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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。
$ ^7 k+ s  y- r; I. _9 ?那么,平局、主胜、客胜就有以下表达式:
+ \* ^/ ?" \8 ]! Q9 YA(d) = {W(ij)|i=j, i∈N, j∈N}
0 r8 j, k. U  X; ]& DA(h) = {W(ij)|i>j, i∈N, j∈N}1 S3 t# Z8 m+ B' u- A8 ^0 m
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]:3 m  x$ t1 V# F% C* f* Z* T8 d5 S' n
P(i)=P(Ai), i∈{0, 1, 2}! ~0 r0 V. j. d5 f; E* b# n* ~
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)
: `; |4 o1 ?/ \; ]. Q  W: D% X0 Z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:2 Q; f: d# ?  [+ _& Q* u
{b(h) , 即上面所述的A(d)结果发生+ h2 o* n- Y% {1 G
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
1 k. W# I( X' t4 W; Q{0 , 即上面所述的A(a)结果发生2 x1 Q. |9 Y* b
以及! Y$ W$ I5 |1 q, q
{b(a) , 即上面所述的A(d)结果发生
2 N4 ~7 z' U7 A2 _; A9 _R(2)={0, 即上面所述的A(h)结果发生
7 J% o  O" ]' D' i) B{O(a)*b(a),即上面所述的A(a)结果发生
% k$ g3 k9 E3 o8 w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
+ ^) }# |5 ~& ^! S& J9 R. o那么投注主客的期望回报总数分别为
! H+ }% E) H4 b3 XE[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]) ]' J3 e! Y* y2 i' e
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]1 I' i- V* [/ [1 J! ?
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9 }/ v2 H6 O! r& \# A2 D
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
$ h# K* W% Z# h. }' @" M' lP(d)+p(h)O(h)=16 K* p- N: }' j6 ?3 m  Z5 g) {0 l
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
+ H" F4 C+ l6 P' q6 G  L, _E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
# B3 G/ K! A3 X' SP(d)+p(a)O(a)=1/ b, R! c6 s2 c; q  ~9 d0 n3 b
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
' j# Q# Y* l; @+ S: K6 q5 D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; G8 |' X- L* R; E; \# m; H9 o9 Y. X
三、半球盘的计算描述3 K1 u  Q1 P, l/ G7 y7 v; Y" P
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
1 C$ H/ Y% q" c0 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:
( Q2 p! L" N; a# B: Z' d8 ~# k{O(h)*b(h),即上面所述的A(d)结果发生
' Q# \4 b7 a0 W$ P% s6 WR(1)={O(h)*b(h),即上面所述的A(h)结果发生( T& a0 `, [" b# }% Y- y. L9 }. n* E
{0 , 即上面所述的A(a)结果发生1 j7 x% g/ G" t8 F% F' }
以及
9 v! z7 V/ o' ?) ]{0 , 即上面所述的A(d)结果发生
: U3 V% a% @& hR(2)={0, 即上面所述的A(h)结果发生
+ R& D! p% r3 B; a/ B& I{O(a)*b(a),即上面所述的A(a)结果发生
3 Y5 b8 w+ c, y$ y# n: `+ ~如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率- S. Q4 h; c( M: [9 z
投注主客的期望回报总数分别为4 O" x! n; P  A# g5 ]: t% d
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]3 P8 ^, p9 ]. o8 [- x5 K
E[R(2)]=P(a)*O(a)*b(a)
; d! j2 b7 D: \, ]$ v, W! n6 s0 o假设实际投注回报与期望投注回报相等: [6 `2 Y5 I2 U" M% W0 Y& L
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)# F: g. `, m: F" e: ]  H0 i, q
O(h)*[P(d)+p(h)]=1
' |/ Q  V9 C) Z  B+ |( G. UO(h)=1/[P(d)+p(h)]8 P4 d3 u& A! O# ]" e& j# g
E[R(2)]=P(a)*O(a)*b(a)=b(a)+ d! _1 I- U9 M, p
P(a)*O(a)=1
4 o6 X* z) I6 e& m1 g8 E6 [3 l* yO(a)=1/P(a)
' O, H( c: j, w- d同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率, y7 H6 ]; Z# Y1 a
O(h)=1/p(h)
6 R: I3 n0 t( x/ l& x% mO(a)=1/[P(d)+p(a)]
+ _  m- g8 v0 O* k6 q$ z$ ]/ ]四、平半球盘的计算描述, \( I' |+ q' V7 R3 O, ^  R
这个稍复杂一点
