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[体育菠菜心得方法] 亚洲让球盘的数学描述
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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 t4 Q- [7 _3 z* b9 U9 G" w/ ~那么,平局、主胜、客胜就有以下表达式:
7 C  L& J4 k& TA(d) = {W(ij)|i=j, i∈N, j∈N}
9 U% m9 a: e  H  w( n) T4 IA(h) = {W(ij)|i>j, i∈N, j∈N}
( E- n# l) I3 O/ [3 aA(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]:
  N: S5 g: O+ y) K& nP(i)=P(Ai), i∈{0, 1, 2}
1 ?6 f: B8 K9 X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)
$ f$ u9 r- ?" {, j! x/ S6 R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:9 J  ^5 q7 u. `  g! u3 y! [1 t7 }
{b(h) , 即上面所述的A(d)结果发生
" r  n' [7 o$ Y/ l0 y7 ]R(1)={O(h)*b(h),即上面所述的A(h)结果发生8 {3 k; a* H/ \2 w
{0 , 即上面所述的A(a)结果发生
0 L- H6 d8 t6 H9 |4 d: b. Q以及$ L- W+ w! `, g; x- m9 |& f, l- b( z- Y
{b(a) , 即上面所述的A(d)结果发生  D% [% P+ B% F
R(2)={0, 即上面所述的A(h)结果发生
) f& _0 h/ n7 C* Y" F( c8 J; M{O(a)*b(a),即上面所述的A(a)结果发生4 {' k& a4 B3 o& M0 x9 F/ U: F: [9 F1 c8 S
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( Y2 i9 G% H3 h% K' j6 X0 h2 T
那么投注主客的期望回报总数分别为& F8 M$ M' w* e7 i# y( O3 E
E[R(1)]=P(d)*b(h)+P(h)*O(h)*b(h)=b(h)*[P(d)+p(h)O(h)]! \9 A' i! P! H+ {5 G" D* F
E[R(2)]=P(d)*b(a)+P(a)*O(a)*b(a)=b(a)*[P(d)+p(a)O(a)]! B; G2 G' t! i4 |6 s; C
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
" i# g  Y9 f; X5 AE[R(1)]=b(h)*[P(d)+p(h)O(h)]=b(h)
; x8 m) |4 t% \P(d)+p(h)O(h)=1' ?. ^& I2 r. p8 e
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
+ W4 u" V. R1 p8 m+ \E[R(2)]=b(a)*[P(d)+p(a)O(a)]=b(a)# V2 S0 _: f: z( a
P(d)+p(a)O(a)=1
4 p5 q( }$ u0 W1 D1 FO(a)=(1-P(d))/P(a)-----这里就得出平手盘下计算客队赔率的公式
' H5 T( C/ A3 i# T  R5 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' S5 u  Q8 n: q( i
三、半球盘的计算描述6 t+ C" ]8 b; \( p; `& W
接着我们来看看主队(HOME TEAM)受半球(1/2:0 Handicaps的情况)& K& O0 j$ Q5 p: M% g) T
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:
% a. v, M7 r, k0 W* C- h; c4 r( `7 e7 R{O(h)*b(h),即上面所述的A(d)结果发生
! y8 p% _, D3 k6 b' Z2 yR(1)={O(h)*b(h),即上面所述的A(h)结果发生' Z3 E; [! u" E7 Z
{0 , 即上面所述的A(a)结果发生
2 o3 o6 N  O1 a以及
) j- E8 w$ W9 w% b8 S{0 , 即上面所述的A(d)结果发生
8 u! K! M% |! Z- NR(2)={0, 即上面所述的A(h)结果发生
8 c3 X# _1 s+ F5 z{O(a)*b(a),即上面所述的A(a)结果发生
1 C$ r: H8 s6 x& K, ]如果O(h)表示受半球盘下的主队赔率,O(a)表示客队赔率: ~) [3 T  C( [. }8 g3 N
投注主客的期望回报总数分别为
: i7 b7 O$ u1 n7 cE[R(1)]=P(d)*O(h)*b(h)+P(h)*O(h)*b(h)=b(h)*O(h)*[P(d)+p(h)]
* q/ V8 e7 P8 `' T' h) a. wE[R(2)]=P(a)*O(a)*b(a)
0 I: ~9 C- v' V4 c$ v" k) O$ x# N假设实际投注回报与期望投注回报相等, t# u( H3 R- f0 D( f6 c
E[R(1)]=b(h)*O(h)*[P(d)+p(h)]=b(h)
( @  S  h/ a; i' S: ^O(h)*[P(d)+p(h)]=10 S0 k: K+ V- n/ ?
