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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$ x* e- p; L那么,平局、主胜、客胜就有以下表达式:
' C; j D; o& M O. V9 B* }& _; yA(d) = {W(ij)|i=j, i∈N, j∈N}8 L) f1 _7 t, O0 P3 u
A(h) = {W(ij)|i>j, i∈N, j∈N}6 B3 D3 N+ x D4 a1 t! s
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]:( P) u, @" ~, u# l# M: g' d/ D' n# V
P(i)=P(Ai), i∈{0, 1, 2}
' M" n/ P4 \4 Z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)0 L% H( d% M5 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:
4 g) U4 z: G) a' V; b' ^; h6 k& d+ A{b(h) , 即上面所述的A(d)结果发生" }6 C/ Y1 Z8 ~. A1 e- \
R(1)={O(h)*b(h),即上面所述的A(h)结果发生8 B8 [, A& b _
{0 , 即上面所述的A(a)结果发生% H* c# Y7 \) A/ F: \6 N
以及! n9 q- `% v9 {
{b(a) , 即上面所述的A(d)结果发生
7 k/ `- O* d! q9 o# bR(2)={0, 即上面所述的A(h)结果发生
$ U4 S/ ?( f7 @. P{O(a)*b(a),即上面所述的A(a)结果发生 o6 [1 @( N. b c
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. t" M9 b' \( x" K! e, V Z- U
那么投注主客的期望回报总数分别为
1 d9 K) T2 W3 _) b) V E ZE[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]
1 P" P: G5 L: o3 OE[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
% i2 [0 Y" J; T1 C8 _0 m Y! @: 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
! h" y9 |' ?. {! b6 TE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h); u$ n, V3 g& ?6 N
P(d)+p(h)O(h)=1. A1 ^8 ^# ^+ k: H7 p' T
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
! L9 S: A: E9 {% }$ U4 z+ xE[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)
2 ~* A) ]# H0 @P(d)+p(a)O(a)=1
6 R( B& p8 B3 M2 E: TO(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式8 Q) |. u9 a1 N! h
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
C/ m3 ^5 `' w5 ^9 A6 T/ `三、半球盘的计算描述
9 A' B6 f8 {" t0 d接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
3 T# b6 i7 z3 ]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:
- H3 G9 E, }# s' e: ]( y7 [8 n{O(h)*b(h),即上面所述的A(d)结果发生 p% X0 s! r6 Z9 R9 \: K
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
) F; Y! T0 G: @{0 , 即上面所述的A(a)结果发生
/ T) @9 M: f. g7 i+ ?以及3 m5 K j7 z0 V* U* b ]7 S
{0 , 即上面所述的A(d)结果发生
8 l1 L: }" h6 q8 S* X$ p- n5 FR(2)={0, 即上面所述的A(h)结果发生# s/ Z$ G- w# p& }% W3 F7 `
{O(a)*b(a),即上面所述的A(a)结果发生+ U3 \* g6 t+ G* l T7 |9 ^
如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率" X( \+ d$ L( a( _ _7 Q6 o
投注主客的期望回报总数分别为; E# K; I" U$ W# H; Y( ]$ j# N
E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]! I+ M6 H" q9 F" @
E[R(2)]=P(a)*O(a)*b(a): s* Q L2 g, v4 O' p
假设实际投注回报与期望投注回报相等# E; M4 R$ L; k" N" E
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)) f5 D( Q& ~5 N
O(h)*[P(d)+p(h)]=12 i, e) I) O% C$ f1 N0 K4 T
O(h)=1/[P(d)+p(h)]
, j+ R) `( E; P. ?/ IE[R(2)]=P(a)*O(a)*b(a)=b(a)/ N1 R$ @3 a1 y: I' ?- `
P(a)*O(a)=15 D0 N3 N" b9 d# p: `7 ?7 x% v5 }
O(a)=1/P(a)" I4 K) M; m/ y q& \3 i1 c ^9 U
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率* F5 c$ }/ W; j/ F: t& z6 E
O(h)=1/p(h)- |% g3 Q W* B5 P5 K6 y
O(a)=1/[P(d)+p(a)]3 ^/ f T2 _. \. y3 k2 Y- z2 ]9 [
四、平半球盘的计算描述
1 ?* S4 s+ T: J; f4 r, O) u这个稍复杂一点: u+ b; i, j5 e, 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 i0 |" N o( h/ u
