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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。
* a* {9 F& r7 M( U那么,平局、主胜、客胜就有以下表达式:) S6 h* M; n f" R! t: D5 h/ C
A(d) = {W(ij)|i=j, i∈N, j∈N}# @6 T3 x: b" r) t$ ^3 p6 O$ E
A(h) = {W(ij)|i>j, i∈N, j∈N} M& L$ Y R# Z& o
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]:
{( `! f+ Q4 x" l# S$ a, bP(i)=P(Ai), i∈{0, 1, 2}
- }2 L$ }+ w, ^# z# d0 |: ?' 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)
4 Q/ u- G j/ W* T# j. D. z; l7 Y' R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:8 y+ R0 u6 k7 M" E" Z; L
{b(h) , 即上面所述的A(d)结果发生
) P& E/ N6 Q" E. CR(1)={O(h)*b(h),即上面所述的A(h)结果发生
U( F9 B; j/ j0 L, T6 [9 l{0 , 即上面所述的A(a)结果发生: k; [7 i" ~ I6 u, _4 H) z
以及
) z: N8 c0 d E/ o& E9 Q{b(a) , 即上面所述的A(d)结果发生
- X) u! Y% t: |. n0 @8 N BR(2)={0, 即上面所述的A(h)结果发生: N% j' N/ p8 ~. O" C0 b1 i
{O(a)*b(a),即上面所述的A(a)结果发生2 ^% u* v1 G. j2 H- X8 F& ` m
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
3 r3 y, ~0 g0 R; `. Q' ]) r那么投注主客的期望回报总数分别为
/ o: P- R. Q) c: F* }( hE[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]
) y/ `) v7 ^8 I0 p8 O2 wE[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
4 @6 P. S7 h3 J8 M9 T$ W6 W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
# Y0 t* ~2 G9 `5 |, J3 P( i& VE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)% o9 o) w1 m+ M: B) E* c$ D
P(d)+p(h)O(h)=1
) s6 c6 M) X: q' b ~# vO(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式
- @( s' t r! a; G! }4 p# D# }E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)9 r$ t+ P9 f$ p- W& ]
P(d)+p(a)O(a)=13 j$ F4 X4 t6 B
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& I% Z, P4 f3 n1 i' s' }1 [& F2 W/ s1 j2 J
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! N: C2 r. z7 D/ W
三、半球盘的计算描述0 ^* V- N/ b4 f8 c6 d. e
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
/ P# V# K% l$ ?# O: O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:
+ E: I# o; N( O% w{O(h)*b(h),即上面所述的A(d)结果发生2 { b9 ]" k! X4 F. D/ }+ \
R(1)={O(h)*b(h),即上面所述的A(h)结果发生7 M+ J' @2 n2 _
{0 , 即上面所述的A(a)结果发生/ ^& p' o& E( z
以及! C, B) o& b# h) M5 U
{0 , 即上面所述的A(d)结果发生
2 x4 D& E- z4 l$ cR(2)={0, 即上面所述的A(h)结果发生" ]8 a) e! o6 A3 Z
{O(a)*b(a),即上面所述的A(a)结果发生
: m" c/ n) {& s" E/ r如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
; {5 K; O2 s" \" G" P6 p+ o投注主客的期望回报总数分别为 j) Z; b& v5 G; T$ K
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]3 f0 W1 y5 q( s" L% h7 d0 U; ~4 P
E[R(2)]=P(a)*O(a)*b(a)2 s2 l; v( c& B9 F% }
假设实际投注回报与期望投注回报相等
- ?7 P1 Z7 ]* O- m% B3 W; v% kE[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)5 {. l8 q# o# l" Y. t. r
O(h)*[P(d)+p(h)]=1
) ^. B/ ^# f5 X, U, \0 R7 sO(h)=1/[P(d)+p(h)]! R* i- l6 W2 a; _
E[R(2)]=P(a)*O(a)*b(a)=b(a)
0 E4 O/ c# Z3 m# f- T3 nP(a)*O(a)=1
' F) {3 `4 M0 S) M* _* b% pO(a)=1/P(a)8 z# p( ?" G; F" F, q/ Q ?7 C
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率! y3 P0 D+ D) Q( f5 g4 w: n
O(h)=1/p(h)
^. r1 G( L' ]( CO(a)=1/[P(d)+p(a)]3 ^3 V, X9 i8 }) q7 ?1 @7 _
四、平半球盘的计算描述
+ R, G) T+ W, P4 C [: d8 N这个稍复杂一点