O(h)=1/[P(d)+p(h)]; P# C! V$ n- `7 e6 Y$ o
E[R(2)]=P(a)*O(a)*b(a)=b(a)6 W! Z. D1 p. O1 R3 C4 a- _- q
P(a)*O(a)=1
( x- Q9 o' G! P/ }% KO(a)=1/P(a)
0 x# w7 ^7 O! }+ C5 o' j, i9 I同样道理可以计算让半球(0:1/2 Handicaps)的亚洲盘赔率4 d0 V+ y- X* @% Z+ @
O(h)=1/p(h)
+ `' [5 K- g* g$ bO(a)=1/[P(d)+p(a)]' {0 c, Z' u* y. D1 ~' T
四、平半球盘的计算描述
, I5 \0 Y. S7 X/ L0 b' j2 s# F8 V这个稍复杂一点
0 P1 ~! L0 c$ p$ n2 K6 {4 ?; ]接着我们来看看主队(HOME TEAM)受平半球(1/4:0 Handicaps的情况)
* @- t( I$ ?$ v5 D; |8 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计算:1 B- N% _' {2 n' ^7 t
{[O(h)+1]/2×b(h), 即上面所述的A(d)结果发生+ P% |- R% J; \4 ^
R(1)={O(h)*b(h), 即上面所述的A(h)结果发生
6 w* i& T! ^( Q3 e8 z% V8 O6 H{0, 即上面所述的A(a)结果发生5 G. _7 t- p7 P! z
以及
1 i% C$ G- u% u0 y2 S; j. T& \2 W( m{1/2×b(a) , 即上面所述的A(d)结果发生7 H+ U7 `) }/ ]* T
R(2)={0, 即上面所述的A(h)结果发生
5 z  E8 M$ t# Z* u- i6 c1 u{O(a)*b(a), 即上面所述的A(a)结果发生8 G+ i$ x& k/ v6 [9 w( w1 ~
投注主客的期望回报总数分别为
* P' s. U8 p1 C3 S4 ]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))
( v9 c$ Y8 ~+ R* u( O3 j( o+ mE[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 _5 g2 f' s5 M0 o, t和上面计算过程相似,得出:" M+ y( b" h- M- t
E[R(1)]=b(h)*(P(d)×{[O(h)+1]/2}+P(h)×O(h))=b(h)
: o* K$ C; H% q0 qP(d)×{[O(h)+1]/2}+P(h)×O(h)=1  M3 j+ d5 [- V9 h5 r# f8 m
O(h)*[1/2*P(d)+P(h)]+1/2*P(d)=1+ q( q2 N6 T3 V8 z9 S# x" i
O(h)=[1-1/2*P(d)]/[1/2*P(d)+P(h)]=(1-P(d)/2)/(P(d)/2+P(h))* }# ^1 j) i0 Z/ A9 L/ \
E[R(2)]=b(a)*[1/2×P(d)+P(a)*O(a)]=b(a)
6 Z. e0 _  u6 J3 }1/2×P(d)+P(a)*O(a)=1
* e( L7 f. p1 }' K: ^O(a)=[1-1/2×P(d)]/P(a)=(1-P(d)/2)/P(a)
- l2 b' W  H! H  G0 f' A7 e同样主队让平半就分别是
* ~5 H) V5 w. G# Q! ?/ @+ iO(h)=(1-P(d)/2)/P(h)1 ]( ?( r1 X; d$ y$ P+ B2 w; N
O(a)=(1-P(d)/2)/(P(d)/2+P(a))) o# u/ H& f7 {: B
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)
4 a0 Y  z1 Z6 y: h0 r  O' ^' w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: ?$ [! `# q  ^1 C+ ^
B(d) = {W(ij)|i=j+k, i∈N, j∈N,k∈N}$ N/ K! n$ F5 a' b
B(h) = {W(ij)|i>j+k, i∈N, j∈N,k∈N}5 u0 o1 o7 V5 w9 @
B(a) = {W(ij)|i i,j分别表示主客队的进球数,k代表让球数; f8 Y; T+ x3 f# _
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( c6 }" v
{b(h)*O(h) , 即上面所述的B(d)结果发生, @  x+ _, O1 J0 ]2 Y7 R- Z
R(1)={b(h)-O(h)*b(h),即上面所述的B(h)结果发生1 Z! N! Q& o* U  a! L, P
{0 , 即上面所述的B(a)结果发生
. F/ u, f4 s8 j3 w; y4 D+ P- i以及
- K) e" J& z2 ?6 h{b(a) , 即上面所述的B(d)结果发生& K2 @4 C1 z2 y, h4 r& p; d
