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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。# e6 ]" L6 F( r+ L, E+ ?% H0 L
那么,平局、主胜、客胜就有以下表达式:
% i) y# X, R' S9 DA(d) = {W(ij)|i=j, i∈N, j∈N}2 ]2 @! P6 G7 R+ y0 [! h
A(h) = {W(ij)|i>j, i∈N, j∈N}- c9 P  F' s* z5 E
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]:
  D2 M" ^( N$ `8 \. |! CP(i)=P(Ai), i∈{0, 1, 2}
0 w9 @/ E: q, y7 z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)
) Y5 o, N/ ^$ e9 D* w  t3 k4 ]6 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:$ V! d$ ]) |1 B
{b(h) , 即上面所述的A(d)结果发生, [( n* w( }8 X3 I
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
0 A3 [* c0 Q: q3 p' ~- g( F{0 , 即上面所述的A(a)结果发生1 J3 ^7 t) ?. y+ ~2 t. w2 L' G# N
以及/ a5 Z7 B* _* [6 X
{b(a) , 即上面所述的A(d)结果发生' m! z  U& ?" g5 ^& Y/ ~" F* o
R(2)={0, 即上面所述的A(h)结果发生9 a0 f, _4 g* P9 G  j) P( q
{O(a)*b(a),即上面所述的A(a)结果发生
1 q9 z  [0 j# n$ n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
1 J7 x2 w9 |  ^那么投注主客的期望回报总数分别为; v: v" [: c6 }- h5 K3 d/ {
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]) t2 g3 G2 w' a) E$ }
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]' \' g- F: s$ o$ R# {+ @
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. [" s6 i2 d, \/ U# {& t
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)8 p& S6 p7 K9 O, A
P(d)+p(h)O(h)=1
; d0 `  M1 S- r/ M* \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& D( d5 j* @  I! y9 _; l# c, T6 _& P0 K
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)6 V' @* o0 S2 s5 f7 }
P(d)+p(a)O(a)=16 x1 b  D, f- ]& j. ^, J3 H4 V* {4 t  m
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
8 A( ~$ I! l! k( [# Y" g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; W% y4 W! P; m  O2 C3 h
三、半球盘的计算描述. D7 r+ }! k; q8 H6 ]% c
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
, w0 W7 [; H* Y% _* G5 X9 f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:9 v: _( i# X" H. n+ W& Y0 R! A
{O(h)*b(h),即上面所述的A(d)结果发生7 ?5 w6 f1 M, x. _$ k. s
R(1)={O(h)*b(h),即上面所述的A(h)结果发生0 w$ u2 R/ Y  i  o% i& C6 S
{0 , 即上面所述的A(a)结果发生8 w) J; F  X# r; Q6 s& H- K
以及! ?! Q, q$ N  E
{0 , 即上面所述的A(d)结果发生' ^; v2 N! m) E  B
R(2)={0, 即上面所述的A(h)结果发生9 P! [" L5 j4 |& S1 ~! H  _
{O(a)*b(a),即上面所述的A(a)结果发生/ g( G* [4 K5 v; p7 ~$ 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
! ~/ Y1 f) x9 l/ a投注主客的期望回报总数分别为5 Z9 W6 D$ U- S' `7 F
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]1 L; a6 L. H6 c# Z/ L" I5 Y+ J; O
E[R(2)]=P(a)*O(a)*b(a)( l. [. O. a1 p/ h1 J1 b
假设实际投注回报与期望投注回报相等
! {8 `$ H* d1 [9 XE[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
7 v. l. U" d' j- |- {: t( f/ N5 \O(h)*[P(d)+p(h)]=15 t" A* u/ b5 r! p) n
O(h)=1/[P(d)+p(h)]
8 h# ~) {3 S" U" w* x$ Q4 q5 P$ N3 pE[R(2)]=P(a)*O(a)*b(a)=b(a)
( o, j0 A$ m& u( v5 |P(a)*O(a)=1% b4 }. W5 J2 X- D5 N5 t6 Z+ H
O(a)=1/P(a)9 Q: x- }1 _9 A2 g" z7 c0 M0 u
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率
: \' e' {* _. M3 AO(h)=1/p(h)1 K$ _6 P% w9 ?# C9 l
O(a)=1/[P(d)+p(a)]9 ^7 k# S" t! ^5 m5 C. T* l
四、平半球盘的计算描述+ Q- f( P& M! U. `( W. Q4 ^
这个稍复杂一点1 V/ g$ \9 d1 }: W. t
