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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。3 W! [& p4 Q. t2 q; |! A5 y
那么,平局、主胜、客胜就有以下表达式:
' U4 p/ E  ^% p9 f6 TA(d) = {W(ij)|i=j, i∈N, j∈N}
- g9 }  E% O7 EA(h) = {W(ij)|i>j, i∈N, j∈N}
/ r# I+ b* `: G3 \0 t! f! f4 ?7 G( OA(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]:
7 O5 T5 t# c; B* ]) H2 g) d* }& dP(i)=P(Ai), i∈{0, 1, 2}, J& J0 ~$ L8 p- ^$ j
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)
$ k1 z, {# O: ^' G  n# m% L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:' @) g4 ~+ k6 t' o
{b(h) , 即上面所述的A(d)结果发生
( c& `' E7 [& a# T% KR(1)={O(h)*b(h),即上面所述的A(h)结果发生
& r! @3 y$ l! {  q, t9 O{0 , 即上面所述的A(a)结果发生4 V+ R# E0 d, U) Y4 S3 z/ q" {
以及' I' H  Z0 I  z& m( E- I
{b(a) , 即上面所述的A(d)结果发生
6 ~; {( Y/ O  Z; W! `: lR(2)={0, 即上面所述的A(h)结果发生" \# j. d( k5 @* Z% Z
{O(a)*b(a),即上面所述的A(a)结果发生
) F# t! C; w. ?- K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; D1 x0 }$ ]5 E1 f" s5 Y
那么投注主客的期望回报总数分别为2 W) R( R" Y% j& X
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]) L$ }$ X+ Q& J3 m+ ?  {% s7 I
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
; [$ ]9 G: J# z' 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5 G, K* ~8 V; N+ Q/ b7 l6 s
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)  `3 q2 V3 ?/ c- d. M: P7 l$ N
P(d)+p(h)O(h)=1
7 L( W$ ?' V6 X& PO(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式
- i- a8 f/ `. h& O' JE[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
: q5 l; Q  n1 g) Q- m( VP(d)+p(a)O(a)=1; j( z5 ~. _5 W6 {( L* N
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! G" a/ P* _: i' B+ f
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
2 I! J3 G' s( v2 _三、半球盘的计算描述
1 z6 w2 u% ~! H接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
3 u1 `1 v) M4 @. i6 _3 C# P7 a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:
* q& p$ f, r9 I{O(h)*b(h),即上面所述的A(d)结果发生5 T% }7 X* a2 M; L( I
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
! n5 I% f) }# K/ I& N{0 , 即上面所述的A(a)结果发生$ e8 M  w; `( w4 N# J5 G9 ^' C
以及
! U( q1 I0 Q# J+ ]6 C; u& m{0 , 即上面所述的A(d)结果发生$ D2 z9 Z1 V! n
R(2)={0, 即上面所述的A(h)结果发生3 v% }5 z* a' [( _' A  {
{O(a)*b(a),即上面所述的A(a)结果发生4 B2 u! S4 p: G; H
如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
# g& `$ O# u+ E  J投注主客的期望回报总数分别为
! J$ r& e9 s8 }! wE[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]+ r& F' w+ N# g9 X3 e
E[R(2)]=P(a)*O(a)*b(a)# A  i4 B8 h& B# \
假设实际投注回报与期望投注回报相等9 ~5 G* G" R2 q" N
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)$ h3 N7 N7 N9 Y8 y" p" _3 g: A
O(h)*[P(d)+p(h)]=1& j2 _: \2 o1 ~: S, c3 Y
O(h)=1/[P(d)+p(h)]! m7 b  {7 j4 q6 Q+ g# \  R3 D
E[R(2)]=P(a)*O(a)*b(a)=b(a)  a1 f. N% ?: d0 v  ~  I
P(a)*O(a)=15 `" b+ U) l8 B* Y! |2 B
O(a)=1/P(a)2 S! L7 v& Y) M
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率& z+ o, _/ s9 l; a' W
O(h)=1/p(h)
* U. R$ O& M) o$ {" v8 F/ |O(a)=1/[P(d)+p(a)]
( E: C8 {6 V% V2 O9 |$ N四、平半球盘的计算描述
/ c' P" e: I9 G% W% L这个稍复杂一点
5 v3 r" y1 X! p1 g, L接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
