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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。
9 D+ k9 n' q/ U1 n- ]% _$ r那么,平局、主胜、客胜就有以下表达式:. w- ~- E" S! @6 Q) l6 A
A(d) = {W(ij)|i=j, i∈N, j∈N}
+ P! m. k# Z: }A(h) = {W(ij)|i>j, i∈N, j∈N}* E3 C I, \- E1 T1 j
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]:7 @. L' g9 i# e- Q
P(i)=P(Ai), i∈{0, 1, 2}
9 b E3 U, _% `0 T: |3 T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)6 s7 i; P2 g4 d. e( K. s0 y1 L
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:; `0 ]7 D% P: d2 ?
{b(h) , 即上面所述的A(d)结果发生& D3 t7 ^# M, z' _* A' N
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
* G/ i& A% _( ~- i) s{0 , 即上面所述的A(a)结果发生1 t2 X/ @2 H) D, j. d
以及* n I/ v% n* z; I" k- f
{b(a) , 即上面所述的A(d)结果发生
' I4 d( D$ c' c2 R9 _( \2 tR(2)={0, 即上面所述的A(h)结果发生% Z0 x; C" B. i5 v( d) m1 N
{O(a)*b(a),即上面所述的A(a)结果发生0 u" m4 I, k" F; f9 p7 u1 O( ^
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# L0 \) w+ N3 ~4 X! e) j
那么投注主客的期望回报总数分别为
" [) g x* x: R) E& d7 \E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]
# H9 G( @; R* ?8 a$ HE[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
( i0 u( _8 a: P ~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 g8 t6 P2 d. ?' i" S) dE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)# A5 D* |" m$ c. r, Y! L
P(d)+p(h)O(h)=1& p6 X- ^5 q' z' r- Z8 d) k% g8 v
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, X% Z1 a+ h0 e5 q- e6 @0 b$ H8 ?; R
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)5 b N$ T! u" P2 ]* ?; |. W4 K A8 M
P(d)+p(a)O(a)=1" |; D9 q( F0 M: R* _3 z- v7 ` F" L
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0 B4 w; V, I* @3 G3 L* m
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
' `5 F0 t% \% n. j6 L' W; x8 o( h0 f三、半球盘的计算描述+ U% W4 G. M( f. s( I
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
% a& K2 F! R9 I6 T5 x$ E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:' k8 M: q( B, W# ^0 l" F) i& N' k
{O(h)*b(h),即上面所述的A(d)结果发生1 ?, i; K+ y P3 }3 ]
R(1)={O(h)*b(h),即上面所述的A(h)结果发生; k9 t/ W F5 _ R1 \
{0 , 即上面所述的A(a)结果发生6 ? G: M+ Z2 m( x0 x, l' s7 g
以及
5 k( n* I% H- |* Z) `0 l' W+ q{0 , 即上面所述的A(d)结果发生0 R. H* ]6 f2 n( g1 `( a( E* v
R(2)={0, 即上面所述的A(h)结果发生 p+ C2 p* h3 q; d/ p, q! |/ L
{O(a)*b(a),即上面所述的A(a)结果发生
& g5 _. f- K0 U% o. t8 ~! @如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
+ V' k" z x; j9 w4 G投注主客的期望回报总数分别为6 R$ f* L! k" q% m+ R5 V& Y `; V& Y
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]; i7 M( q/ F4 e/ _8 h& u0 h" t+ B3 c
E[R(2)]=P(a)*O(a)*b(a)1 b* |% T9 y' V% b2 V% {; m
假设实际投注回报与期望投注回报相等
1 f0 x" S$ I9 l" W% IE[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)( O6 Y: r2 ]- ]
O(h)*[P(d)+p(h)]=1. J; }1 M8 t7 [0 q3 ~
O(h)=1/[P(d)+p(h)]' K3 U' x' f) }0 C6 r( l
E[R(2)]=P(a)*O(a)*b(a)=b(a)# D8 e* W% t/ h# K
P(a)*O(a)=16 s/ u0 a9 D2 N
O(a)=1/P(a)7 O. G$ T- s% Z
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率
, V. q: D$ ]* C* y/ oO(h)=1/p(h)( J3 y- x) P e+ Z
O(a)=1/[P(d)+p(a)]
0 P: D( V& E, }* d. e四、平半球盘的计算描述
! b8 f, b: A1 a6 M/ F8 b这个稍复杂一点
