Optimization Investment of Football Lottery Game Online Combinatorial Optimization

Transcript

1 27 :26788 (27) 2926,2, 2, 3 (, 76 ;2, 749 ; 3, 64) :, ;,,, ;,, : ; ; ; ; ; : TB4 : A Optimization Investment of Football Lottery Game Online Combinatorial Optimization HU Mao2lin,2, XU Yin2feng 2, XU Wei2jun 3 (Department of Mathematics, Ningxia Normal College, Guyuan 76,China ; 2School of Management, Xi an Jiaotong University, Xi an 749,China ; 3School of Business Administration, South China University of Technology, Guangzhou 64,China) Abstract : Based on the compensating rate in Europe lottery, we set up the mathematics model of the football lottery that is the dark2horse analyses of the win2and2defeat game Combining the numerical analysis, we use the online algorithm to analyze the disadvantages of the traditional lottery investment method that is the multimode strategy, find that the competitive ratio of the multimode strategy is larger and the risk is higher Further, we propose the method of the dark2horse expectancy strategy and optimize the multimode strategy by the dark2horse index so as to reduce the competitive ratio and risk degree of the multimode strategy Key words : football lottery ; online algorithm ; multimode strategy ; dark2horse expectancy strategy ; competitive ratio ; risk degree,,,, (offline),,? (online), :, ;,, :22222 : (973,7473) ; (247) : (963 - ),,,,, :, E2mail : com ; (962 - ),,,, ; (97 - ),,,, :

2 2 27,,? [,2 ],,, ( ), ALG ( ), I = { i, i 2,, i k } O = { o, o 2,, o k } C ALG ( I), C OPT ( I), I I : C ALG ( I) C OPT ( I) +, ALG, ; =, ALG [,2 ] 2,, 2 3, 24 4 : 4, 3 : 3, ; ;,, 3, ( ) 4,, 2,, % : 4 ; : 3 ; : 2 ; [3] 3,,, :,,,,,,, :, 3 4,,,,,, :,, [4 6 ], :,,, ;,,, ;, 2, 3, 4,,, [7 ], (, ) William Hill

3 2 H i Q i x i y i z i, Π i { j j 3, j N}, : x i y i or y i z i i H i vs Q i x i ; x i = y i = z i, y i, z i, y i, z i ( i 3),, i 2 i H i vs Q i x i, y i, z i, max{ x i, z i }, x i z i, ; y i, 3 i H i vs Q i x i, y i, z i, max{ x i, z i } <, x i z i, ; y i, : {3,,} 32, a a 2 a 3, a i {3,,},, s = a a 2 a 3, s i = a i a i2 a i3 ; 3 3, {3,,} 32, S I = { s i s i = a i a i2 a i3, a ij {3,,}, j =,2,,3} S I,, S ALG = { s i s i = a i a i2 a i3, a ij A j < {3,,}}, S ALG S ALG 4 s = a a 2 a 3 s 2 = a 2 a 22 a 23, { i a i - a 2 i, i 3}, d 2 = s - s 2 s i = a i a i2 a i3, l i, a ij, l i,2 a ij, l i,3 a ij, l i,4 a ij, l i,, l i,2, l i,3, l i,4, ; S ALG = { s i s i = a i a i2 a i3, a ij A j < {3,,}}, max s i S ALG l i, j = l j ( j =,2,3,4), S ALG l, l : l, l 2, l 3, l 4 6 S ALG = { s i s i = a i a i2 a i3, a ij A j < {3,,}}, s = a a 2 a 3, min{ d i d i = s i - s, s i S} = d, 3 - d ; d i = s i - s = d s i S ALG, S OPT,, S OPT = ; = S ALG S OPT = S ALG 7 S ALG = { s i s i = a i a i2 a i3, a ij A j < {3,,}}, R = - S ALG S ALG,, R = S ALG 3,,, RIS : m, ( ) ; 3 - m,, 2 ( ) 3 ( ),, S RIS m, m, m 2

4 22 27 : S RIS = 2 m m 3 2 ) l = 3 - m 2) = S RIS = 2 m m 3 2 3) RIS, R = - S RIS S RIS = - 2 m m m m 3 2 = - R = S RIS = 2 m m m 3 3- m 2 m m 2 3 2,, m, m 2,,,,,, ; m, m 2,,,,,,,,, : 39, 66 ( 2) [8 ] (3) 2 AC () () () () (3) () () () () s = 33333, 7 :,2,4 :34276, :79 [9 ] S RIS = { a 3 a 3 a 4 a a 6 a 7 3 a 9 a a 3 a 3 a, a, a 6, a 7, a 3 {3,,} ; a 3, a 4 {,} ; a 9, a {3,} ; a {3,}} ; 3,, S OPT = {333333}, 6 :2,4,,,7,8 ; = S RIS = 2 3 = 7776 ; R = - S RIS S RIS = ; 2 S RIS = 2, ( ), 79, : ,,, 777

5 23, , ; ; : , , , ; 33333,3333,3333,333 ; 3333,333,,,, S RIS, l : l, l 2, l 3, l 4 ; S RIS l, l 2, l 3, l 4,,,, ;,,,,,,, l 3,,,, S RIS,, S RIS,, ;, : S RIS ( l l, l 2, l 3, l 4 ), - S RIS S RIS, : k k,, k 3, (, k = k + + k 3 + (6 k 9) ), k l, l 2, k 3 l 3, l 4 S RIS k,, k 3, S CAS ( k k,, k 3, ) ) S CAS ( k k,, k 3, ) 2) - S CAS ( k k,, k 3, ) ( k k,, k 3, ) S CAS ( k k,, k 3, ), S CAS S CAS ( k k,, k 3, ) S CAS ( k k,, k 3, ) : S RIS ( l l, l 2, l 3, l 4 ), 2 m,, l 2,, l 4 ; 3 m 2,, l 2,, l 4, S CAS ( k k,, k 3, ) ( x < y, x y = ) ) S RIS ( l l, l 2, l 3, l 4 ) k a k, l 2, k l 2 ;

6 24 27 b k -,, l 2 -, ; k - l 2 - ; c, k, l 2 - k, l 2 - k k, k k l 2 + k - l 2 - l 2 - k k 2) ) k 3 ),) k 3 ),2), = k 3 l 4 + k 3 - S CAS ( k k,, k 3, ) k k 3 l 2 + k - l 4 + k 3 - l 4 - l 2 - l 4 - l 4 - k 3 k 3 l 2 - k k l 4 - k 3 k 3 S RIS (,,7,8) 7776 k, k,, k 3, k = = ;, k = 6, k 3 = 2, = 4 S RIS (,,7,8), = 2 9,, 3 (),3 (), =,,6,7,3, (3),3 (),3 (), (3),3 () ; l 4 = 7,3,4,,6,7,,3, (3), (), (),3 (),3 (), (3),3 (),3 (), k 3 2 l 4 = 2 2 l 4-2, S CAS (6,,2,4) = 2 2 = = 3, k = l 4 - = 2 4 = =,, 23, 7776, ; = S CAS (6,,2,4) = 23, R = - S CAS (6,,2,4) 2 S CAS = 47, 79, 743 S CAS (6,,2,4) 23, [ ],,,,,, ( 3 )

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