B& h& e* X7 w5 NE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))5 m/ Q9 z% b. S6 p5 h* _
假设实际投注回报与期望投注回报相等  G9 _- h  y7 D
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
/ _# C" f! k  ~: A# A7 MP(h)*O(h)+P(h1)-P(h1)*O(h)=1- o' p6 q4 X+ _" W6 U' P1 r
O(h)*(P(h)-P(h1))=1-P(h1)3 D$ I0 b! k) |2 K0 y" z  G; c
O(h)=(1-P(h1))/(P(h)-P(h1))9 r2 X' P6 `7 m+ Q0 x
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a): P7 Q* f+ \0 p- L# E" Y4 _
P(h1)+O(a)-P(h)*O(a)=1
- o/ {6 T/ ?6 I; l7 wO(a)*(1-P(h))=1-P(h1)
+ W, ^, i2 G; h2 n7 C; @. jO(a)=(1-P(h1))/(1-P(h))# v. u( g- |2 v6 J
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。* ]( E% m; I$ u, v7 ~: L, L1 V
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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