( W8 i! M9 V$ |/ D$ o接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)5 `4 q$ d& X" N0 h
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:! N3 K3 ^7 W) f- y( H1 r% }
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
/ O6 V- C- I3 ]+ C9 z$ C. YR(1)={O(h)*b(h), 即上面所述的A(h)结果发生 M9 D& ?2 T2 Q3 X0 u. A" |: A- v
{0, 即上面所述的A(a)结果发生
* \ E. \( f9 c& S6 g R3 Y以及
* ]: m3 V7 W }" J& P5 h2 K2 W. @3 R{1/2×b(a) , 即上面所述的A(d)结果发生* }7 v( x- ~5 ^
R(2)={0, 即上面所述的A(h)结果发生$ T6 g% K7 b5 I1 f' a6 J# F, l
{O(a)*b(a), 即上面所述的A(a)结果发生
+ c- N) ]/ D P5 {+ n* u; h投注主客的期望回报总数分别为
7 v7 |- T- D0 s! q LE[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))
: {9 i5 P. B9 Z4 K5 kE[R(2)]=1/2×b(a)×P(d)+P(a)*O(a)*b(a)=b(a)*[1/2×P(d)+P(a)*O(a)]
* {! Y6 e4 B' v- W3 a和上面计算过程相似,得出:8 F, c: _! W1 w
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)9 v/ r, w2 _0 p6 \$ o; L3 j6 w% g
P(d)×{[O(h)+1]/2}+P(h)×O(h)=19 {& w6 i9 B$ |* _( V+ A
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=15 ?6 v3 N' @' ^9 _6 q
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
3 m; }7 i' x* |& N1 V! ME[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)* _- A' L& m" v2 R9 {* }: `
1/2×P(d)+P(a)*O(a)=1
& q+ E _ U/ F# h% |O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
, g. k4 |/ L) M0 d+ B同样主队让平半就分别是
( D1 t" q; r- x0 o8 b& v; rO(h)=(1-P(d)/2)/P(h)
# H* z6 S; f4 K2 ?7 rO(a)=(1-P(d)/2)/(P(d)/2+P(a))
; h/ ]4 z( C6 n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)
) H9 V- ]' q' S0 Y. U* R6 i( ~% S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
+ {) r* d" s. E7 `) V; J/ y) ~( [B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
" V: K* ~0 {, cB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}, Z {0 j- o. H5 {
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数- d! g: a; Q/ h/ \
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:
) W$ s5 l9 z0 Y0 f, B/ d{b(h)*O(h) , 即上面所述的B(d)结果发生% _- g: C0 k: X; l N
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生% N L" W0 i+ P6 }4 V! }
{0 , 即上面所述的B(a)结果发生
! P" R! a. E5 E4 u% P: I! e' A1 O以及4 z8 a! Z5 E: D' J+ r: }2 y
{b(a) , 即上面所述的B(d)结果发生+ E- n+ d8 W: W7 K4 g7 m7 _, _
R(2)={0, 即上面所述的B(h)结果发生
; Z/ c0 T5 T+ l; J' \: _2 O{O(a)*b(a),即上面所述的B(a)结果发生. B/ Z5 N. W' ~; b4 `* C1 S
投注主客的期望回报总数分别为- k1 V0 Z: f1 W" 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)]
- g, o: g$ R# i7 M0 |4 fE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))# `) `5 L5 E- F( Y# y0 X4 O( E
假设实际投注回报与期望投注回报相等
+ b6 O7 y3 W/ Z2 yE[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
/ k# ]! p8 G3 g) x2 x, kP(h)*O(h)+P(h1)-P(h1)*O(h)=1 W: M( F/ }6 A. o/ |& |
O(h)*(P(h)-P(h1))=1-P(h1)1 L( o0 t& ~4 W4 r: Q) H
O(h)=(1-P(h1))/(P(h)-P(h1))
& `6 g, a# `* a' q! f8 tE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
2 v- F. q" e3 OP(h1)+O(a)-P(h)*O(a)=1( S7 D- H9 d6 q+ b7 @
O(a)*(1-P(h))=1-P(h1)
# I m4 g0 K$ ^( g6 CO(a)=(1-P(h1))/(1-P(h))
, y7 j: {" M8 b E [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 m% E6 U3 \$ s+ b5 K5 D# [3 A
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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