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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。
4 D4 v9 U; i% r5 B5 l那么,平局、主胜、客胜就有以下表达式:/ g$ |4 ]+ |1 ?7 }+ A3 l: {5 k3 o9 u3 k
A(d) = {W(ij)|i=j, i∈N, j∈N}# w: ~; ?1 g: @) g6 t7 M) R7 }
A(h) = {W(ij)|i>j, i∈N, j∈N}
* q8 [. y- }& _3 g7 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]:
3 m0 o& d+ E, q2 {- NP(i)=P(Ai), i∈{0, 1, 2}
% L A# S7 h, _$ G/ ]; k. a1 p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)
! I$ m5 |: y& Q2 h0 k) W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 f1 F$ j) K; u{b(h) , 即上面所述的A(d)结果发生3 x7 R, ]: v% R7 h- f5 i1 J
R(1)={O(h)*b(h),即上面所述的A(h)结果发生' B! r9 J" b5 l
{0 , 即上面所述的A(a)结果发生
6 W' O M* g+ P6 \以及2 s, \$ @6 r& Q+ C0 G/ @) T1 E& p
{b(a) , 即上面所述的A(d)结果发生) O4 K5 R# x% W& s
R(2)={0, 即上面所述的A(h)结果发生
& `$ `7 E y% G/ J' G" \{O(a)*b(a),即上面所述的A(a)结果发生! l) `, ~' D" R+ e2 j. k
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
: b) Y8 _+ |( q6 i! S5 c那么投注主客的期望回报总数分别为; D$ b$ S. p- I
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]) O7 U* C; u+ h: `! T9 E
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
. b9 q q0 x# k) {2 r9 H/ y7 }7 M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
- T$ X: a8 ?) f" w9 h% M4 l2 OE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)+ A0 L) ?& Q/ r) \$ C
P(d)+p(h)O(h)=1/ J/ z5 X- X9 U
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
3 C, ?/ r9 Y. z" ?/ K: JE[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
- u, z- p# k, }$ s# \" V/ PP(d)+p(a)O(a)=1+ g1 w9 E$ V/ e* s( C# p
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
9 \6 j5 G; T/ `/ b; z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
. W6 }8 R: n& C8 |2 V三、半球盘的计算描述
2 f5 P6 `/ a* p0 u: r6 t/ T接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)" h9 c% J C0 m$ l
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:
" }, i1 M5 @5 R: ]# W7 f- R9 e. I" l{O(h)*b(h),即上面所述的A(d)结果发生3 w' L5 o8 l# B; c% Y4 m: Y' W1 P, S- ]
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
, {5 J* O- l: ]" d" u& s{0 , 即上面所述的A(a)结果发生$ O. X) H2 u' ~% y K. ~8 L
以及
3 @- D) c6 `* f7 I{0 , 即上面所述的A(d)结果发生
/ N+ f+ H9 J# E% @R(2)={0, 即上面所述的A(h)结果发生
1 j! ]! q& u' x4 p* a: Z{O(a)*b(a),即上面所述的A(a)结果发生
7 G. ^; ~& H6 X如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
, Z1 U# ^- G' M3 _( ~投注主客的期望回报总数分别为" h) L0 \$ u1 m1 t, D" G$ P
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]2 L* b6 M, P, H" H2 d
E[R(2)]=P(a)*O(a)*b(a)
7 C8 l* M1 j1 C假设实际投注回报与期望投注回报相等' t4 q) c0 J! V6 B! e
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
4 h& [# _4 G; y' H' ]- Q2 KO(h)*[P(d)+p(h)]=1
, z$ l/ z8 h9 @! f0 V/ I vO(h)=1/[P(d)+p(h)]7 q; g4 x) ?# k) @* r+ K
E[R(2)]=P(a)*O(a)*b(a)=b(a)5 `, R, p: B' N6 h8 v3 M6 l: O/ Y8 W0 l
P(a)*O(a)=1* r' x7 r) Z5 X- x( J2 L3 ]0 P
O(a)=1/P(a)
8 Q! o) \6 n6 N同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率! \' L, z( s8 R
O(h)=1/p(h)
7 P& o* |. U: O. r/ q' m: X( lO(a)=1/[P(d)+p(a)]
/ Z6 Z& |+ u0 C- K ?& ^" g8 n9 Z四、平半球盘的计算描述1 f( C5 Y5 z+ [6 T
这个稍复杂一点1 Y2 e: L8 T7 p+ A. S
