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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。
* k. w: e2 H: M- r! a0 @1 E; c* R那么,平局、主胜、客胜就有以下表达式:1 N. b0 f* a% i: {% G- W' `
A(d) = {W(ij)|i=j, i∈N, j∈N}
* \, @3 s1 M3 i$ cA(h) = {W(ij)|i>j, i∈N, j∈N}! Y( ]) q3 r0 A( ]" g
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]:
9 K* ] v) B* A7 G8 h5 N9 ?P(i)=P(Ai), i∈{0, 1, 2}# F! d/ o* O; J& [! _4 q
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)
% Q; B1 F+ X3 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:9 Z3 T% o6 m) `# p0 S: m% O8 D
{b(h) , 即上面所述的A(d)结果发生
{2 w3 e4 \9 E/ zR(1)={O(h)*b(h),即上面所述的A(h)结果发生6 c4 @1 ~9 y$ x) M6 q R
{0 , 即上面所述的A(a)结果发生
4 j, {( i1 K( \6 I8 m以及, q4 V) \: \" ~/ l5 a
{b(a) , 即上面所述的A(d)结果发生9 J9 y" a; y5 E4 {+ {$ W6 T+ \
R(2)={0, 即上面所述的A(h)结果发生
+ ?6 g- r! ^$ a{O(a)*b(a),即上面所述的A(a)结果发生3 v4 L% |4 q8 z
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
, ]6 ~/ O9 r0 _% L7 Q那么投注主客的期望回报总数分别为
$ _; t+ _& q; @. z$ UE[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]2 O& z2 x( I3 E/ `" e: l! |
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]! F2 |8 F& _' F) y5 d
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7 H$ L7 H) e' Q, _5 Z3 Z% K* ]" P1 A
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
( ~1 G; _$ u9 ]% cP(d)+p(h)O(h)=1
# i. `4 |+ l9 `+ H& p7 d2 N9 XO(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式
2 \$ @/ o5 r- U; yE[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
0 ^6 _. w& t% eP(d)+p(a)O(a)=1
4 H: k% B3 A8 E2 \) M- v+ y. RO(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式
" k( f1 @- X" p9 t9 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
) r" T2 L! M V' y! {7 ^三、半球盘的计算描述8 W- x8 t$ O) z9 o8 k+ Y- c8 G
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
$ I. L- w* X! @! B$ Y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:7 l3 ^5 I1 l+ ` J4 W
{O(h)*b(h),即上面所述的A(d)结果发生: F$ m& Y A1 ?9 ]+ W6 @, r
R(1)={O(h)*b(h),即上面所述的A(h)结果发生- O7 p, a+ _$ I! i! Q( q) y
{0 , 即上面所述的A(a)结果发生
8 d g: }( A, F9 V! B8 @以及
: r/ I7 E3 g$ T" s" s{0 , 即上面所述的A(d)结果发生
% [( c$ M( I! M0 {: S J4 zR(2)={0, 即上面所述的A(h)结果发生
+ t# o) s( b& v$ @' G{O(a)*b(a),即上面所述的A(a)结果发生
7 Z/ ?# I+ A& s1 a! V% T9 i2 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
+ `) O5 k+ U- y" h+ j% u: M投注主客的期望回报总数分别为. f l! W! T6 h; d
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)], _. h0 l/ a) _# j! o6 a+ J! u
E[R(2)]=P(a)*O(a)*b(a)1 ?" F! `- K. t& N2 Q* K: L* K
假设实际投注回报与期望投注回报相等
* C, |' }4 o3 [2 HE[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
& v4 A" d9 s1 x$ q2 [- OO(h)*[P(d)+p(h)]=1
7 _* p, ?! u- xO(h)=1/[P(d)+p(h)]
% J+ i+ |6 r. ~E[R(2)]=P(a)*O(a)*b(a)=b(a)
5 f: x! z7 ^1 Z7 g; |. vP(a)*O(a)=18 ^! g9 U# m9 \1 @
O(a)=1/P(a)
* u% U, h/ l4 `! Y# @, y% h同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率) A9 U0 d8 f* l. x2 s: j8 T1 a
O(h)=1/p(h)
3 @' d4 {- u7 W) r% s7 bO(a)=1/[P(d)+p(a)]
4 q7 f6 |2 {5 ~2 m四、平半球盘的计算描述
- ~% s7 C3 B6 [9 T5 L这个稍复杂一点
