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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。
8 Q0 f2 {) K5 J, X. W那么,平局、主胜、客胜就有以下表达式:
% ?/ h7 g6 p {. U, D+ nA(d) = {W(ij)|i=j, i∈N, j∈N}
3 V, z* v+ e& R: FA(h) = {W(ij)|i>j, i∈N, j∈N}
) G) y; | ?/ f2 K- A: fA(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]:# a. @4 S% L \( S
P(i)=P(Ai), i∈{0, 1, 2}; @6 j" t: T9 s/ |
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)
7 a8 P& ?' C! V: q- t+ ~5 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:4 x* V1 b4 I1 \. g9 z2 j1 g' k
{b(h) , 即上面所述的A(d)结果发生
% N% J+ l# r& O0 f, CR(1)={O(h)*b(h),即上面所述的A(h)结果发生
0 v6 s- x6 i; l) z' |. S{0 , 即上面所述的A(a)结果发生
" P8 T2 t# p$ n" H6 e1 R以及
$ X" d, L5 y8 I- J x{b(a) , 即上面所述的A(d)结果发生! N2 H. ?( @8 q% i' O; D
R(2)={0, 即上面所述的A(h)结果发生
. b9 L7 w( h& t: E1 h{O(a)*b(a),即上面所述的A(a)结果发生
; X% K. f- i- A7 b$ s7 p- E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! T' A6 L# w; r0 w$ o
那么投注主客的期望回报总数分别为7 y; v# j& K/ i, L3 p c% W; L
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]( E' @" Y# r" @ q2 l' Z! z1 ~: F
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
, O& C3 l7 I% 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3 p( V* U. Y, W1 u. H) M+ p: \
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
. ]9 Y9 i* L I# ]5 S: J5 pP(d)+p(h)O(h)=1+ ` B1 c7 I/ l) d. a' b q5 o
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1 p( L: f" n' \' a: \" e$ `
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
4 _" s# h! r$ q1 S) f" e: bP(d)+p(a)O(a)=1
) X$ B2 T, l) |9 K9 Y/ S1 t. y& dO(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式
+ W# k' j3 H/ I; M; s* o2 E: U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
r0 L% e6 B0 k三、半球盘的计算描述
; F- a! X- L% D! w/ @3 f接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)( b# o+ |! z7 S$ u
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:5 V: J% a1 E/ j/ ^3 H$ `
{O(h)*b(h),即上面所述的A(d)结果发生
1 X0 |; I3 _- R. W) k& JR(1)={O(h)*b(h),即上面所述的A(h)结果发生' i& l% w. F" @& ]" z
{0 , 即上面所述的A(a)结果发生; p) O2 Q# V% E2 j: R8 r
以及
. `5 h1 C2 k$ v4 z: ~3 T. y; n5 G. q{0 , 即上面所述的A(d)结果发生
, m& \5 `9 i' H$ r# w0 i/ KR(2)={0, 即上面所述的A(h)结果发生
8 ?& l! e0 D! E" }7 s& \4 S0 ~; s{O(a)*b(a),即上面所述的A(a)结果发生
' D# g5 Y6 q# ?如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率2 j- n: Y8 a5 O7 w1 ?& P. ]! ?
