博弈論實例Kelly課件.xlsx

5 Round Gambling How much of your available money do you bet in each round Type in numbers from 0 to 100 into the cell All pink cells get the same value The parameters of the whole game can be changed in the two blue cells 10 probability for winning a round9 100 net odds how much of your bet you win in case of winning10 036 049 9 0 01 1 002 702 0 10 9 911 457 9 0 09 100 180 1 00 9 911 457 9 0 09 91 064 0 90 9 82 777 9 0 81 10 009 10 9 911 457 9 0 09 91 064 0 90 9 82 777 9 0 81 9 098 9 9 82 777 9 0 81 8 270 8 10 9 7 518 9 how much of your wealth you risk in each round7 29 1000 amount 100 probability9 911 457 9 0 09 91 064 0 90 9 82 777 9 0 81 9 098 9 00 9 82 777 9 0 81 8 270 8 10 9 7 518 9 7 29 909 90 9 82 777 9 0 81 8 270 8 10 9 7 518 9 7 29 826 81 9 7 518 9 7 29 751 72 90 9 683 65 61 The resulting money after 5 rounds Two utility functionsand the probabilityLOG x 1 SQRT x LOG x 1 100 450 8118 00195345110022 51519100 450 8118 001953451 0 0010 0 0010 0 0010 0 0010 0 0010 9 122 7686 9601266883020 3920619 122 7686 960126688 0 0090 0 0090 0 0090 0 0450 0 0450 9 122 7686 9601266883020 392061828 5145 918300358 0 0090 0 0090 0 0090 0 8100 0 8100 828 5145 918300358910 227426175 2444 8764788 0 0810 0 0810 0 0810 7 2900 7 2900 9 122 7686 9601266883020 3920616 8343 834709771 0 0090 0 0090 0 0090 32 8050 32 8050 828 5145 918300358910 22742616212 793518638 0 0810 0 0810 0 0810 59 0490 59 0490 828 5145 918300358910 2274261 0 0810 0 0810 0 0810 100 0000 75 2444 8764788274 3067623 0 7290 0 7290 0 7290 9 122 7686 9601266883020 392061 0 0090 0 0090 0 0090 828 5145 918300358910 2274261 0 0810 0 0810 0 0810 828 5145 918300358910 2274261 0 0810 0 0810 0 0810 75 2444 8764788274 3067623 0 7290 0 7290 0 7290 828 5145 918300358910 2274261 0 0810 0 0810 0 0810 75 2444 8764788274 3067623 0 7290 0 7290 0 7290 75 2444 8764788274 3067623 0 7290 0 7290 0 7290 6 8343 83470977182 66527428 6 5610 6 5610 6 5610 9 122 7686 9601266883020 392061 0 0090 0 0090 0 0090 828 5145 918300358910 2274261 0 0810 0 0810 0 0810 828 5145 918300358910 2274261 0 0810 0 0810 0 0810 75 2444 8764788274 3067623 0 7290 0 7290 0 7290 828 5145 918300358910 2274261 0 0810 0 0810 0 0810 75 2444 8764788274 3067623 0 7290 0 7290 0 7290 75 2444 8764788274 3067623 0 7290 0 7290 0 7290 6 8343 83470977182 66527428 6 5610 6 5610 6 5610 828 5145 918300358910 2274261 0 0810 0 0810 0 0810 75 2444 8764788274 3067623 0 7290 0 7290 0 7290 75 2444 8764788274 3067623 0 7290 0 7290 0 7290 6 8343 83470977182 66527428 6 5610 6 5610 6 5610 75 2444 8764788274 3067623 0 7290 0 7290 0 7290 6 8343 83470977182 66527428 6 5610 6 5610 6 5610 6 8343 83470977182 66527428 6 5610 6 5610 6 5610 6212 79351863824 91206383 59 0490 59 0490 59 0490 Expected utilities Expected Moneyfor LOG utility for SQRT utility 19 9143 314167070 65787 SQRT x 10022 51519 0 0010 3020 392061 0 0450 910 2274261 0 8100 274 3067623 7 2900 82 66527428 32 8050 24 91206383 59 0490 5 Round Gambling How much of your available money do you bet in each position Type in numbers from 0 to 100 into the corresponding red cells The parameters of the whole game can be changed in the two blue cells 10 probability for winning a round20 100 net odds how much of your bet you win in case of winning12 535 360 9 0 01 1 264 920 0 10 9 1 151 077 9 0 09 127 641 1 00 9 1 151 077 9 0 09 116 153 0 90 9 105 699 12 0 81 9 910 10 9 856 453 9 0 09 86 423 0 90 9 78 645 9 0 81 8 721 9 9 78 645 9 0 81 7 936 8 10 9 7 222 9 7 29 1000 100 9 1 558 012 9 0 09 157 216 0 90 9 143 067 15 0 81 9 919 9 00 9 83 553 9 0 81 8 431 8 10 9 7 672 10 7 29 910 90 9 249 170 9 0 81 25 143 8 10 9 22 880 30 7 29 819 81 9 17 600 30 7 29 573 72 90 9 401 65 61 The Money distribution How much is how likely below 100059 0 1000 9 99919 7 10 000 99 99917 5 0 0020 03 100 000 999 9993 2 more than 1 000 0000 5 below 1000 1000 9 999 10 000 99 999 100 000 999 999 more than 1 000 000 0 0 10 0 20 0 30 0 40 0 50 0 60 0 70 0 Two utility functions LOG x 1 SQRT x 260 735 4978 41620016316147 3062 0 0010 0 0010 0 0010 10 028 2887 001226857 3166 747284 0 0090 0 0090 0 0090 11 407 1787 057178257 3377 451407 0 0090 0 0090 0 0090 1 047 4816 0201463711023 46496 0 0810 0 0810 0 0810 11 407 1787 057178257 3377 451407 0 0090 0 0090 0 0090 1 047 4816 0201463711023 46496 0 0810 0 0810 0 0810 1 047 4816 0201463711023 46496 0 0810 0 0810 0 0810 96 1864 98311821 310 1393321 0 7290 0 7290 0 7290 8 487 4516 928777341 2913 323051 0 0090 0 0090 0 0090 779 3725 891745585 882 8207126 0 0810 0 0810 0 0810 779 3725 891745585 882 8207126 0 0810 0 0810 0 0810 71 5674 854718834 267 5200783 0 7290 0 7290 0 7290 779 3725 891745585 882 8207126 0 0810 0 0810 0 0810 71 5674 854718834 267 5200783 0 7290 0 7290 0 7290 71 5674 854718834 267 5200783 0 7290 0 7290 0 7290 6 5723 817746584 81 06628138 6 5610 6 5610 6 5610 15 439 8997 188644494 3929 363737 0 0090 0 0090 0 0090 1 417 7916 15161251 1190 710276 0 0810 0 0810 0 0810 1 417 7916 15161251 1190 710276 0 0810 0 0810 0 0810 130 1915 114583277 360 8194754 0 7290 0 7290 0 7290 828 0075 918034649 909 9490218 0 0810 0 0810 0 0810 76 0334 881007575 275 7407366 0 7290 0 7290 0 7290 76 0334 881007575 275 7407366 0 7290 0 7290 0 7290 6 9823 8440318 83 55737738 6 5610 6 5610 6 5610 2 469 2766 392569762 1571 392924 0 0810 0 0810 0 0810 226 7455 355539239 476 1772713 0 7290 0 7290 0 7290 226 7455 355539239 476 1772713 0 7290 0 7290 0 7290 20 8214 31852592 144 2954148 6 5610 6 5610 6 5610