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:
% b" v& n5 l+ b7 Z: R% L; @{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
- a& G7 \+ K- P# o# A) JR(1)={O(h)*b(h), 即上面所述的A(h)结果发生
" g- M$ m, h9 h0 Q& F( S3 i{0, 即上面所述的A(a)结果发生
1 U& l- Q. r; `) z3 L1 h, X" J, d以及
2 d8 G/ E( y+ W Q7 D9 `{1/2×b(a) , 即上面所述的A(d)结果发生
1 W) W! [ P* q! h5 E: v" Y, bR(2)={0, 即上面所述的A(h)结果发生8 {. R; M3 ~- u% |4 F. e/ y! r! G
{O(a)*b(a), 即上面所述的A(a)结果发生) U6 w3 ]- F( C% K7 n0 m4 `
投注主客的期望回报总数分别为7 } s) ^" i* B% a3 g N
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))
( o. g: [5 Y: ^9 r4 j2 Q! uE[R(2)]=1/2×b(a)×P(d)+P(a)*O(a)*b(a)=b(a)*[1/2×P(d)+P(a)*O(a)]
, s* p9 j2 ~( r4 U8 ]! n6 k0 h# V和上面计算过程相似,得出:
9 R! M2 n' l" ~( KE[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
. I# l( t1 ^! |) CP(d)×{[O(h)+1]/2}+P(h)×O(h)=1
( a! [. U$ c gO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1: c. i# y* s1 C! h5 w- B
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))
9 Y4 _9 { G3 W0 E& LE[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
! |; ^7 p, v% \1 h5 i1/2×P(d)+P(a)*O(a)=1 s: ^. v3 K# |- j
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)& r- C" {; o( A9 v# ^
同样主队让平半就分别是4 g- S# a- w0 Y& p; M V+ b" p
O(h)=(1-P(d)/2)/P(h)+ o1 O j- i. e) G& H S
O(a)=(1-P(d)/2)/(P(d)/2+P(a))
" I& d2 g6 B! T' {' Y7 t2 v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)$ H5 N) w4 T! W5 i5 z
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, G7 s* T" `4 ~) C
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}
: o3 v4 B% n- Z% ] M' X" S& aB(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}
- J- S* e! e& |3 xB(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
, C7 Q2 }. L8 y& B* L2 ]. 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:$ ^3 j3 `% P8 i6 S3 s
{b(h)*O(h) , 即上面所述的B(d)结果发生
7 e: w- X. z' a6 e V; B) n7 Q! l" ~R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生5 J; u+ R2 P: n3 N+ a, v7 f
{0 , 即上面所述的B(a)结果发生% t( J$ l$ c% Q& O2 n6 v
以及/ k) i. j T5 o( E0 i+ S8 F
{b(a) , 即上面所述的B(d)结果发生* e3 @7 S G9 c! G; S
R(2)={0, 即上面所述的B(h)结果发生
2 O& X) D) u. u{O(a)*b(a),即上面所述的B(a)结果发生! d5 A1 _8 G# `; q) N9 ]3 l
投注主客的期望回报总数分别为
/ e. z: p, o5 N. L7 N% mE[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 {4 d: b( L( d- C6 V* \E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
! J2 t: Q% p5 y; U假设实际投注回报与期望投注回报相等6 n+ o1 e L4 u( F
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)
) Q' g" \. Z: w/ N2 }P(h)*O(h)+P(h1)-P(h1)*O(h)=1/ F. k5 _+ q5 }
O(h)*(P(h)-P(h1))=1-P(h1)+ i& d+ d5 X4 a: L; K/ n$ T5 p& O
O(h)=(1-P(h1))/(P(h)-P(h1))$ `8 p8 {# I7 [7 z: Q
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)
3 p- h3 y9 {, z) J$ e: b$ iP(h1)+O(a)-P(h)*O(a)=1# @0 Z& Q+ N/ v; x2 O* Z
O(a)*(1-P(h))=1-P(h1)
2 Z& S9 W- F" ^( ^' @9 Q$ hO(a)=(1-P(h1))/(1-P(h))
4 f$ `* ~* |5 f$ i/ @5 \& Y1 C8 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。
7 u- X$ h) 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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