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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。) |: S$ Y9 E7 m1 y
那么,平局、主胜、客胜就有以下表达式:( p0 \% d+ }- E6 n( K/ r: U; f
A(d) = {W(ij)|i=j, i∈N, j∈N}
2 l; a! X, z, ~A(h) = {W(ij)|i>j, i∈N, j∈N}- R; q! y8 Y+ O7 {
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]:
1 T4 Z; p- \* z( _ l5 m6 WP(i)=P(Ai), i∈{0, 1, 2}
4 e* g6 B. y8 D5 @- }# P1 e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 A, k& E, N' @. w4 V& A
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 |# {% R. r7 t+ C: J{b(h) , 即上面所述的A(d)结果发生5 n! X) }/ V7 q" p1 H( W) F; t2 e
R(1)={O(h)*b(h),即上面所述的A(h)结果发生2 A) x0 @. G: O: K" j
{0 , 即上面所述的A(a)结果发生
& l" |- _! p, G y: ?7 I以及7 a% ~; @$ O/ `* b4 A% N0 c3 {9 K
{b(a) , 即上面所述的A(d)结果发生
9 w+ ?2 R5 {4 u4 K) Z" N4 v, QR(2)={0, 即上面所述的A(h)结果发生
5 s9 g! i/ g! @2 v{O(a)*b(a),即上面所述的A(a)结果发生
+ x4 p! B1 F2 X u' ^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 a6 e8 K1 a: A9 n9 s( Z
那么投注主客的期望回报总数分别为4 X) U% A) L3 }% `9 o
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]
9 R' K; M3 H$ h+ H8 eE[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
8 r1 X# G0 `6 j$ ?7 E; r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
q( Z, u* [, n1 F0 ]) |" c$ fE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h). e+ U4 l$ }7 M8 `5 C% V
P(d)+p(h)O(h)=1
8 V' f1 R' }* n3 y/ \) 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. w; Y2 d: V( K$ c
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)0 }2 z; n* A! ~
P(d)+p(a)O(a)=11 Q+ P8 R4 A- ]3 ^
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
4 d, I/ A {+ `7 P4 k" 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
8 e- O% m) h: z" @# P/ W! d' H三、半球盘的计算描述
\4 @7 {/ E! `+ L+ l接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
" ]1 R( @* k8 i9 f1 f- \$ p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:2 O( B0 M2 I4 e' P1 j, z
{O(h)*b(h),即上面所述的A(d)结果发生
/ v: R% v$ p& g( RR(1)={O(h)*b(h),即上面所述的A(h)结果发生0 T; z M/ f; {# w N: {
{0 , 即上面所述的A(a)结果发生5 O1 W# X3 \9 v0 T6 X( v. C
以及
" D' P- N& d# w8 P{0 , 即上面所述的A(d)结果发生
+ V: ]- m9 z1 \6 I- c$ X3 e# w5 UR(2)={0, 即上面所述的A(h)结果发生3 N# H- l7 Q+ k \; `! o7 F' |9 C3 J1 {
{O(a)*b(a),即上面所述的A(a)结果发生
, [6 b% N* K! S$ i) ^( b% e如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
7 P+ U( s5 c3 l1 g; x* M) ]投注主客的期望回报总数分别为
+ k+ |, R: ^5 [E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]2 t0 s f1 c- q% z
E[R(2)]=P(a)*O(a)*b(a)
R" o1 K# F( i8 R# q K' u假设实际投注回报与期望投注回报相等* q7 Q. B/ |9 j0 o" n1 z* d1 V, v
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)* b+ ^- s2 v0 M: ]& |1 k, e
O(h)*[P(d)+p(h)]=1- ^; f6 D$ c9 h& G! ^
O(h)=1/[P(d)+p(h)]0 d6 i) t3 c. _3 u0 U$ t) B6 W, v; H
E[R(2)]=P(a)*O(a)*b(a)=b(a)
6 f, Q8 q8 p9 \. w; X' RP(a)*O(a)=1& e8 {/ m$ Z8 N7 z# F; \
O(a)=1/P(a)0 L, H' V+ e5 j+ q3 f1 A
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率
7 {6 Y: y8 O/ R& p# N; K/ [O(h)=1/p(h)5 l) w N3 k; y9 H0 }
O(a)=1/[P(d)+p(a)]& L; ?2 y. L/ N) \
四、平半球盘的计算描述
$ |8 r4 M! B; f9 F" j, c这个稍复杂一点3 C4 O7 Y8 P! o( i
接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