接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
3 r* b( A3 Y0 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计算:
4 e3 v* p, t% R/ y% i* E; q{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
, ?' W' x3 ]; F* CR(1)={O(h)*b(h), 即上面所述的A(h)结果发生
/ y  Z$ m% a$ V. `+ e: _{0, 即上面所述的A(a)结果发生
! A, T* v5 p1 F8 u0 _以及3 `. L5 i% u+ [5 j% @  V
{1/2×b(a) , 即上面所述的A(d)结果发生
4 k- u  E1 n3 O2 X- u/ ?- I: J0 LR(2)={0, 即上面所述的A(h)结果发生- x0 x2 a8 a6 l
{O(a)*b(a), 即上面所述的A(a)结果发生
5 V8 [* z% r, }投注主客的期望回报总数分别为
3 G: r; q+ F" J: H  \0 _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; J/ u9 n, n5 ]4 Z1 {2 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)]$ R  j+ @1 l! q! B$ L! O
和上面计算过程相似,得出:
0 D9 x: E" t; ^( jE[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
! R) Y+ Y& g# V# L0 H2 Z- p5 UP(d)×{[O(h)+1]/2}+P(h)×O(h)=1
1 Z( G3 H) z4 V/ x! VO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
7 ~  M2 @0 V8 d$ G+ xO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
# X5 n! v$ S9 O) PE[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
4 {' n) U5 R2 f0 J1 C  {1/2×P(d)+P(a)*O(a)=1& U  h5 @( U0 ^  q) d
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
  O- k" i% f# V8 x" C. v( y同样主队让平半就分别是
1 d  @8 v% h% N3 T  lO(h)=(1-P(d)/2)/P(h)  j3 i) `2 ?0 _, k; h
O(a)=(1-P(d)/2)/(P(d)/2+P(a)); I- a  \, A6 m8 S9 ]5 A( ]
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)$ L  r3 ]( t) h7 l/ `
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. H- t( F# ^' d; J' @' J; B
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}$ }8 v  [5 ]; {) ^5 J* h+ D
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
. C- X1 }9 i& v0 t- w; NB(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数5 ~7 l( S8 z5 o+ u
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:' v. E; k9 w  q; a+ V
{b(h)*O(h) , 即上面所述的B(d)结果发生' L0 ^* A. J8 c
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
3 X& `# Z, q0 `; o" r{0 , 即上面所述的B(a)结果发生
; m3 O/ ?- s3 z: X8 L以及
" }" l/ z3 ^4 K) O% [) d5 r{b(a) , 即上面所述的B(d)结果发生  [# h! i, R- @& q& f
R(2)={0, 即上面所述的B(h)结果发生6 \4 U0 U+ G& _, c8 Y  X+ H# g
{O(a)*b(a),即上面所述的B(a)结果发生
  e8 c) ]% c! v$ u' ?8 s" S投注主客的期望回报总数分别为2 o8 ?+ z4 B9 c  P" M8 t
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)]
/ \. |% d  `) n& D3 d  |E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
9 L; R( _9 o1 Q0 E假设实际投注回报与期望投注回报相等
+ J0 e( g7 m7 k5 S& QE[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
7 G* Q+ d8 }& y5 A5 ]. O/ d6 UP(h)*O(h)+P(h1)-P(h1)*O(h)=1$ d( L" q8 [2 w1 d
O(h)*(P(h)-P(h1))=1-P(h1)
) ~  J% B8 |; Q5 D! |6 y6 F  HO(h)=(1-P(h1))/(P(h)-P(h1))
4 S6 o1 s) p8 p% |  l( aE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
, x" u6 h$ a( {6 H5 lP(h1)+O(a)-P(h)*O(a)=1. H. b: _; i0 T
O(a)*(1-P(h))=1-P(h1)3 ?  c! I$ T3 d: f# t
O(a)=(1-P(h1))/(1-P(h))9 F, U4 F$ U, D* V5 o- @7 o8 f
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。
. Y: H7 A/ e7 R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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: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:
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