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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。0 h; \4 q) M$ x
那么,平局、主胜、客胜就有以下表达式:
) ` t; X3 q! j/ [1 BA(d) = {W(ij)|i=j, i∈N, j∈N}1 a( v+ t- }7 L3 u# z
A(h) = {W(ij)|i>j, i∈N, j∈N}
8 i3 {5 o7 W' v- y9 P/ [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]:1 v5 f& l7 D O
P(i)=P(Ai), i∈{0, 1, 2}
/ \& T3 Z N. l7 g7 @& _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)( U0 h: E& x7 M6 ]5 q$ R/ P% K/ J
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:
) K) |5 f, r3 |' r" q{b(h) , 即上面所述的A(d)结果发生7 F1 L) n2 f K6 [
R(1)={O(h)*b(h),即上面所述的A(h)结果发生& L }+ _2 s7 s. e! c0 ^6 N% r
{0 , 即上面所述的A(a)结果发生, _. v( h! q3 B0 Q* `+ ~# {
以及) A1 q- f U2 c9 O
{b(a) , 即上面所述的A(d)结果发生4 T2 h5 v9 I7 o* L
R(2)={0, 即上面所述的A(h)结果发生, H" l6 \* Q. o2 @. _: o
{O(a)*b(a),即上面所述的A(a)结果发生3 D* Y& X( ^( o& I& ?. b V
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
* P& [5 o5 H' ^4 W5 i那么投注主客的期望回报总数分别为8 r/ v* J! D: k* W% L" H
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]3 H* \6 C$ z. P, w$ s$ G( P) F
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
/ I6 N$ K$ e' z( J6 ]6 V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
; Q. Y/ C) P& q% L' j! q( l- wE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)$ ?7 ^. f, _3 k+ \! q3 b+ V
P(d)+p(h)O(h)=1
o; ~9 A$ d+ h6 _6 ]7 AO(h)=(1-P(d))/P(h)-----这里就得出平手盘下计算主队赔率的公式: Q' L) g; Y. F' Y: n) U
E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)# j3 K$ h& x! v* b4 I
P(d)+p(a)O(a)=1
0 b! N1 I* s! n/ l( F+ aO(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式
v& t0 c$ `( p6 b- @9 I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 Y" Z- s" s2 z9 N/ U) m
三、半球盘的计算描述
' G* ^+ m; ~4 N6 L" R. O接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)
9 D6 g' H3 g9 D$ k& ~% o, 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为:
& v) z7 V1 G0 z9 b4 {5 Y! Y* y{O(h)*b(h),即上面所述的A(d)结果发生& ^4 B4 S. h; N; u9 D2 _" h0 l
R(1)={O(h)*b(h),即上面所述的A(h)结果发生( A: j1 k3 W* `8 n( e9 X
{0 , 即上面所述的A(a)结果发生
) G, a! M0 S" h以及
+ H5 Z$ t" z2 G; c' X{0 , 即上面所述的A(d)结果发生: j4 }3 \- ~! V/ }) q# r
R(2)={0, 即上面所述的A(h)结果发生
3 T/ S; D/ b% @) U{O(a)*b(a),即上面所述的A(a)结果发生
2 z1 s: r7 P* |如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率/ {# n2 S ]: `( y
投注主客的期望回报总数分别为
- ]$ T8 p$ d3 C& @8 {E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]3 b7 l% F) O7 X: p
E[R(2)]=P(a)*O(a)*b(a)
( Y# }9 h! E; G4 c* n7 `假设实际投注回报与期望投注回报相等5 a) D% W! F0 S8 O" R4 r
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
$ @$ Z* g4 k3 o( @1 @4 BO(h)*[P(d)+p(h)]=1
+ e1 t* U+ W; I+ G/ M- EO(h)=1/[P(d)+p(h)]
: ]$ g# z- Q" E% y+ x! jE[R(2)]=P(a)*O(a)*b(a)=b(a)# x2 a. U: U$ r, q+ V. Q
P(a)*O(a)=1
- a$ w% h& z! t, W. PO(a)=1/P(a): S1 D, K6 t+ b5 {" _4 f
同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率
& i1 W/ [1 o8 C+ GO(h)=1/p(h)
+ s1 j6 _! R) _. C1 {O(a)=1/[P(d)+p(a)]# n' i& e9 l. o! M7 S# l
四、平半球盘的计算描述* [7 m+ ]( ]- F4 E3 u1 m/ W0 k
这个稍复杂一点
+ q' v/ x' Z! s+ g% ~# h接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