! b# ^7 i! n% E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:: D# x/ J( s# ~6 x$ I3 O" S3 G
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
. N0 U# ~# E9 t4 D8 MR(1)={O(h)*b(h), 即上面所述的A(h)结果发生0 c$ s; K! o8 O3 P. C! v2 o$ F
{0, 即上面所述的A(a)结果发生2 H& Q: F" L6 S  d+ y( ^8 D5 b
以及
3 U: o% q/ ?) \! L# S4 z* r{1/2×b(a) , 即上面所述的A(d)结果发生
3 N  Z% Y7 W& ^R(2)={0, 即上面所述的A(h)结果发生
  w/ K7 B& V. z2 P3 g3 P{O(a)*b(a), 即上面所述的A(a)结果发生
% ^  x$ y/ Z+ P9 L1 R投注主客的期望回报总数分别为
3 k1 `$ l: {9 T$ r8 x4 P+ M% iE[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))# u' A+ O5 C. t2 B9 j( \0 t
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 G" D* J- Y4 ]* {和上面计算过程相似,得出:# W/ y2 s& B1 o. V* E
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
3 b  ?' l6 u) C% ]; O- h: ZP(d)×{[O(h)+1]/2}+P(h)×O(h)=1) q  g+ F2 r* c$ W
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
: A! b9 }+ I; S6 ]& H- LO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
" s* v% Z& y, R3 h' m# mE[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)+ |1 J4 W" H% p# [9 q7 Z* s8 y
1/2×P(d)+P(a)*O(a)=1
' m$ i6 w3 e6 D/ v, c3 s5 l7 w. OO(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)- a" R# ^4 m3 A0 r& R5 j
同样主队让平半就分别是
1 s7 U% z; x  b7 Q3 \& ]- [8 wO(h)=(1-P(d)/2)/P(h)! R/ D# F! U6 C6 T6 S/ P2 V8 @
O(a)=(1-P(d)/2)/(P(d)/2+P(a)). W+ |  k6 Z2 |: M
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)
  p+ n* b; a, }+ S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
& j0 [" P) y, Z$ aB(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
: r& `% W2 {  fB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
7 U3 |8 b! \! r. y  l2 o$ P1 V. QB(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数. B: r+ y" H# y2 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:
0 g( s: _4 J! h' U+ ~{b(h)*O(h) , 即上面所述的B(d)结果发生
9 r8 x6 G3 n8 eR(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生& z0 ^# G- I* P4 a8 _# S, S5 w
{0 , 即上面所述的B(a)结果发生
# V8 |, ~2 |) w+ j5 S! |- o% L以及) w0 M9 q+ L; ^: C
{b(a) , 即上面所述的B(d)结果发生
2 q# {& e% c0 ^6 U. G5 X. I# L3 e, qR(2)={0, 即上面所述的B(h)结果发生- X: U) U0 ?& X$ a7 B! N  z7 _
{O(a)*b(a),即上面所述的B(a)结果发生
2 Q/ V6 k3 G5 L' T& }4 n5 n投注主客的期望回报总数分别为
% E# C  g5 R. }) eE[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)]+ p! Z1 ]: c# s# p' ^/ v
E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))  N0 [' d8 [3 q: P) Q" L  Y3 r
假设实际投注回报与期望投注回报相等# \" [2 N, Q; z# ^2 J, x
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)6 _! m) `5 e- Y2 U/ e" H- L
P(h)*O(h)+P(h1)-P(h1)*O(h)=1+ m% n$ t2 Y$ ^& k2 E2 b- w  E
O(h)*(P(h)-P(h1))=1-P(h1)0 v# G* m( }6 S9 P* X6 m
O(h)=(1-P(h1))/(P(h)-P(h1)), s+ f: V& o' O: A! y
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
, m& ^( }# G8 _P(h1)+O(a)-P(h)*O(a)=1* X- ^1 C: l5 {! w8 O. `( n
O(a)*(1-P(h))=1-P(h1)/ Q& T# w' ?7 V. L/ I6 J9 x* ]
O(a)=(1-P(h1))/(1-P(h))4 a& c8 D3 k( w; i9 M: W6 [
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。; Q9 R! J, s" D
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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