投注主客的期望回报总数分别为. Y+ w" i* E# l$ |+ B2 z- y
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]) p2 j$ b: I# E- l1 h) I; V) m
E[R(2)]=P(a)*O(a)*b(a)
0 x l& M4 D+ Q! @0 e$ u! w假设实际投注回报与期望投注回报相等
) T$ b. G- `% p( U* o, e3 P2 sE[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
* c& t8 }& K5 m$ u J# mO(h)*[P(d)+p(h)]=1
" D& M& s6 b+ c Y, ^O(h)=1/[P(d)+p(h)]% M& d/ H# M- M' D- G
E[R(2)]=P(a)*O(a)*b(a)=b(a)
) w* E0 A; l% \; \; VP(a)*O(a)=13 d0 d4 o6 t+ w7 g/ d: A
O(a)=1/P(a)
8 J ^3 E# p o2 `同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率
& J1 K% |! i4 o" K0 q8 h6 D" VO(h)=1/p(h)7 T" y M! H0 K
O(a)=1/[P(d)+p(a)]
. y0 b9 Y& O# x: Q四、平半球盘的计算描述' ~" s, o0 x r1 z# ~+ N+ I$ j# u# H
这个稍复杂一点0 p5 i$ ~' F6 o5 f/ j7 ]2 u$ q
接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况); I$ n/ `; l3 t& @. 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:
% _. O- S2 e) w6 n8 a{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生7 T' Y8 S. t! x
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生
6 Z* ]1 {7 U& g2 T- ~# c{0, 即上面所述的A(a)结果发生+ c w; y: J6 B7 V7 v
以及7 v. _+ E9 Q1 `$ r
{1/2×b(a) , 即上面所述的A(d)结果发生3 `8 ^% q0 I* \; [
R(2)={0, 即上面所述的A(h)结果发生2 L# K$ f( f6 C
{O(a)*b(a), 即上面所述的A(a)结果发生4 @, [$ `2 \0 b" @2 O: u; k
投注主客的期望回报总数分别为
3 b* a8 e. M6 S7 ]8 T1 `E[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% Q6 C- D9 f( v& S( m$ ^
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)]
' D- L. b9 s( T和上面计算过程相似,得出:7 Z2 n# O8 x( l/ L
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)) c% E6 _ ~# k1 O3 L/ T
P(d)×{[O(h)+1]/2}+P(h)×O(h)=1
' C) N% d9 I# p0 fO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1' H3 s* |( S; b% i
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
" i- ~, A1 c# D2 u" E) v2 |E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
6 a7 t% z1 ~2 ?- x. a- J9 P5 d1/2×P(d)+P(a)*O(a)=17 x' {3 [4 ]9 o6 b
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)* _9 E, _) d- E1 g$ {: y
同样主队让平半就分别是% v% Q, N" i9 x' _7 B# R
O(h)=(1-P(d)/2)/P(h)
# r& ]5 g" I# L" [" K4 ~8 A/ dO(a)=(1-P(d)/2)/(P(d)/2+P(a))
! G2 w& L: Q$ n' y7 d3 ^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)) X, j" Z P2 P# N( I8 [
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, U* A. d |2 j# e3 L+ N
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
; m- G' }! q# I+ d, G, L4 rB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}0 d; q) z; C* d$ z4 W _
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
0 d5 N+ r7 W* {$ i7 ~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 m8 p. [! n, C1 [3 \
{b(h)*O(h) , 即上面所述的B(d)结果发生+ u: F3 M5 G+ y* v7 ~
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生0 _# b( N: T4 V+ n7 ?' O
{0 , 即上面所述的B(a)结果发生
( x- y- B; A" {5 Q/ z: U: X以及
5 F* i& D! ]7 o P{b(a) , 即上面所述的B(d)结果发生
! v8 d* Q& z6 g* @R(2)={0, 即上面所述的B(h)结果发生
, z S* G8 r, g! I{O(a)*b(a),即上面所述的B(a)结果发生; Z* m; r) A. w/ Z1 N
投注主客的期望回报总数分别为+ d q9 I* t3 t* I
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)]
' C$ c# a: f2 z, EE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))6 W# ~5 n# c/ O* s0 x" @" F
假设实际投注回报与期望投注回报相等( z+ p a/ p6 f' b ~! y9 F# c
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)) g& x e, x$ w# y! \8 t) n9 x
P(h)*O(h)+P(h1)-P(h1)*O(h)=12 q' X! u! [1 N+ `% h$ F5 c
O(h)*(P(h)-P(h1))=1-P(h1)
- p' j# N8 r1 QO(h)=(1-P(h1))/(P(h)-P(h1))& p" S! e5 [% \# j( W
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
1 s' o/ V @, h! x3 {/ l1 ~P(h1)+O(a)-P(h)*O(a)=1
; R r+ ~( D8 U" gO(a)*(1-P(h))=1-P(h1)
: x B0 R/ y1 Z* ]. eO(a)=(1-P(h1))/(1-P(h))
' L% R$ i- L! j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 z( z/ Q7 u$ C& M2 B8 q) L# t
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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