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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。7 k# b* r7 P( o, D; H( |' a
那么,平局、主胜、客胜就有以下表达式:2 D6 S' W* V0 p
A(d) = {W(ij)|i=j, i∈N, j∈N}
b- U% O' R7 [4 W: y2 ~A(h) = {W(ij)|i>j, i∈N, j∈N}( ^, [( C$ P/ g# k/ a4 d! A! x3 |
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]:
9 G h9 D& j1 o; YP(i)=P(Ai), i∈{0, 1, 2}
" d6 m. M D J# d e2 _( b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)3 J; F8 w2 n1 J$ 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:4 o2 U& w' ]9 M H
{b(h) , 即上面所述的A(d)结果发生* y' H/ u3 v' I- C- A$ j% o, t
R(1)={O(h)*b(h),即上面所述的A(h)结果发生
* W2 x) |$ O1 I5 n2 }7 j{0 , 即上面所述的A(a)结果发生
( f7 y4 F1 ]" K! v! k9 \以及 S+ T; P4 F. w1 r" a+ m5 u7 }& `
{b(a) , 即上面所述的A(d)结果发生' ]( ~5 {6 s. s. |) [
R(2)={0, 即上面所述的A(h)结果发生# S, l0 K3 @. q+ E; t& ^, X
{O(a)*b(a),即上面所述的A(a)结果发生
6 Y2 V0 }8 Y+ h9 p9 ^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! S. r$ {8 h$ o. {% R) @
那么投注主客的期望回报总数分别为
1 y9 r/ \& z, j) X5 b/ o* f( GE[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)], y5 b& q* J2 }
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]
% ^% v4 F9 r, l W; r; s' h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4 C% R6 h8 ^% a# Q4 }8 c/ j# ]
E[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h). k0 r2 K! m, ~6 q$ W" u4 y
P(d)+p(h)O(h)=1' \1 n. v" ]* C Y
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
; T# f. B& j- s5 jE[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)4 f( ?3 d* ^/ e# |2 ]
P(d)+p(a)O(a)=1% e5 z6 R9 E0 d" x/ @7 G
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
# C q6 H. U& }8 F: O: @0 v; g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
+ ?( @6 q* U2 c; H4 l三、半球盘的计算描述
% U1 [. w6 Q9 Q8 x8 ^接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)' q0 `! i( G1 u: x2 t+ b# w
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:
8 M8 {* v. c* D* Z1 S0 n( f( w1 V{O(h)*b(h),即上面所述的A(d)结果发生* N ?! i/ G# b: s0 x
R(1)={O(h)*b(h),即上面所述的A(h)结果发生; Z+ s( I7 p0 k" r5 {- O
{0 , 即上面所述的A(a)结果发生9 i3 c( l# T$ U; k2 C
以及" D8 x! s& c/ x x
{0 , 即上面所述的A(d)结果发生
; L9 I0 n0 E; x, uR(2)={0, 即上面所述的A(h)结果发生5 j2 S B" }9 y! E" N$ A& U
{O(a)*b(a),即上面所述的A(a)结果发生
9 E$ J7 Q! Z* L4 h如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率
7 C8 R3 {7 g) M9 U* D投注主客的期望回报总数分别为
5 I M4 p5 p1 N6 e) E% m& f) `8 `E[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]" n$ H" D T0 G8 A" `
E[R(2)]=P(a)*O(a)*b(a) D* |' a: f7 V N& B3 \( C
假设实际投注回报与期望投注回报相等6 o- R9 u. t$ `0 {1 [- F
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
6 z/ c! |4 U. F0 t. JO(h)*[P(d)+p(h)]=1
# Z" k# n0 v6 GO(h)=1/[P(d)+p(h)]
0 ?$ i) X9 T7 ]E[R(2)]=P(a)*O(a)*b(a)=b(a)
$ q% f" W0 ^' hP(a)*O(a)=14 G5 I' v' A/ ^* f5 Y
O(a)=1/P(a)
( u V5 ]$ w ~3 D. o同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率
/ ]8 H& Q+ y3 Y/ |( s. _- P, |( ]2 |4 FO(h)=1/p(h)
0 N. }' @* R0 _4 }, HO(a)=1/[P(d)+p(a)]
$ g/ E2 O% k! X6 @四、平半球盘的计算描述
% r6 I1 Z& q8 r. F- A这个稍复杂一点
6 L$ N& V8 K: w# ~0 \; e接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)/ B" U4 {+ U2 g& ~* L# z 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:
