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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。
& }8 t; t) I! k; p2 ~# a那么,平局、主胜、客胜就有以下表达式:! n; v! y: K( Y' c
A(d) = {W(ij)|i=j, i∈N, j∈N}
5 h$ c, l2 s5 \! C& JA(h) = {W(ij)|i>j, i∈N, j∈N}
1 b$ s1 [0 b2 @4 C A3 DA(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]:& t0 v. i7 F: i( Q) Y* O
P(i)=P(Ai), i∈{0, 1, 2}
6 e4 h9 K4 E: ?3 H" z o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)
) b7 |8 e& U4 K$ U; V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 F% i/ O) N e. C6 H{b(h) , 即上面所述的A(d)结果发生5 u: `( h" X0 \- Y+ [
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
& U! t% o* c( W{0 , 即上面所述的A(a)结果发生
; Z( h( u- W# q8 X3 q1 K: l以及9 M# W8 \+ L" d
{b(a) , 即上面所述的A(d)结果发生- |' f6 R# [0 U
R(2)={0, 即上面所述的A(h)结果发生3 V, [3 E6 x% v- @. Z$ D/ L
{O(a)*b(a),即上面所述的A(a)结果发生$ R* i3 w0 Z0 v. y3 N l; b
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
0 A0 x( t; e% g, V+ @0 i那么投注主客的期望回报总数分别为
2 @5 C8 |5 @: O( nE[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)] g1 ?* W, _4 V6 e" Q+ m: V5 L
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
6 O" _' E" h6 K1 b4 O% V. a' N4 [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 v& B5 k4 y: G' m& `* N0 G
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)2 s# b/ @; p8 B
P(d)+p(h)O(h)=1( i( T8 {7 S0 \4 b
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5 ^* \" b. A9 V+ X, q
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
9 N2 s4 L/ @: u- tP(d)+p(a)O(a)=1
" ?- z. \$ N" d$ r5 WO(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式
; a' F$ T. C: [$ v0 G/ l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( V/ c5 I8 {& u% Z ?$ F+ \
三、半球盘的计算描述
* c: }* u% g" P! f$ P接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
. X0 }9 i% g' h; S0 f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:4 ]( {! O4 n/ c5 q
{O(h)*b(h),即上面所述的A(d)结果发生! v8 V8 j* L) K+ U N* l F1 w$ o
R(1)={O(h)*b(h),即上面所述的A(h)结果发生9 `& X7 Y% s- Q, G! F* ^
{0 , 即上面所述的A(a)结果发生
# v0 g/ B. G% n" \以及
7 k/ v# [% a; w. V) P: I{0 , 即上面所述的A(d)结果发生' c2 ?; h/ c$ _
R(2)={0, 即上面所述的A(h)结果发生
& N: o& }/ w' Y) P{O(a)*b(a),即上面所述的A(a)结果发生8 Y( _4 G! [5 {* h a3 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
; r) J9 l2 }& s# B/ t% {) R投注主客的期望回报总数分别为2 @( ^! N" W' |- O3 A% p
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]3 u: y5 s" N0 V% A
E[R(2)]=P(a)*O(a)*b(a)
5 k% X6 P* a6 A6 g假设实际投注回报与期望投注回报相等
% ~% m' s y" C+ VE[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
% c! U1 p; F, t/ ~6 qO(h)*[P(d)+p(h)]=14 d1 M# m+ j- F! k8 K2 ?. t" V
O(h)=1/[P(d)+p(h)]
. C. y1 d. l- z; s, F" F* J" p) pE[R(2)]=P(a)*O(a)*b(a)=b(a)
n) B8 C+ R7 gP(a)*O(a)=1
4 e) ^! u6 |( l7 n6 KO(a)=1/P(a)
! J& y% d4 `" }同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率8 Z6 x# \: Z8 s. d
O(h)=1/p(h). J7 S% w# i8 C( o( D6 }+ Q: Z
O(a)=1/[P(d)+p(a)]
- R! n1 A. {, M P2 n$ Y5 T& C四、平半球盘的计算描述
# ?2 b/ ]1 I- u3 V这个稍复杂一点
7 H. X% g; q2 Y( ?7 ^ W. p接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)* e s f1 N+ R, X6 i( k