; ?9 }+ C- s* n接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)1 l' n1 B& v+ c2 C1 j
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:
# y6 n1 ~4 o8 e: A) `' s{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生% J* H: }( A, p
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生  ^% N6 N0 I8 q8 O. m
{0, 即上面所述的A(a)结果发生7 \( Y5 `9 d+ v; k
以及4 E. q3 h1 P; G
{1/2×b(a) , 即上面所述的A(d)结果发生
0 j0 z3 D" O1 X! V7 dR(2)={0, 即上面所述的A(h)结果发生
1 ^$ D/ j! H$ y+ `1 F5 q! P7 A{O(a)*b(a), 即上面所述的A(a)结果发生
3 W8 \+ o1 N% h( F1 E) e投注主客的期望回报总数分别为
/ W# @2 Q& e" ME[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 }- Z7 K- n7 s+ y4 e
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)], Q8 Q. i/ m8 E. l9 X' }- G, t; \
和上面计算过程相似,得出:# J9 T1 o  q. I0 i
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)9 g- u) B) p- b3 ]# G
P(d)×{[O(h)+1]/2}+P(h)×O(h)=11 P# D6 M& M/ Q, S
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
# r5 {0 u3 @0 D6 a' AO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
4 z( X* Y6 D- y- l& n+ JE[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
7 z5 f* o" ~+ |' t+ T1/2×P(d)+P(a)*O(a)=1
3 m+ q7 h$ L, o3 W7 ~, pO(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
( X+ M# P$ F) U: b* m+ j  q同样主队让平半就分别是
: t. D9 I$ ~8 e2 X+ TO(h)=(1-P(d)/2)/P(h)
5 ?# w, ?' W: u2 ZO(a)=(1-P(d)/2)/(P(d)/2+P(a))  h$ P3 C" K1 {; w
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)4 R% n# @, O% L2 I+ 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/ G. M  b4 j+ m' X
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}) u  l7 v* a0 m& B) }* l8 i* w
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
% A+ x: A* g" `0 r1 L2 ~B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
1 O1 B# C$ d3 i3 T3 V" s, E8 ]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:
: g. e: }6 z, s% f' M( r/ g# L{b(h)*O(h) , 即上面所述的B(d)结果发生: O1 K$ e: q* ~
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生5 D$ H* a3 \; b0 n4 t& {$ [
{0 , 即上面所述的B(a)结果发生
4 u- y) Z- U+ I: Q- _& @以及# E' c  M0 B$ x/ y+ h) p# J
{b(a) , 即上面所述的B(d)结果发生# R* A. l/ ~- K
R(2)={0, 即上面所述的B(h)结果发生2 m3 p2 {# E, s; E6 d: U9 H% \" u1 x
{O(a)*b(a),即上面所述的B(a)结果发生
$ F& a2 _( w# ^# }3 J8 @. f投注主客的期望回报总数分别为7 |& `. z) ]* X6 k- G. \4 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)]7 k) q4 J+ A0 d9 {6 f7 f  S; `; S
E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
& h# B- }( S* m+ U4 m8 S+ f4 T$ \假设实际投注回报与期望投注回报相等2 B. g4 l- t) Y% X* M8 ?
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
; e" n- H3 \9 W' S: lP(h)*O(h)+P(h1)-P(h1)*O(h)=19 m; V' S! {+ u& T+ @9 b3 Q
O(h)*(P(h)-P(h1))=1-P(h1)
1 }; M9 w! ^0 g: b' @: X2 gO(h)=(1-P(h1))/(P(h)-P(h1))
; M  H7 s; r, Z8 G+ o5 H  Y/ DE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)* T* t  s# x1 |" m
P(h1)+O(a)-P(h)*O(a)=1# k) c; L9 ]* n* U
O(a)*(1-P(h))=1-P(h1)
$ d& ^/ I* G# C/ `7 I& C' Z9 G5 lO(a)=(1-P(h1))/(1-P(h))$ o3 b% K8 n' _6 u
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。/ t" K9 A! k( n# x
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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