! x% S# ^* u; u2 P{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生5 R% m, U2 J* W( ^; `- n& q
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生
% f( w$ b1 }8 f- w7 |* Y( o% [{0, 即上面所述的A(a)结果发生
) g& |" a( A; J" w0 n( q H; ]以及
; p) e2 L$ L6 Y+ x! X! u8 p{1/2×b(a) , 即上面所述的A(d)结果发生
9 p) H6 q( T# h& k1 }" yR(2)={0, 即上面所述的A(h)结果发生
7 Q! C. Z; p6 ]* [$ k* ]7 w{O(a)*b(a), 即上面所述的A(a)结果发生
& t5 h+ Q7 p0 _7 v+ \. ~2 O; v投注主客的期望回报总数分别为( u& R4 ]5 m* V) }
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))
. G1 ?' E6 p: e- s1 Y A2 B7 J2 P2 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)]3 Z9 C! \4 p k8 I" `. q
和上面计算过程相似,得出:- o) X1 n% L, F& B3 X
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
& a. u: ?" d ~2 G" m! b' m4 e7 tP(d)×{[O(h)+1]/2}+P(h)×O(h)=1
( E# o& @+ o: m, a* ZO(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1
1 S" G) U0 v7 m& g, h0 u9 O- EO(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h)): x# @6 L$ [9 ?( i! ?
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
4 P/ }% R( R4 |! ?, e" N1/2×P(d)+P(a)*O(a)=1# Q$ _0 I4 r S; B" I
O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
1 Q+ u0 r" D3 F5 z同样主队让平半就分别是
^) F$ |8 P* a* a( M) ~O(h)=(1-P(d)/2)/P(h)2 }4 U ?5 U% A7 S& ~8 N. y9 J
O(a)=(1-P(d)/2)/(P(d)/2+P(a))2 j% i0 b T! `, D
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)7 Z1 P0 x. R, H) t2 C3 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3 r% w& e+ d) o2 v
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}3 g& m' f) @9 Z6 R, D* p
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}+ Z9 [& @! i) k
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数
" O5 H: e' B: V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 j; }8 U; E# y: P5 p{b(h)*O(h) , 即上面所述的B(d)结果发生
7 Q/ L' z; s( g# h# h. l: Q$ E5 v+ i& Q& eR(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生 p3 c3 Y7 ?3 [; w3 g2 w( |
{0 , 即上面所述的B(a)结果发生
5 p, ?8 v, p1 f: J3 v4 `/ x! M以及
) }! q! C: c! c# C{b(a) , 即上面所述的B(d)结果发生
& l9 S4 ?0 K! q6 K& \) h9 mR(2)={0, 即上面所述的B(h)结果发生$ p! O2 C+ H( {+ j
{O(a)*b(a),即上面所述的B(a)结果发生# b- b6 ]3 A# u
投注主客的期望回报总数分别为
6 A+ \, Q$ i7 y _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)]
, U1 U6 |. C. tE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))! b! c5 T F7 A" i: M$ r# y
假设实际投注回报与期望投注回报相等
* ^% W7 |3 o1 f2 u8 j& g. `3 oE[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h)+ ^/ v, n: X N! c
P(h)*O(h)+P(h1)-P(h1)*O(h)=13 S; \% p1 y" C2 ~- c: {6 a6 K
O(h)*(P(h)-P(h1))=1-P(h1)
4 I7 a, e0 ^& `! w) R3 E' E+ s2 mO(h)=(1-P(h1))/(P(h)-P(h1))
/ `1 E1 T- P. J/ C' [% e0 sE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)) [7 I# m/ V; i' k6 g! b- o# B
P(h1)+O(a)-P(h)*O(a)=1# S& c! x! Y. @6 x1 X7 l
O(a)*(1-P(h))=1-P(h1)
, s" A- a+ X& H, C7 ]5 [O(a)=(1-P(h1))/(1-P(h))
+ p, x0 g5 O1 h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。
; I% u1 \4 D, x 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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