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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。
/ x% m. ^3 w: N那么,平局、主胜、客胜就有以下表达式:1 M- _+ B2 h G) L0 @1 M
A(d) = {W(ij)|i=j, i∈N, j∈N}; Z- @* P7 i& v) x+ Q% W
A(h) = {W(ij)|i>j, i∈N, j∈N}
! o+ P9 a+ P, G6 X+ E% `7 QA(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]:
# d* R, _+ o s/ ]P(i)=P(Ai), i∈{0, 1, 2}7 j% T1 R6 H7 P: M j3 C
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 r" c% ?$ Y: 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:0 L+ V0 k2 j" V6 m
{b(h) , 即上面所述的A(d)结果发生
, _4 ~0 L7 @. L& wR(1)={O(h)*b(h),即上面所述的A(h)结果发生
' Y. v& [6 o' \, E/ p2 ?# W{0 , 即上面所述的A(a)结果发生
/ S& v/ K- D: K以及
) t+ u; d8 o: p3 I9 e" A{b(a) , 即上面所述的A(d)结果发生, \; {' q8 [6 U& M2 S1 ~9 s0 X
R(2)={0, 即上面所述的A(h)结果发生0 Q) J! M9 D6 }2 C* x4 g" h
{O(a)*b(a),即上面所述的A(a)结果发生
! B* V) R* e. x* 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
" o$ {/ ~1 k; A+ [# G1 ^6 C那么投注主客的期望回报总数分别为$ h" j2 {/ V% i+ B9 M
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]3 L0 W: l& v- k3 R4 U8 r
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]9 V3 r i6 q' O, F" ~$ n
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 z' {1 \! y# }" KE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
) k1 X! ^2 X$ L4 ]6 M6 j2 fP(d)+p(h)O(h)=18 H4 q/ \' C- T" u' C
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$ q6 [# ~2 W0 x
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
7 w. [+ @( j, gP(d)+p(a)O(a)=1) ?+ V, @$ @6 d* _, u
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9 T. ^ j0 x" |2 o% r
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
4 S! Y& o) H% U* T* U1 o三、半球盘的计算描述! I, M4 b3 a0 N% p6 }3 W0 w ~
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
1 t' {- d3 a9 m t% s* w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:
0 b/ H/ \. c/ m7 D+ V R/ n{O(h)*b(h),即上面所述的A(d)结果发生
) H f L2 {1 S% K# q5 ~R(1)={O(h)*b(h),即上面所述的A(h)结果发生" C% v! F2 Y6 K$ T: u1 J
{0 , 即上面所述的A(a)结果发生
0 k- V7 D: V% M! J0 ]3 h3 S以及8 L6 I9 j" X7 s
{0 , 即上面所述的A(d)结果发生! D4 K; g( o2 r/ r9 S5 A9 x' f0 W
R(2)={0, 即上面所述的A(h)结果发生
6 u5 e4 I; n! z( H: e) D{O(a)*b(a),即上面所述的A(a)结果发生2 m) n/ g% P. z& x5 i$ u
如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率' E/ ^7 H& e, n/ C0 L4 l
投注主客的期望回报总数分别为
$ s3 e* N; q0 I6 N! }: iE[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]
2 H; y& I8 P# uE[R(2)]=P(a)*O(a)*b(a)/ u+ \( v# e# W) i
假设实际投注回报与期望投注回报相等
" x$ C5 C) [9 u$ ?E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
5 _2 C( O5 d# {0 V" c/ NO(h)*[P(d)+p(h)]=1- d5 P) N- k' e- U# s1 }: Y0 W5 n
O(h)=1/[P(d)+p(h)]3 m8 |1 e( M( \- P/ `
E[R(2)]=P(a)*O(a)*b(a)=b(a). m9 P) D" J h; z
P(a)*O(a)=11 {# t5 t1 q7 \# U
O(a)=1/P(a)+ w3 V6 g: v1 U; L* d$ L& k* u- W
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率- [' B( ]1 K/ m9 q4 u! {
O(h)=1/p(h)
7 H0 _$ ~6 H1 u' I* sO(a)=1/[P(d)+p(a)]$ Y B; s. G+ P- ]" |: R
四、平半球盘的计算描述2 A, o5 v6 w" v
这个稍复杂一点% N* i7 Z2 Y; N" h( b: ?' ^
接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