2 r* }% B6 R. V. J% B! b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:
3 O7 z& X3 i& i; B% b J# o9 |% w{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生
' j1 ^9 p1 k' z% v* t& h. e( N. DR(1)={O(h)*b(h), 即上面所述的A(h)结果发生& z9 i4 }5 K$ L' {
{0, 即上面所述的A(a)结果发生
& y1 X- i/ H+ o& g1 T以及
* b" T2 ]! ?, L3 w, D* {{1/2×b(a) , 即上面所述的A(d)结果发生
5 J9 b; I1 _2 Y bR(2)={0, 即上面所述的A(h)结果发生
# k* R0 [& S# X{O(a)*b(a), 即上面所述的A(a)结果发生
: Z- P! x" p$ b" @3 B投注主客的期望回报总数分别为* ?9 d+ [: u; c5 X- S& P3 ]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))7 n4 |8 N6 I L4 a0 c
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)]0 }7 t( e& U" f- C" r0 ^
和上面计算过程相似,得出:% k4 ~( v! E# l D! Z
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
( k+ i: Q" d( U) pP(d)×{[O(h)+1]/2}+P(h)×O(h)=1
8 z; s0 z! F# }% E6 hO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1* ?# h" I/ z* r6 I/ U% J/ q! M
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))5 C" D+ T8 z) A- U
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
' F% Y6 B1 }! B" W1/2×P(d)+P(a)*O(a)=1
* w7 c1 S& K7 w4 q: \O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
" H$ @; @) U% a9 m4 w同样主队让平半就分别是) N. i7 P. i9 v4 N W' R3 h
O(h)=(1-P(d)/2)/P(h)' f3 x" W# b& I8 @1 q6 N0 @( q4 T
O(a)=(1-P(d)/2)/(P(d)/2+P(a)), [: |3 B) v4 a) n+ q
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)
8 m9 E/ P: 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
4 ^1 q# w7 g8 _+ L( nB(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}) Z6 u0 ^( M; a9 j8 k
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}( @; U" n1 l3 |
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: q- w% e9 A9 U c0 y
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:, r& q9 h2 W! Y& }, j4 s
{b(h)*O(h) , 即上面所述的B(d)结果发生+ S% J& ~% v- h" h5 O
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生
0 S# ? N) y/ Q0 r c2 o7 d{0 , 即上面所述的B(a)结果发生2 [" v0 R! M! d5 [
以及7 u& H4 ]2 h; u7 |$ ~, p7 j% V$ b
{b(a) , 即上面所述的B(d)结果发生' ]: q& D' `3 Q" k$ V4 O; _
R(2)={0, 即上面所述的B(h)结果发生$ [0 ]/ a& b0 }' F& u- P
{O(a)*b(a),即上面所述的B(a)结果发生
0 V$ S: d: J; R$ E9 V' }8 g投注主客的期望回报总数分别为* {' T3 Y) B3 [' U. P
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)]# F0 p. {. s6 W
E[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))' h; A( U7 _) B/ `8 p9 p
假设实际投注回报与期望投注回报相等3 q3 D3 m; I6 E/ |8 Y$ Z% ]" ^( a4 g
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)) t, j8 H2 }9 a$ x( ?! n
P(h)*O(h)+P(h1)-P(h1)*O(h)=16 A9 Z o' u# y
O(h)*(P(h)-P(h1))=1-P(h1)
: p; m0 i6 {/ ^; W7 r4 WO(h)=(1-P(h1))/(P(h)-P(h1))) [" z9 Z6 B' Z0 e; D4 s- `
E[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a), G' ^" W2 q7 x
P(h1)+O(a)-P(h)*O(a)=1; _. v) b% c9 t: U* c& l- q
O(a)*(1-P(h))=1-P(h1)
: B2 b" ~; D$ n7 {$ \$ NO(a)=(1-P(h1))/(1-P(h)) E& p4 A/ D! s2 K! v
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。 k/ ]% ? V+ \' ]
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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