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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。
0 d+ A% r( Y8 s6 \% y5 z- o. N: Q9 g那么,平局、主胜、客胜就有以下表达式:) }" y4 S6 D9 F3 K. @7 i# j
A(d) = {W(ij)|i=j, i∈N, j∈N}! X( R8 C, e' a9 f
A(h) = {W(ij)|i>j, i∈N, j∈N}; h6 i6 g  E7 ?4 c' P
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]:9 \' d; b& |0 P5 j  _# ^
P(i)=P(Ai), i∈{0, 1, 2}5 c4 z2 q/ h+ T: r, C
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)) `; j* Y" L' r3 q7 Z3 I
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 b9 X; I* x, a; S{b(h) , 即上面所述的A(d)结果发生& W) j) d& N. X" F
R(1)={O(h)*b(h),即上面所述的A(h)结果发生6 P+ R& \& j* A# t. J2 F1 a
{0 , 即上面所述的A(a)结果发生# _9 c: x9 E) w3 r5 V
以及6 S9 v0 Y. y) |# Y+ @+ u: O
{b(a) , 即上面所述的A(d)结果发生
: y4 n% V! |1 k5 ~& d" S. e8 Z" `R(2)={0, 即上面所述的A(h)结果发生
* z% k1 E9 \1 E$ P{O(a)*b(a),即上面所述的A(a)结果发生$ S5 P% u7 A# R
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
$ ]+ n6 s" r8 K. [那么投注主客的期望回报总数分别为
5 N6 H( b8 W- Y, IE[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]) B+ w, D6 Q+ \% Q/ w6 B9 X
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]$ ?3 Z, W6 N& g7 x2 z
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
7 s" e0 @. ~9 `/ S" xE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
+ i" H! |- t% O- VP(d)+p(h)O(h)=1
% ?5 {% \  Q3 g0 {# w* X( ~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/ L, }/ ?4 r" B) G
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
7 B( l& u7 L% I- F: B* Q6 LP(d)+p(a)O(a)=14 a/ J9 _* ~. g" C$ 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% R$ x1 @( r, `! Q
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) z$ v4 K4 o7 \2 Y1 h. Q9 k
三、半球盘的计算描述; O- v3 B) @1 W; X, H1 s: i6 ^
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
6 k- U$ w+ c- _) R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:
6 F! M2 A9 Q$ d" h( `% f4 h3 @5 e{O(h)*b(h),即上面所述的A(d)结果发生8 p' t1 W; A7 @8 N0 y+ G
R(1)={O(h)*b(h),即上面所述的A(h)结果发生$ T# u& V% F6 d+ c2 L) o1 Q& t
{0 , 即上面所述的A(a)结果发生. v9 d* N0 q3 l) Y' c
以及; _7 L( e, G& M# t
{0 , 即上面所述的A(d)结果发生
, ]; z: Q% b" d. C- H$ F" QR(2)={0, 即上面所述的A(h)结果发生
  j" |# p% A% G9 [7 j) b{O(a)*b(a),即上面所述的A(a)结果发生
4 I6 C9 P0 A5 Z如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
( ~$ j1 |/ k5 p) F& [投注主客的期望回报总数分别为
; P6 ~9 J0 M  c7 `E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]
% u8 _' [) u# n  [" KE[R(2)]=P(a)*O(a)*b(a)
' o: q8 s! J) S/ r0 q假设实际投注回报与期望投注回报相等" `. d# v1 V  v1 y
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
8 q; v5 u4 J: z1 y: e7 Q; j, i# C  \O(h)*[P(d)+p(h)]=1# C" P* Q4 f) @
O(h)=1/[P(d)+p(h)]- y9 j4 F: w; h
E[R(2)]=P(a)*O(a)*b(a)=b(a)
& B* K, f: N/ sP(a)*O(a)=1
) {" l" K' O3 ]1 e4 r" DO(a)=1/P(a)
- {  G. _. J0 X6 |7 }! W* P同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率; B0 O; v: l. ]5 Q8 O9 q
O(h)=1/p(h)
& E" Z. o5 n! NO(a)=1/[P(d)+p(a)]
) s; M5 Q2 T$ a% p4 R0 P( C四、平半球盘的计算描述
7 [4 F3 q# `4 n' n5 Y* g* [这个稍复杂一点
" N8 y$ f+ J7 V( C接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
( Q, N1 S! \7 L, V/ M3 F! Y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:
( p  \; r: l3 p' V7 `{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
; r+ U' B6 n( IR(1)={O(h)*b(h), 即上面所述的A(h)结果发生
1 _; Y( a' w  Y7 W{0, 即上面所述的A(a)结果发生3 \# R9 `' R2 K$ B4 @( o& v$ V
以及4 l) [" }' e' S/ Q0 ^
{1/2×b(a) , 即上面所述的A(d)结果发生
7 [! {! ^/ ]7 y% ^9 u$ w! WR(2)={0, 即上面所述的A(h)结果发生
+ s+ U/ I6 B. R' g3 H) p4 D! ?/ _2 Y{O(a)*b(a), 即上面所述的A(a)结果发生
2 v% \6 k5 v3 R- L5 Y投注主客的期望回报总数分别为
4 S3 ~: _8 G% s$ [# QE[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))
- I, T' u8 s9 }% \" `* ]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 k5 `9 ~, V) p. X和上面计算过程相似,得出:
! a. k) D- h) o1 _3 ?4 O1 v" NE[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
9 V" Y  N: f4 u$ m9 qP(d)×{[O(h)+1]/2}+P(h)×O(h)=1
7 S8 _: _1 }" N% b: rO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=14 r- J7 H# D8 v. ^% _4 G
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))# W9 ~! G! l/ p
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)- @+ {) B; j! m) x1 {$ g
1/2×P(d)+P(a)*O(a)=1
2 S3 r8 l- N. T, p5 J" |O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
6 o! ?3 {0 {" _同样主队让平半就分别是
$ O/ |& e- @% y: D! ?: y5 nO(h)=(1-P(d)/2)/P(h)
" u/ `+ ^' Y# J* n! |/ b6 S% iO(a)=(1-P(d)/2)/(P(d)/2+P(a))" ]; ^5 z1 A8 T
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): v, X1 t, x% z7 K0 L3 g5 W; @. p
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
! D* f4 [/ v% U1 H" VB(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
" M# C) s7 N+ c  B5 z( TB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
% |* A- V* P7 w2 W1 j3 v4 bB(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
  t4 X# J! ]. o7 r8 e& p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:
9 J4 t! {7 S3 E% H  G{b(h)*O(h) , 即上面所述的B(d)结果发生
  K( K5 H4 k! ER(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
& B5 K; i2 s  s8 O2 _- R{0 , 即上面所述的B(a)结果发生- T& V3 w, R6 [2 j1 f
以及4 m3 _2 F) ?) s! G6 l
{b(a) , 即上面所述的B(d)结果发生
- h  W' p$ \; ^R(2)={0, 即上面所述的B(h)结果发生
" S6 L) r, v( d; e# o- y$ w' w{O(a)*b(a),即上面所述的B(a)结果发生) p: D5 u, G- m" K* \
投注主客的期望回报总数分别为5 F( c# t( K0 _% T& j6 Y
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 |- C8 Z7 k# M0 j/ n2 D7 yE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
( \% d+ w. x4 j: w: X0 G假设实际投注回报与期望投注回报相等
, {& y. F6 Y5 u, x. |& ?8 @8 QE[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
9 _& [! L  U, w3 FP(h)*O(h)+P(h1)-P(h1)*O(h)=1
. \9 g: J% \! L% l8 X0 f3 RO(h)*(P(h)-P(h1))=1-P(h1)
. C% S' \: N, P, M( gO(h)=(1-P(h1))/(P(h)-P(h1))
% G" A" U) `1 K; Y; \% ?; rE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
; B# j3 b( L& RP(h1)+O(a)-P(h)*O(a)=1
9 H& Q& l9 w1 T, n1 i! oO(a)*(1-P(h))=1-P(h1)
$ i: @2 z- Z% k0 s% G( pO(a)=(1-P(h1))/(1-P(h))  Y, m; e+ Q( j6 }9 n' o+ V
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。
1 j( f/ X7 }! n5 E. _4 K  r4 o. 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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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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