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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。) ~, q7 a; M$ X. _ j. x
那么,平局、主胜、客胜就有以下表达式:- Z6 @* n% H5 N* d' B1 q
A(d) = {W(ij)|i=j, i∈N, j∈N}
9 v6 R2 H6 ]7 u7 tA(h) = {W(ij)|i>j, i∈N, j∈N}
( O- P" o. m3 B( ]8 Z9 W7 zA(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]:
# E6 ]. a2 d& g! X6 [5 X( _P(i)=P(Ai), i∈{0, 1, 2}
6 R7 m: n) ?- I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)
' u2 W8 _! }3 V, }+ E- g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:
; p2 s- @# u6 k# o{b(h) , 即上面所述的A(d)结果发生, Z6 W+ T' E" m! }
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
/ i: F& @& W% W8 O; j n, \{0 , 即上面所述的A(a)结果发生 L1 q" j8 Q2 j
以及
# R3 \: i {. J1 h6 a9 p) F4 e{b(a) , 即上面所述的A(d)结果发生
+ j- ~/ Z2 J% W/ z9 H( I) sR(2)={0, 即上面所述的A(h)结果发生$ l& |! ^/ `0 r4 N: L
{O(a)*b(a),即上面所述的A(a)结果发生
: O7 s% n& D- ^& K" P; h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 V" Y5 t, T2 {/ c9 n
那么投注主客的期望回报总数分别为
7 R4 I6 @& ^% O8 X- X% I$ G/ CE[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]& e0 k+ b$ X7 G( H7 V. b; n9 T
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]4 l1 ?4 t; O6 P( R7 \; H5 j8 M1 ~
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
4 v3 \% M. \2 r8 g3 u2 K+ Q% X, nE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
5 ~% T" q+ C7 O) J% X7 l; q1 B- M' t/ cP(d)+p(h)O(h)=1
R! |' t) `8 l5 zO(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 u+ J" Q' A! S3 L
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
* y1 W8 I' S1 i! c2 t/ x/ NP(d)+p(a)O(a)=1% z3 a! P% `7 ?/ u' 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( N- J7 w, V( ~- C8 i
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
+ I8 b7 c. j9 {4 Q8 c1 D三、半球盘的计算描述& G/ J! j' r! ]* s9 Y/ v0 s; @' N
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)6 H$ Y8 }; [8 c: o; j6 k4 ~
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:8 H& a1 w1 k& F" n9 Y% a/ p1 z
{O(h)*b(h),即上面所述的A(d)结果发生
& P; R- C; i) W8 N4 YR(1)={O(h)*b(h),即上面所述的A(h)结果发生# P3 q2 i) M9 j/ n
{0 , 即上面所述的A(a)结果发生
5 W) C' s. |0 F5 n以及! H/ u7 H) U5 b
{0 , 即上面所述的A(d)结果发生
* \3 u1 ^) G. |+ G6 l9 hR(2)={0, 即上面所述的A(h)结果发生
$ h) v- d5 M/ n) `/ N6 Z! Y{O(a)*b(a),即上面所述的A(a)结果发生) Z* Y3 Q; W: ~$ A, f" R
如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
4 L# _; X8 ~8 x$ z1 X# f0 c投注主客的期望回报总数分别为- G; i% J d0 W% c
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]. {, ~4 i1 J! j# v6 |, u3 V
E[R(2)]=P(a)*O(a)*b(a)
7 K2 g: M9 M; H% u: y5 E假设实际投注回报与期望投注回报相等
: f0 Z3 u# m; {( [1 F7 W# I+ DE[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)& U7 N2 G2 H$ w/ N- i1 R' n
O(h)*[P(d)+p(h)]=1
9 M; g1 I5 ^9 X: n% dO(h)=1/[P(d)+p(h)]
9 D1 }) L' |% {! b, GE[R(2)]=P(a)*O(a)*b(a)=b(a). V5 K" F' K3 h4 A( v ]0 r
P(a)*O(a)=1
E; `2 `1 u- V; I* p6 V: k; sO(a)=1/P(a)8 \8 t( f6 I) N. k9 h
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率1 V* o# s# t+ ^' ~$ W5 f2 D
O(h)=1/p(h)6 b: l+ m. X w, s( }
O(a)=1/[P(d)+p(a)]
4 P8 ^6 N# n$ i+ o) i5 g5 M, N四、平半球盘的计算描述1 X7 s, u' C1 P7 ^+ u5 k
这个稍复杂一点% ?! n6 C$ a; z4 L$ H7 T4 J