7 r" Z0 r# Z6 \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:4 p1 _4 Y' ]% Y. ]; r% a& _
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生 z# b6 l& K0 a, F* o4 O8 i
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生; f' U# g0 D) I" {
{0, 即上面所述的A(a)结果发生
1 z, J P( U! e. p3 W2 A以及
& Q3 a/ r- f$ s3 C{1/2×b(a) , 即上面所述的A(d)结果发生
- I- ?3 r, l* H; b8 i- FR(2)={0, 即上面所述的A(h)结果发生: n( z) P# Q g
{O(a)*b(a), 即上面所述的A(a)结果发生, p: S5 c" S3 n7 c8 y3 U0 Z
投注主客的期望回报总数分别为
1 i/ `1 q9 e; f7 l5 h) V2 yE[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+ {6 Z, }- C; x+ [$ C+ u' ]
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)]% p$ g9 w* y& s! K
和上面计算过程相似,得出:
2 C! x) L _$ r; A6 z( {9 ]4 f5 p; TE[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)1 T) n3 i7 F& O5 P" j$ R
P(d)×{[O(h)+1]/2}+P(h)×O(h)=1. ?+ q+ F! Q9 T( K( w4 `
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1& V) N$ H# @$ f! b3 ?# C
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
7 ]: a6 q, W' }8 T+ ~E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)2 Q+ P0 R" X. r. {7 m# Q( u" J
1/2×P(d)+P(a)*O(a)=14 l) M% p$ X- M p# c$ G% h7 c; C B
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
* f* Y1 A: G& b, m同样主队让平半就分别是9 J+ z' y! ]9 ^
O(h)=(1-P(d)/2)/P(h)
$ M* R) u9 r7 V6 \O(a)=(1-P(d)/2)/(P(d)/2+P(a))
3 h8 o- O. c" H- T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)
/ h7 m0 Z% J- c% F+ I: {& b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
/ M Y i; [! I, q( ]B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
/ _% g7 d3 S, ]. H: @- s, qB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}& |' \, q0 `: h" k, h% E: ^$ S) e1 s
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
: ~6 @; `0 J9 ]) D- D) m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:
K" ^8 J w0 Y; n" g/ T' e# V/ K{b(h)*O(h) , 即上面所述的B(d)结果发生/ \( s @. I8 {, K. T
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生) N- K7 X# A: P3 V
{0 , 即上面所述的B(a)结果发生2 {- q. |# t5 b6 {4 f& E
以及
! _, I: W4 `8 N$ |, Z{b(a) , 即上面所述的B(d)结果发生
6 B% M$ D3 I4 E, C( V( L' ~, v% I1 R6 KR(2)={0, 即上面所述的B(h)结果发生
! r6 E" ?, F8 R! c5 @{O(a)*b(a),即上面所述的B(a)结果发生6 T; F) \( j* m d& h" [
投注主客的期望回报总数分别为) H# [8 `1 j# y, S3 N$ {) T3 w
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)]
# a' P# n0 K) G& r% F& j7 ~$ V! ^8 KE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
: k5 k% h7 W& u0 s1 v' U假设实际投注回报与期望投注回报相等* o$ _3 K/ D2 v- g3 H9 p) H
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h); Q* x5 b7 s. H" y; J- g
P(h)*O(h)+P(h1)-P(h1)*O(h)=1
G* y. x! g9 ^O(h)*(P(h)-P(h1))=1-P(h1)
1 N& H% }$ v; C- CO(h)=(1-P(h1))/(P(h)-P(h1)). k- E/ v6 x' i: G
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)4 h$ z6 \: e7 m) m2 H- h
P(h1)+O(a)-P(h)*O(a)=1
" ~; q5 P8 G3 O% A5 YO(a)*(1-P(h))=1-P(h1)
' m5 i6 J% k6 `$ F# mO(a)=(1-P(h1))/(1-P(h))' d2 n D( E- k( u
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。+ q+ z& F( r# \5 D" E% x/ T/ n9 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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