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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。
- S5 |# v9 p8 h9 U- F( [那么,平局、主胜、客胜就有以下表达式:
( u" |9 ]. t& ]* \A(d) = {W(ij)|i=j, i∈N, j∈N}
t6 S: M8 n% \. t4 @1 UA(h) = {W(ij)|i>j, i∈N, j∈N}/ r' c7 d1 d4 v: l* L
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]:* x$ f' w; \9 m2 S- Q3 `0 n* ]
P(i)=P(Ai), i∈{0, 1, 2}
" o7 W1 R3 b) |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)
: \3 G. S+ |/ [- f: ~$ M( j q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:
6 k! y, O# q( S! g{b(h) , 即上面所述的A(d)结果发生
/ a4 i' P- v: a; `2 k5 O8 L6 G$ X& SR(1)={O(h)*b(h),即上面所述的A(h)结果发生* v! Z( A2 H4 |- ~! w: A
{0 , 即上面所述的A(a)结果发生
$ z- `: L! V5 \7 }8 z1 N( e# [以及7 Q V" f, X, V- I8 c. m
{b(a) , 即上面所述的A(d)结果发生4 C3 a& [) D' Y% n% t" `
R(2)={0, 即上面所述的A(h)结果发生
+ A& s" j0 {& \! m! ~& \{O(a)*b(a),即上面所述的A(a)结果发生
, ?8 w% T) F+ N1 a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* l6 G1 A0 Q" I P0 |9 F9 t
那么投注主客的期望回报总数分别为
6 f7 y) n2 W }E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]
( Z3 w/ `# R6 q2 dE[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
% u) P) i% [. v* E1 h- ^ E: ]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' H* Q! d/ K5 m" h3 E
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
! A0 J3 D- o: @' s2 \# O9 v6 uP(d)+p(h)O(h)=1 r2 u& Y# I& F* p/ G6 i
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: F2 B0 ^9 [6 k: z( F% u
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
6 Q$ K) ^$ T! FP(d)+p(a)O(a)=1
& m' H& E8 X8 mO(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式
- D# B9 ]. K; c3 {4 v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 b5 C2 _$ q* d4 U4 K三、半球盘的计算描述
( ?4 F) L3 D7 u; a! K接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
* |( R$ C0 T& Q8 z1 V9 e, C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:
. N; Y. x2 y$ x7 b{O(h)*b(h),即上面所述的A(d)结果发生
/ D4 C: I" d* u( iR(1)={O(h)*b(h),即上面所述的A(h)结果发生
' I5 I) |% d5 a, l: g n' G{0 , 即上面所述的A(a)结果发生
6 ?/ Z' o# u/ R) {8 H; {以及) e2 f3 J! Z" P& ^4 W7 O- |. ?6 r7 w
{0 , 即上面所述的A(d)结果发生1 g6 y1 |+ X' z7 l1 ?9 {& t0 c
R(2)={0, 即上面所述的A(h)结果发生- S; j1 L! T; i$ n9 \
{O(a)*b(a),即上面所述的A(a)结果发生
0 Q' O u, B9 `5 r" q4 N7 I如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
# J7 w. z/ d/ r. O6 B投注主客的期望回报总数分别为- Q3 D6 l$ P. E. @2 |* s; [7 W
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]7 k7 l" Q2 L; j' C6 `( F9 x
E[R(2)]=P(a)*O(a)*b(a)
. n! T) z& ?( E& {/ Z假设实际投注回报与期望投注回报相等0 Q9 H* N( r& K, R5 g8 [
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)2 o' c5 t4 R% B2 c
O(h)*[P(d)+p(h)]=1
) K0 R9 R1 i% }! E9 E7 J6 AO(h)=1/[P(d)+p(h)]
% N# d* W7 p- L2 W' HE[R(2)]=P(a)*O(a)*b(a)=b(a)1 G! Y1 S* R2 T) D% d
P(a)*O(a)=1- y$ M' A+ c( t+ A2 m
O(a)=1/P(a)
; I8 S/ E' L- y# h8 M9 u- d E8 b8 l同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率
$ ?- r* R6 P+ D0 L* z! KO(h)=1/p(h)
; C& j, P) J+ G4 mO(a)=1/[P(d)+p(a)]
9 x, u; \$ p( Q四、平半球盘的计算描述8 _. a3 O( r/ }% V( G) F
这个稍复杂一点
' v' d' n2 b" D& y, @ [& d接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况): z; y& g; ]1 {7 K! x3 i" R" V