接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)3 _% x9 u t+ x1 g2 R. v3 z5 i
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:" u S+ i7 J# Z7 }) k
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
' f6 k/ b2 r9 qR(1)={O(h)*b(h), 即上面所述的A(h)结果发生
9 W* e& R% l& Y( p{0, 即上面所述的A(a)结果发生& Y$ z5 }$ \- W
以及- I! e# p8 ~0 c- ?4 e- G, Y$ n
{1/2×b(a) , 即上面所述的A(d)结果发生8 R$ T. s& `0 S3 U, H1 Q% x
R(2)={0, 即上面所述的A(h)结果发生2 c+ V9 w" e/ W$ d1 x
{O(a)*b(a), 即上面所述的A(a)结果发生
# r* Y$ z8 p' E投注主客的期望回报总数分别为* N: r0 m& H: G' {& h5 e. R: [; }
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))
# s# Q: i; P1 iE[R(2)]=1/2×b(a)×P(d)+P(a)*O(a)*b(a)=b(a)*[1/2×P(d)+P(a)*O(a)]% f @6 U- A {1 U3 U
和上面计算过程相似,得出:. r0 y$ x4 y" V9 R9 P9 J) }& e5 k
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
, n4 `0 v: F- `6 k% y2 t+ K6 CP(d)×{[O(h)+1]/2}+P(h)×O(h)=1
6 Q. D% B3 _' w5 e( g8 C# x* d" CO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
7 H! X* i* ]3 R _2 A9 }8 {! F8 ]) QO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
0 Y7 y* Z8 c0 V1 R8 U' S2 dE[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)! d3 i( f" U" p8 ]& [8 t- z$ R
1/2×P(d)+P(a)*O(a)=1
; o7 `. x6 _$ i* OO(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
3 d$ o9 b5 Z4 U同样主队让平半就分别是0 [8 i1 B: Z O2 w0 a" u1 B
O(h)=(1-P(d)/2)/P(h)
$ T% n9 @* ` r2 ^! @- W& rO(a)=(1-P(d)/2)/(P(d)/2+P(a))
0 T$ H- o& s6 N3 H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)
) g) R" z, v! a6 P& d3 p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( R1 F* e+ l- ]+ }% K+ s
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
$ `7 v, A) R6 u7 `9 o! A2 ^6 F* FB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}4 y# C# s. x4 J& D' {. p
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
o4 Z1 l7 W8 ~8 p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:
6 O* y5 M' k4 ^. A$ k7 e{b(h)*O(h) , 即上面所述的B(d)结果发生
5 d& v! H- E8 }+ c5 cR(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
3 F* ?0 Y* f' W{0 , 即上面所述的B(a)结果发生
6 C! N3 W0 A5 k$ F/ W以及
# g# u( s+ d; {5 E0 @1 ` s{b(a) , 即上面所述的B(d)结果发生/ Y1 N- O& k( X( k. s- O; b
R(2)={0, 即上面所述的B(h)结果发生
6 r5 P3 `# Z C% b) K{O(a)*b(a),即上面所述的B(a)结果发生
- t8 a( Y/ U$ i d, N% u3 d1 B投注主客的期望回报总数分别为
1 U8 \8 e% E) G$ BE[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 P7 r5 r+ n: r4 _- M% uE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
; d* l. W- U/ m2 ^3 c1 e# d假设实际投注回报与期望投注回报相等
0 [0 W s3 s1 D1 t1 [* S$ E4 G2 jE[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h) q2 D, f# V. b
P(h)*O(h)+P(h1)-P(h1)*O(h)=1
4 s" H' x" @' |7 V# N7 LO(h)*(P(h)-P(h1))=1-P(h1)
8 }2 y4 K, O& YO(h)=(1-P(h1))/(P(h)-P(h1))
/ t: j0 l; ]2 f" K. c* c& h" y! `5 ^E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)- ]- p) g, d* s" |! W, [. b
P(h1)+O(a)-P(h)*O(a)=1
$ ^- G& n( x& l b @1 G9 j' }O(a)*(1-P(h))=1-P(h1)1 V5 C, O( `8 t
O(a)=(1-P(h1))/(1-P(h))
/ l; t' e& ?8 Z/ @1 v* }1 c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。
% f$ x `; \5 R7 N$ H/ R0 Y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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