% u% V9 V6 r( a* `& [% p) P接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
' U; e6 a7 i5 [% @* p& L$ Z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:$ Z; e2 j) T7 Y( H$ W9 x
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
5 H+ n9 A1 M% V( j) @R(1)={O(h)*b(h), 即上面所述的A(h)结果发生
# v3 v/ Q$ N$ C% G9 x5 h1 p{0, 即上面所述的A(a)结果发生" T d) m" @$ L* f( C
以及( w6 B3 R+ C+ ~9 Y3 q
{1/2×b(a) , 即上面所述的A(d)结果发生7 l% ]$ j2 e: V; X3 F
R(2)={0, 即上面所述的A(h)结果发生
# y" v6 ~+ I$ F, k M{O(a)*b(a), 即上面所述的A(a)结果发生- q1 j! z0 S& W$ m- @* O" T3 y; C. e
投注主客的期望回报总数分别为/ y5 O& N6 B# ^; c
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))0 w) Q5 O" M9 f% } B2 Q/ |) z
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)]
* j {" f5 K' J% d+ f5 n和上面计算过程相似,得出:) u) W6 n% n' h/ H
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
$ N/ r# f% |0 dP(d)×{[O(h)+1]/2}+P(h)×O(h)=1- Z) H% e7 Z3 K
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1+ h% @/ ~5 ?* ~; s& o# o% ~
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
5 f( n9 J7 ]% b! CE[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
7 Y& u8 Y4 U0 o# p1/2×P(d)+P(a)*O(a)=1. a% M' ]0 E9 _0 c7 g
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
2 C* v9 m+ p, e- O: W同样主队让平半就分别是
8 g3 c. k& V) t' O w- {( W& P; KO(h)=(1-P(d)/2)/P(h)
* O9 `: P3 K7 Z$ NO(a)=(1-P(d)/2)/(P(d)/2+P(a))
; |5 t, M' z; r! O+ l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$ _, F/ X0 ^' c9 h: f! f6 d
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% I- P! ?6 R8 s) W% E
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}" ^/ P* J$ _& i* v+ `" H% ^" t7 @9 _
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
. K: O" j1 f' Q+ jB(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
: g' x9 i; h: C8 n- c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:
2 }+ {" q' x: a{b(h)*O(h) , 即上面所述的B(d)结果发生
- E+ l* T V; MR(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生, n2 D5 [9 F% t% U, O* l
{0 , 即上面所述的B(a)结果发生
+ y- i) [5 n2 }以及+ X/ U5 W( ]; H& ^, _
{b(a) , 即上面所述的B(d)结果发生
% ]8 y" X0 l5 |( ~R(2)={0, 即上面所述的B(h)结果发生
4 `9 R, u& ~ a: [{O(a)*b(a),即上面所述的B(a)结果发生
8 f! o7 R% }' C5 N: d6 S4 H9 b# ~投注主客的期望回报总数分别为
1 x! N+ V( ~: Z9 @. i2 KE[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)]
4 k+ b; ]+ b. b6 L. ~' d3 bE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
8 ^9 Z% i# n1 {4 f9 x" q1 z假设实际投注回报与期望投注回报相等
' _( W) m" [( s( QE[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)! X; y5 f1 x: t$ @
P(h)*O(h)+P(h1)-P(h1)*O(h)=1: j* L8 N9 \1 P7 j, G2 H( @6 o
O(h)*(P(h)-P(h1))=1-P(h1)9 E( O/ Z. j F) o
O(h)=(1-P(h1))/(P(h)-P(h1))4 n8 S# |* A1 \) A- c3 n
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)' z: E+ C! G( L) u/ d: m
P(h1)+O(a)-P(h)*O(a)=15 |/ u A+ ^' ]# [
O(a)*(1-P(h))=1-P(h1)3 Q- n5 w/ ]% C: @7 h/ n
O(a)=(1-P(h1))/(1-P(h))$ S" F. ~0 H0 k3 j) s( j- I
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。; U& C: U* B' l* U6 M3 a5 H e
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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