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:
1 d$ @' s8 h0 F9 G# g: c{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
7 p! B) o% o8 V) U) {R(1)={O(h)*b(h), 即上面所述的A(h)结果发生5 Y% e* U+ J& n2 h$ H: F
{0, 即上面所述的A(a)结果发生2 n) }+ R2 i) w" D7 t# B" t
以及+ f+ v+ E9 Y3 ]& K, H
{1/2×b(a) , 即上面所述的A(d)结果发生
# C8 e( w3 A+ w. P7 xR(2)={0, 即上面所述的A(h)结果发生3 \7 N! J6 D( A, D+ k x
{O(a)*b(a), 即上面所述的A(a)结果发生
1 p% y* [+ h. ]0 t4 E投注主客的期望回报总数分别为
4 A; f7 T1 B7 Q8 _* P3 Z) U$ a# fE[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 \8 L7 D4 l9 p$ q( qE[R(2)]=1/2×b(a)×P(d)+P(a)*O(a)*b(a)=b(a)*[1/2×P(d)+P(a)*O(a)]
2 x. w4 [, C3 a和上面计算过程相似,得出:- B1 d. {3 K. W6 i" `
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
! i8 R& b* e) S0 T; a. Q: [$ nP(d)×{[O(h)+1]/2}+P(h)×O(h)=1( X! @/ o( N0 F
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
( i4 V$ S$ U5 m1 X0 b- F7 HO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h)): j! `. U+ M. U9 d; p @- t
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)7 `5 K. G0 e. ^+ H0 o0 @) Q
1/2×P(d)+P(a)*O(a)=1
0 k4 u, ~: w* L* C3 L+ [O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
# t1 A9 }# j1 M% o" p9 x同样主队让平半就分别是8 H/ S; L6 d. S# {+ x" F% a
O(h)=(1-P(d)/2)/P(h)
) ~1 E+ I& R4 j8 D5 f1 Z/ t1 IO(a)=(1-P(d)/2)/(P(d)/2+P(a))
/ _0 H; H$ u: f$ F k0 ?5 d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)5 D6 L: ]6 K+ T8 x' k8 |- u: Q! D; X
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
$ e! \7 G8 J- P- Q# BB(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}0 {& @9 T, {" _. S) U- R
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}+ }" {+ i# f9 j- R. M; _
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
& ]% V* u) c5 e2 @. B/ f; w4 v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:
, e) q/ M7 X/ v1 O' E' D{b(h)*O(h) , 即上面所述的B(d)结果发生. v$ F5 v1 t: a; l3 @
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生, V9 S: ?0 g4 H% Y" j) P
{0 , 即上面所述的B(a)结果发生
+ }5 K3 P V+ Y7 r8 M以及8 F) h5 r$ f' B1 i1 P
{b(a) , 即上面所述的B(d)结果发生
% Y) R4 j8 f3 R' vR(2)={0, 即上面所述的B(h)结果发生' b9 h& I3 s+ b; V# t
{O(a)*b(a),即上面所述的B(a)结果发生
- ~9 y: L# P) S$ q; t6 Z投注主客的期望回报总数分别为
7 Y9 i! L7 t6 i- H0 M8 A: V6 jE[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)]
1 e o7 `/ ]% w# d6 S3 ^E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
3 x) O1 n5 }1 F8 e+ d5 z- f假设实际投注回报与期望投注回报相等7 o% o* O& u6 F* b) ^! S
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
6 q+ C" Z/ m2 P9 _. B' QP(h)*O(h)+P(h1)-P(h1)*O(h)=1
) l3 I6 Y; G7 L/ E0 ]3 QO(h)*(P(h)-P(h1))=1-P(h1)( a9 O: v: ^; E
O(h)=(1-P(h1))/(P(h)-P(h1))
" T8 b! U- e) [* eE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)3 S1 b% H$ D. F1 u2 i
P(h1)+O(a)-P(h)*O(a)=1
# B( a! |' A% y# E1 ]. N, b0 D- LO(a)*(1-P(h))=1-P(h1)% o( M$ t# ?* U0 q9 Z/ r% l# \8 C
O(a)=(1-P(h1))/(1-P(h))
! r2 }8 ]; Q$ X+ Q' ~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。6 h# l3 p- b- i$ \, S, V2 e0 h! v
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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