) }8 J# s# ? C9 t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:0 C' X: e- ?5 Y& V. N) K% q }
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
* T: a! n) ]: r; e WR(1)={O(h)*b(h), 即上面所述的A(h)结果发生
& ?4 f- j4 g" }% A2 |& |+ V# W; L{0, 即上面所述的A(a)结果发生
3 l* c( Q6 H7 W3 L" D: |以及
& a& A+ s; i9 j9 a" o+ d& s/ s0 o{1/2×b(a) , 即上面所述的A(d)结果发生4 Q- ^. W+ `, @+ G* e# Z k
R(2)={0, 即上面所述的A(h)结果发生
# V: g7 B& g* K& H- d- K{O(a)*b(a), 即上面所述的A(a)结果发生$ C* A) U) a0 E: x: R
投注主客的期望回报总数分别为1 Z D1 t: l! i( \/ I
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))5 a; }9 ~: W4 ?9 C8 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)]- R R8 q+ U' W5 L: b) H3 m9 [
和上面计算过程相似,得出:
* B; k8 v: `. k8 n; M& {E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h) h% D e0 y4 o5 S, R
P(d)×{[O(h)+1]/2}+P(h)×O(h)=1" D7 H; y* z. x$ L( R
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
4 P- z o! A, a+ q. QO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))8 o* u5 g2 J2 j; B& {( j' z+ J
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
! Z, H2 Q8 R3 {2 H" |0 d1/2×P(d)+P(a)*O(a)=1
1 m! g% C; }+ O8 w/ YO(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)% d; r; O" ]5 S( x- Y
同样主队让平半就分别是% m e/ l2 B9 |7 U
O(h)=(1-P(d)/2)/P(h)
7 y W; ~8 H8 `/ g3 ?4 t6 B1 x/ ZO(a)=(1-P(d)/2)/(P(d)/2+P(a))
3 Y, e8 b" s9 W: G+ C/ 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)% D) {- E8 P& R6 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0 _3 z& E& k: L8 z" o3 f
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
; I1 Z- f9 m' d4 A+ U8 P% a( R9 G. aB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}9 z% h$ ?" _+ Y4 o1 f
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
. N1 _1 t6 P8 [! U0 r, c& m1 F0 J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:
. S: \8 N9 R6 f4 A1 l{b(h)*O(h) , 即上面所述的B(d)结果发生
1 E4 U( ?( K: t6 uR(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生5 V; n, D/ X h# a+ S
{0 , 即上面所述的B(a)结果发生
4 m0 C+ z% _0 ]% U3 Z: h4 F5 {& V以及8 [( P X/ F/ h: }1 H
{b(a) , 即上面所述的B(d)结果发生; z" W: B9 j( {) a
R(2)={0, 即上面所述的B(h)结果发生
) G: i6 _! p3 q+ o! R* L- b{O(a)*b(a),即上面所述的B(a)结果发生
& v0 h, Y% f# w投注主客的期望回报总数分别为
/ ?: f" P& v0 b5 h$ C9 p7 J* ME[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)]& d" N- G$ g2 K4 l. I: n/ 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)); P8 D0 ^" E E5 ?
假设实际投注回报与期望投注回报相等! V- ?5 f: h1 [" u8 [8 U
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)3 i; z6 E2 L4 j H! i0 u
P(h)*O(h)+P(h1)-P(h1)*O(h)=1. @2 H% `. @. C+ Z6 k
O(h)*(P(h)-P(h1))=1-P(h1)- D8 d& [, F: a, h. \1 N: ]" z
O(h)=(1-P(h1))/(P(h)-P(h1))/ x- |! i$ V) {
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
! k* a0 b0 s) m' z8 J0 W+ rP(h1)+O(a)-P(h)*O(a)=1
2 w# `# H) b$ w; J0 cO(a)*(1-P(h))=1-P(h1)
5 v+ M- H0 [5 ?- i6 m5 mO(a)=(1-P(h1))/(1-P(h))
; c9 f. p2 k; H+ B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。, |* y; Q; I' `; o 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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