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:+ M9 d1 H& x; V2 A( }# r4 z5 |
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
% x8 `8 k$ X" l) }R(1)={O(h)*b(h), 即上面所述的A(h)结果发生
" K! [0 P# t" r+ d i8 `{0, 即上面所述的A(a)结果发生
( Q* Q" k2 A4 P: L, \1 F4 v6 A1 r以及
% S% a# {' C, `+ o{1/2×b(a) , 即上面所述的A(d)结果发生
0 d" h9 d, v& E% T& AR(2)={0, 即上面所述的A(h)结果发生- v4 h& e5 R) q% P7 ] k
{O(a)*b(a), 即上面所述的A(a)结果发生/ C T6 C# b% _3 i: Y0 s
投注主客的期望回报总数分别为, ] B1 h$ B3 z' `. M# ]0 {
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))
( H6 j8 L& N0 N. v* dE[R(2)]=1/2×b(a)×P(d)+P(a)*O(a)*b(a)=b(a)*[1/2×P(d)+P(a)*O(a)]
4 C3 s) z! O5 |5 I% o: T8 P/ I和上面计算过程相似,得出:
, P( p5 Y3 {/ s+ [8 R! _! a0 uE[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)' \* p; o# s) }7 L
P(d)×{[O(h)+1]/2}+P(h)×O(h)=1
1 ~6 K7 e: D, ]6 W6 aO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
+ o! L$ W/ q/ r3 Y5 t9 p# GO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
5 V! h$ `6 \! k: v8 }( r4 fE[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
# R& y& S4 u* f1/2×P(d)+P(a)*O(a)=1
0 n0 L6 s3 D) l1 WO(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
% H1 A$ N" U- y. C+ q {同样主队让平半就分别是7 r+ f/ |$ I U& y. ~- B% Y
O(h)=(1-P(d)/2)/P(h)6 b& Q3 P/ T4 m& m( e6 @
O(a)=(1-P(d)/2)/(P(d)/2+P(a))8 \7 B% Y" t* p! C0 F
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)
f6 l, S8 i, M/ t& ^# d' t7 \: R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 Z1 t5 g; f: p5 ]5 G# lB(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}. t3 t5 n/ ?+ x4 R# c( k* L- Q
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
: d: C3 y1 i. p# x- [" hB(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数4 P1 ~( j9 q! w7 h0 `( J) L. 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:
% V( q$ H, Q2 ~; o3 m{b(h)*O(h) , 即上面所述的B(d)结果发生8 l* {) Z" L* w+ @: Z- a
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
5 x" V3 ?& ]; m8 B. g9 c{0 , 即上面所述的B(a)结果发生8 l1 J& R" ~+ p9 @8 n
以及
2 L3 J) ]0 M. v+ N{b(a) , 即上面所述的B(d)结果发生
# r: W8 i l5 wR(2)={0, 即上面所述的B(h)结果发生
1 j( M" g. u/ j, }$ L5 w4 y- C{O(a)*b(a),即上面所述的B(a)结果发生
0 C5 K5 A+ E9 E0 |) J/ P' a9 ]投注主客的期望回报总数分别为
# }3 R7 [' C i+ S; a: B b SE[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 h8 s m, L/ u/ _
E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
2 R* d2 X# d3 e9 U9 C. L9 s$ _假设实际投注回报与期望投注回报相等
4 y x: y) F4 v4 q8 VE[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
( J9 M1 J' c/ R$ qP(h)*O(h)+P(h1)-P(h1)*O(h)=1
+ E- ]$ P/ D- {( w; MO(h)*(P(h)-P(h1))=1-P(h1)
9 x# ~% f) A: j) o1 J& T1 w$ jO(h)=(1-P(h1))/(P(h)-P(h1)), S/ I; b5 S% x% g$ q1 \
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)( k6 \. U3 [8 T( e+ f6 h7 E
P(h1)+O(a)-P(h)*O(a)=1
) H$ @9 y# _4 p5 F- w: ^O(a)*(1-P(h))=1-P(h1)
1 {( F" k; M9 o4 e; E( nO(a)=(1-P(h1))/(1-P(h))( [) [5 a2 _0 S& Z9 i" ]2 r3 k. o6 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。
7 z- g, B- q" f3 B% c) |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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