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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。
9 I& X; `& v& e1 T+ \那么,平局、主胜、客胜就有以下表达式:3 u/ S/ U3 D5 V# l
A(d) = {W(ij)|i=j, i∈N, j∈N}
& b& o2 ~3 u: P- |' Q8 CA(h) = {W(ij)|i>j, i∈N, j∈N}
2 M  x. ^7 j. MA(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]:* e" Y  y# {( O, G. {3 ^) G9 I8 D
P(i)=P(Ai), i∈{0, 1, 2}
* D- Q1 M3 Z' p2 J( R- s" s( 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). G7 {+ ]% @5 m4 z5 ^; h) D
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:
) }3 J3 E% `1 \, Y  d" L4 ]( X, m$ K{b(h) , 即上面所述的A(d)结果发生  V: j+ a1 x7 I$ i6 ]0 C$ ]* G
R(1)={O(h)*b(h),即上面所述的A(h)结果发生3 n& M. g0 @5 M+ Q
{0 , 即上面所述的A(a)结果发生
1 W8 r/ Z0 w. R8 B& |! E6 V以及1 _; v" J9 s- B8 M* T5 C
{b(a) , 即上面所述的A(d)结果发生# R2 X7 ?3 \& o
R(2)={0, 即上面所述的A(h)结果发生1 H5 x6 R( b, l6 _6 I* I" S+ t
{O(a)*b(a),即上面所述的A(a)结果发生2 f' I% N) l5 x8 P! P
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" H0 |. r5 p: [6 `$ X. U* f
那么投注主客的期望回报总数分别为
* c4 g& c2 z% N5 L6 HE[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]( v5 c0 f, r6 Z% B0 j4 j) g5 ?! O
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]8 K" W1 [3 L7 R* _, A6 l
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1 ]* B% M( _; d4 N; K. R2 ~
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)! U5 v, l! p8 i/ w
P(d)+p(h)O(h)=1
! k( c1 G/ z  H* ?* _/ FO(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式7 ?+ c, n$ A% n, Y) X
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)) ]4 @/ [8 z+ }9 N
P(d)+p(a)O(a)=1. J; ?# Q7 w& D& Z1 M: {: K
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; f( ]$ y0 @" A) N3 o" v8 p9 t+ |0 y
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' p3 K: ]4 B  E) f3 T4 }
三、半球盘的计算描述. m/ h5 p/ x" T9 v9 S) X. \
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)' |" W8 h% \2 |3 i0 P
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:' g+ a! r* ]* x
{O(h)*b(h),即上面所述的A(d)结果发生
4 ~4 d! u5 V. t* f7 |5 A* QR(1)={O(h)*b(h),即上面所述的A(h)结果发生
3 c4 O& w* M3 H6 B7 n$ z6 X* Z{0 , 即上面所述的A(a)结果发生
' e: u5 b6 C% Q7 [' D以及" B. R. p& B9 P# M( [
{0 , 即上面所述的A(d)结果发生
6 y2 [% r' ~/ y2 F; vR(2)={0, 即上面所述的A(h)结果发生9 G" M/ W  @8 x$ y
{O(a)*b(a),即上面所述的A(a)结果发生
* f1 p4 m" H! r, j5 S& o如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
3 r) }! `- |8 v" G, e- L, z投注主客的期望回报总数分别为
5 Q# O; o! D3 A4 [! H" ?E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]
1 A6 u0 e% r# ?/ m. o8 L$ |4 l, [E[R(2)]=P(a)*O(a)*b(a)9 ]2 v  _5 E9 f
假设实际投注回报与期望投注回报相等- o1 o$ t& @/ T4 F  M* f
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)! ?4 k9 j% F2 K
O(h)*[P(d)+p(h)]=1
5 u& [) S9 F* Z# J! F1 _O(h)=1/[P(d)+p(h)]
- k& S5 Z1 K$ M+ j- sE[R(2)]=P(a)*O(a)*b(a)=b(a)
' \- m- Q- e3 ~6 v1 M% e. WP(a)*O(a)=14 z' Z" m* r! [* {- c2 T! r5 }8 z
O(a)=1/P(a)1 r7 N- N, O" ~0 P2 X) _
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率
4 S1 O) o9 Y3 t! bO(h)=1/p(h)
1 \; Z4 e, v# x+ o$ A2 E# t- LO(a)=1/[P(d)+p(a)]
. H* F+ O' A2 ^四、平半球盘的计算描述
. P( M' h, q( \: ?7 }这个稍复杂一点