R(2)={0, 即上面所述的B(h)结果发生" v' d7 Y* J- ~+ S
{O(a)*b(a),即上面所述的B(a)结果发生3 e% p4 r1 d3 S/ o
投注主客的期望回报总数分别为
: y1 K) D0 E) a+ t# yE[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)]
3 [" H5 S- Q* N& _* u, G3 BE[R(2)]=P(h1)*b(a)+(1-P(h))*O(a)*b(a)=b(a)*(P(h1)+O(a)-P(h)*O(a))
6 T& b$ W7 o! ^! b9 y假设实际投注回报与期望投注回报相等1 }9 P; g7 H- G8 G8 m* L* @) s
E[R(1)]=b(h)*[P(h)*O(h)+P(h1)-P(h1)*O(h)]=b(h): c/ ^; f1 @9 A# K3 i* N
P(h)*O(h)+P(h1)-P(h1)*O(h)=1
# @+ |0 G. V5 c. s: _: ^& f$ IO(h)*(P(h)-P(h1))=1-P(h1)
0 I3 P  U- ]+ W7 F( w3 y* ~O(h)=(1-P(h1))/(P(h)-P(h1))
8 Y) D. S" b3 V! B9 vE[R(2)]=b(a)*(P(h1)+O(a)-P(h)*O(a))=b(a)) s( `3 F% S+ S8 @* [
P(h1)+O(a)-P(h)*O(a)=1& d( t, J4 }  B& U. J
O(a)*(1-P(h))=1-P(h1)/ |3 J+ v7 q7 p5 i& m1 Z
O(a)=(1-P(h1))/(1-P(h))
# k6 W8 C7 m0 b2 D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。
" c: s; Z' J. ?9 b$ g7 c1 B3 ?" g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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12#
这个看起来真有点复杂。
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这个·好复杂的
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10#
楼主的经验不错啊
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9#
新人来学习下,谢谢楼主。
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8#
徐曹操曹操双方的首发参赛
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7#
谢谢楼主的分享
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6#
谁看的懂啊。就是你们这些家伙把简单的事复杂化
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5#
主题回复处广告图案-天策传媒
好复杂啊!!!!!
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太复杂,有没有简单易懂的??
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在极端情况下,可以认为平手盘亚洲赔率
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2#
好象不是很明白
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:loveliness: :funk: :curse: :dizzy: :shutup: :sleepy:
:hug: :victory: :time: :kiss: :handshake: :call:
:) :( :D :'( :@ :o
:P :$ ;P :L :Q :lol
:loveliness: :funk: :curse: :dizzy: :shutup: :sleepy:
:hug: :victory: :time: :kiss: :handshake: :call:
:hug: :victory:
:) :( :D :'( :@ :o
:P :$ ;P :L :Q :lol
:loveliness: :funk: :curse: :dizzy: :shutup: :sleepy:
:hug: :victory: :time: :kiss: :handshake: :call:
:hug: :victory: :time: :kiss: :handshake: :call:
:hug: :victory: :time: :kiss: :handshake: :call:
:hug: :victory: :time: :kiss: :handshake: :call:
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