接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
5 P4 m) n3 u2 r8 N( G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:
& E! |5 }" y! x, N! _- I{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
& e2 @# `/ I+ q* w# k3 c- V- gR(1)={O(h)*b(h), 即上面所述的A(h)结果发生! ^$ U. X0 `3 z2 z' l
{0, 即上面所述的A(a)结果发生
$ x, h, X6 P9 d) k+ z4 F) a以及
# O$ G2 |6 V4 y: }' \{1/2×b(a) , 即上面所述的A(d)结果发生; v; P& @3 B4 p+ G6 Q% u
R(2)={0, 即上面所述的A(h)结果发生( v- x' d+ T5 Y" r2 ^. i+ ]- R9 h
{O(a)*b(a), 即上面所述的A(a)结果发生
" A& D0 z" T9 |; c" K6 d3 G投注主客的期望回报总数分别为
/ ?3 [3 S8 G9 ^* b3 ], bE[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))
# C* [+ o- Z5 _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)]8 |( i: m5 |, @. {; t! P1 U1 H
和上面计算过程相似,得出:1 F8 z" {1 c! Y0 M
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h), }% u h! ^ V( Z
P(d)×{[O(h)+1]/2}+P(h)×O(h)=1
Q! q3 V6 M5 x! @' ZO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
4 i. \+ V' j1 _( m0 i) K6 T8 zO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))7 ~5 [# h0 P- C
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a), V: ?& H7 f) f a7 _. `3 P
1/2×P(d)+P(a)*O(a)=1& M" ?1 J6 |1 J3 T) S. W
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)( f6 z% @1 ^, D
同样主队让平半就分别是
6 E3 m) o+ X+ ]: J( |! s# NO(h)=(1-P(d)/2)/P(h)
, c7 o! ^; d" c3 W1 IO(a)=(1-P(d)/2)/(P(d)/2+P(a))' D# p2 M) a% 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)
( a& p+ k% Q, I% o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
# _' ^1 r" U' c4 F, FB(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
, N1 X8 A2 }- } X, a7 JB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
7 H |, g7 q3 r: P! g) E* RB(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数* V3 l1 b4 I! H) H
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:! n) e4 M8 S2 {! ~0 ]5 t
{b(h)*O(h) , 即上面所述的B(d)结果发生
* z6 m# R3 ^' z+ p2 e6 wR(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
b1 n+ j& l& J4 A, t; Z{0 , 即上面所述的B(a)结果发生8 r' t% Z5 {' Q" x
以及
; |% X% b! K1 S* c{b(a) , 即上面所述的B(d)结果发生4 P" e. u. p- k) j- B
R(2)={0, 即上面所述的B(h)结果发生% j1 z& ~2 ~# W/ j/ j! ?, g/ J2 u
{O(a)*b(a),即上面所述的B(a)结果发生- k, F- O& m) i$ L: B. M
投注主客的期望回报总数分别为; ?) d, V( \ N: G8 G- m
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)]9 T/ m: P! z- U* L" H+ O
E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
* U5 L! _9 V1 x- O/ s! }假设实际投注回报与期望投注回报相等- Y6 I( b0 k8 _2 K. k% S
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)4 }( N; W: }0 h3 Y" E
P(h)*O(h)+P(h1)-P(h1)*O(h)=13 `$ W* m1 F( L, C( w( w! j
O(h)*(P(h)-P(h1))=1-P(h1)
. h: P) C5 I% R) ~+ j7 J7 N0 `O(h)=(1-P(h1))/(P(h)-P(h1))# }1 c: T' h- q- ~7 K- G( `4 m
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)/ W9 d1 ^. M: v5 L0 ^
P(h1)+O(a)-P(h)*O(a)=10 h1 X2 z) N _5 w: j- B
O(a)*(1-P(h))=1-P(h1)
" |& a4 u' g$ c3 B- gO(a)=(1-P(h1))/(1-P(h))
+ {" E1 y# [0 G, ?6 x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。7 U% B8 x+ V" [7 a4 G2 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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