! Z) o# m8 x# S2 M$ @) P接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)% Y' \8 t( f( F8 P: x' P. W' j
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:
/ A: M* W4 I5 U{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生) _% p; p0 R' k, A0 P F3 C, ^( U3 c, y
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生
( p8 P; V3 c5 E+ X1 P8 Y{0, 即上面所述的A(a)结果发生
" z" b9 s* u7 h+ o以及
2 T, R4 A4 U5 \) \+ P! x! i{1/2×b(a) , 即上面所述的A(d)结果发生9 s# b5 g! M9 r
R(2)={0, 即上面所述的A(h)结果发生; Y, s" h- V% h) l" @, _8 n# ]
{O(a)*b(a), 即上面所述的A(a)结果发生
9 l" {) ]$ A0 z4 x! x. r$ x9 F0 e投注主客的期望回报总数分别为
8 p* s, {/ o/ P4 D6 ME[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))8 C. m8 d t* _/ `0 U2 b
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)]
6 g8 t w! P, A* Z# o和上面计算过程相似,得出:- a" l* i5 h6 z) Q$ X, s) v0 ]5 x
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
8 L4 m* W5 a: @4 X5 q* k" AP(d)×{[O(h)+1]/2}+P(h)×O(h)=1
/ C0 O2 Z0 f+ {! qO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
8 R* j) d4 n d. y/ k! gO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))1 I% C. {. n2 p2 s; y
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a), ]- u; e2 Q7 Q0 \% t
1/2×P(d)+P(a)*O(a)=1
) X3 C# [ D# ^1 {O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)1 W; V! p& a$ M6 ^, e0 c/ j. P
同样主队让平半就分别是$ V: ?6 T- N; u1 F" `: m
O(h)=(1-P(d)/2)/P(h): }' @9 h9 ^% [3 l0 `1 m
O(a)=(1-P(d)/2)/(P(d)/2+P(a))4 [1 ?& g6 g( X
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)
H6 Q) |1 u7 h# n [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
+ L8 k; z1 `# J4 bB(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
0 v8 P4 w+ i7 F7 v5 w. PB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}( B' U1 _) j9 j0 {5 [
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数& s% A0 Y, ^1 B- _
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:
# P& D" n7 a2 y5 D: u{b(h)*O(h) , 即上面所述的B(d)结果发生' A9 g) S% v) ^% P; V2 e! j3 c( m
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
) d7 P/ w+ L# G0 P3 P{0 , 即上面所述的B(a)结果发生9 x2 F/ h8 r0 r- W
以及
% z& E8 O3 U9 Z& z& L+ Z1 `{b(a) , 即上面所述的B(d)结果发生
1 y1 ~; E/ m/ @! i2 t9 SR(2)={0, 即上面所述的B(h)结果发生1 m! q; w4 @: v n# k6 {
{O(a)*b(a),即上面所述的B(a)结果发生/ C3 v; g8 ~8 q
投注主客的期望回报总数分别为. i. C5 \- s8 n$ \. A
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)]+ |$ \" {2 e, d5 ~$ i: S. ?5 X
E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))# j4 Y% }; D' a" k
假设实际投注回报与期望投注回报相等 a& G; v7 T% @
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
- P) r* e3 A; RP(h)*O(h)+P(h1)-P(h1)*O(h)=1! j6 x- X/ H9 N
O(h)*(P(h)-P(h1))=1-P(h1)
) H8 \+ o j1 t6 lO(h)=(1-P(h1))/(P(h)-P(h1))1 z$ p+ D! X+ ^' b5 e! |8 {
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
( }* f4 _" a: x2 S# AP(h1)+O(a)-P(h)*O(a)=1
0 T( ]6 v" X ^$ c0 pO(a)*(1-P(h))=1-P(h1)
% b2 Z# i7 m6 D$ _, ~2 oO(a)=(1-P(h1))/(1-P(h)), b3 h# o' k3 |6 t! F" t
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。9 |# k/ Z; h u; f6 l& K/ b
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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