; ]4 j) T! s3 l! B6 j接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)4 A" e8 z' h2 |7 x/ 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计算:
* ]3 j( L) k2 D3 g# N{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
. c# ~+ u$ \( F  k, m* cR(1)={O(h)*b(h), 即上面所述的A(h)结果发生
! U2 E* ?# F' `4 n  B' i  ~{0, 即上面所述的A(a)结果发生
" T' [/ O4 C# x+ z, W* E/ T以及
/ o! W% m! X! x! N{1/2×b(a) , 即上面所述的A(d)结果发生
. S3 \: B  }6 f  U5 H2 t8 NR(2)={0, 即上面所述的A(h)结果发生9 @9 W0 [% B! s) e* K" f3 G
{O(a)*b(a), 即上面所述的A(a)结果发生
: O  Q$ q9 M% l  [% E投注主客的期望回报总数分别为
- L- g0 Q' ~3 f3 M+ h8 kE[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))3 I. z! k# G( J0 u1 N
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)]
# H( v+ |# H8 R: N7 L' }8 G和上面计算过程相似,得出:
/ |6 G) {9 ?9 `E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)' u& ~/ ^$ n3 B1 e
P(d)×{[O(h)+1]/2}+P(h)×O(h)=1
$ z1 Z# m, w6 Z# S  i; OO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1+ K* e( ^9 s9 g
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))5 ~- t* M, p# F
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
+ i1 C: v: I8 Y) z8 o1/2×P(d)+P(a)*O(a)=1
# Q% t& r7 v* hO(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)3 I. g) s4 l; ?/ E" x
同样主队让平半就分别是0 @7 ]- x& y) C- u9 _) T+ ]8 F& \
O(h)=(1-P(d)/2)/P(h)
% `* r+ C2 f3 b2 |O(a)=(1-P(d)/2)/(P(d)/2+P(a))
0 E& y+ S8 K( d: J% q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)9 b6 k8 B7 p0 j( ^$ Q+ a. X8 \
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4 y+ `+ t: |3 E) J4 u. x
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
) B7 |4 v( Y1 \$ bB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
8 f2 Z" c! A5 u* F2 \% T1 T4 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 |5 J' a, e
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:
0 }1 b: w0 ^) S9 O  v) a2 A{b(h)*O(h) , 即上面所述的B(d)结果发生+ B2 V7 k/ c1 s$ x2 L! r  b! h  t  s: \
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
* N/ R1 }7 ?* M' M{0 , 即上面所述的B(a)结果发生
$ S% R; a. V: t0 _% h  w3 k以及. j# x) \5 n" T
{b(a) , 即上面所述的B(d)结果发生% Q  j" T+ G2 W: j
R(2)={0, 即上面所述的B(h)结果发生3 ], U" M) \$ [4 o7 f- G1 g3 X% |
{O(a)*b(a),即上面所述的B(a)结果发生* {4 M+ C" y. w9 _" f: E
投注主客的期望回报总数分别为
  r# P. l7 n( M+ 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)]( `. t$ D5 S" R+ |8 x0 y
E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
) j. c8 o( J$ Y0 h! P. Y" v& X假设实际投注回报与期望投注回报相等
  g& a1 B2 X* S9 R' W1 r& pE[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
* E" a, N5 `+ Q2 T) o4 S' XP(h)*O(h)+P(h1)-P(h1)*O(h)=1
( R# g! b' D5 I4 }; P" iO(h)*(P(h)-P(h1))=1-P(h1)
: G! g9 U0 z& k( D1 yO(h)=(1-P(h1))/(P(h)-P(h1))
8 s" H' y4 k, ?4 x; V* D* aE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
  c# q/ U; ^3 E0 lP(h1)+O(a)-P(h)*O(a)=1$ ~9 Q7 a% _, t" D1 }0 V$ I: v$ c
O(a)*(1-P(h))=1-P(h1)) x% d( [) A  p$ {' r
O(a)=(1-P(h1))/(1-P(h)), J4 [) g  s- s! q
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。* r  K- @. h9 J& g' K, H
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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