How many times should a risk-averse gambler inisist on playing with Probabi\ lity table [[-1,(i-1)/i],[i,1/i]] for i from 2 to 10 with risk-aversenes\ s 10^(-j) for j from 1 to , 4 By Shalosh B. Ekhad ------------------------------------ Suppose you are offered a bet such that You lose, 2, dollar with probability, 1/2, and you win, 4, dollars with probability, 1/2 The expected gain is one dollar, so if you are rational you should accept th\ is bet. Alas you hate to lose money. If you are willing to take a chance of , 1/10, of losing some money then you should insist on playing this game, 14, times. BTW, the approx. using CLT gives, 15 If you are willing to take a chance of , 1/100, of losing some money then you should insist on playing this game, 47, times. BTW, the approx. using CLT gives, 49 If you are willing to take a chance of , 1/1000, of losing some money then you should insist on playing this game, 83, times. BTW, the approx. using CLT gives, 86 If you are willing to take a chance of , 1/10000, of losing some money then you should insist on playing this game, 122, times. BTW, the approx. using CLT gives, 125 ------------------------------------ Suppose you are offered a bet such that You lose, 3, dollar with probability, 2/3, and you win, 9, dollars with probability, 1/3 The expected gain is one dollar, so if you are rational you should accept th\ is bet. Alas you hate to lose money. If you are willing to take a chance of , 1/10, of losing some money then you should insist on playing this game, 47, times. BTW, the approx. using CLT gives, 53 If you are willing to take a chance of , 1/100, of losing some money then you should insist on playing this game, 163, times. BTW, the approx. using CLT gives, 174 If you are willing to take a chance of , 1/1000, of losing some money then you should insist on playing this game, 287, times. BTW, the approx. using CLT gives, 306 If you are willing to take a chance of , 1/10000, of losing some money then you should insist on playing this game, 419, times. BTW, the approx. using CLT gives, 443 ------------------------------------ Suppose you are offered a bet such that You lose, 4, dollar with probability, 3/4, and you win, 16, dollars with probability, 1/4 The expected gain is one dollar, so if you are rational you should accept th\ is bet. Alas you hate to lose money. If you are willing to take a chance of , 1/10, of losing some money then you should insist on playing this game, 109, times. BTW, the approx. using CLT gives, 124 If you are willing to take a chance of , 1/100, of losing some money then you should insist on playing this game, 379, times. BTW, the approx. using CLT gives, 406 If you are willing to take a chance of , 1/1000, of losing some money then you should insist on playing this game, 674, times. BTW, the approx. using CLT gives, 717 If you are willing to take a chance of , 1/10000, of losing some money then you should insist on playing this game, 979, times. BTW, the approx. using CLT gives, 1038 ------------------------------------ Suppose you are offered a bet such that You lose, 5, dollar with probability, 4/5, and you win, 25, dollars with probability, 1/5 The expected gain is one dollar, so if you are rational you should accept th\ is bet. Alas you hate to lose money. If you are willing to take a chance of , 1/10, of losing some money then you should insist on playing this game, 215, times. BTW, the approx. using CLT gives, 237 If you are willing to take a chance of , 1/100, of losing some money then you should insist on playing this game, 731, times. BTW, the approx. using CLT gives, 780 If you are willing to take a chance of , 1/1000, of losing some money then you should insist on playing this game, 1301, times. BTW, the approx. using CLT gives, 1376 If you are willing to take a chance of , 1/10000, of losing some money then you should insist on playing this game, 1895, times. BTW, the approx. using CLT gives, 1992 ------------------------------------ Suppose you are offered a bet such that You lose, 6, dollar with probability, 5/6, and you win, 36, dollars with probability, 1/6 The expected gain is one dollar, so if you are rational you should accept th\ is bet. Alas you hate to lose money. If you are willing to take a chance of , 1/10, of losing some money then you should insist on playing this game, 370, times. BTW, the approx. using CLT gives, 403 If you are willing to take a chance of , 1/100, of losing some money then you should insist on playing this game, 1259, times. BTW, the approx. using CLT gives, 1326 If you are willing to take a chance of , 1/1000, of losing some money then you should insist on playing this game, 2232, times. BTW, the approx. using CLT gives, 2340 If you are willing to take a chance of , 1/10000, of losing some money then you should insist on playing this game, 3240, times. BTW, the approx. using CLT gives, 3389 ------------------------------------ Suppose you are offered a bet such that You lose, 7, dollar with probability, 6/7, and you win, 49, dollars with probability, 1/7 The expected gain is one dollar, so if you are rational you should accept th\ is bet. Alas you hate to lose money. If you are willing to take a chance of , 1/10, of losing some money then you should insist on playing this game, 583, times. BTW, the approx. using CLT gives, 631 If you are willing to take a chance of , 1/100, of losing some money then you should insist on playing this game, 1975, times. BTW, the approx. using CLT gives, 2079 If you are willing to take a chance of , 1/1000, of losing some money then you should insist on playing this game, 3511, times. BTW, the approx. using CLT gives, 3668 If you are willing to take a chance of , 1/10000, of losing some money then you should insist on playing this game, 5095, times. BTW, the approx. using CLT gives, 5312 ------------------------------------ Suppose you are offered a bet such that You lose, 8, dollar with probability, 7/8, and you win, 64, dollars with probability, 1/8 The expected gain is one dollar, so if you are rational you should accept th\ is bet. Alas you hate to lose money. If you are willing to take a chance of , 1/10, of losing some money then you should insist on playing this game, 863, times. BTW, the approx. using CLT gives, 932 If you are willing to take a chance of , 1/100, of losing some money then you should insist on playing this game, 2933, times. BTW, the approx. using CLT gives, 3069 If you are willing to take a chance of , 1/1000, of losing some money then you should insist on playing this game, 5201, times. BTW, the approx. using CLT gives, 5415 If you are willing to take a chance of , 1/10000, of losing some money then you should insist on playing this game, 7550, times. BTW, the approx. using CLT gives, 7843 ------------------------------------ Suppose you are offered a bet such that You lose, 9, dollar with probability, 8/9, and you win, 81, dollars with probability, 1/9 The expected gain is one dollar, so if you are rational you should accept th\ is bet. Alas you hate to lose money. If you are willing to take a chance of , 1/10, of losing some money then you should insist on playing this game, 1229, times. BTW, the approx. using CLT gives, 1314 If you are willing to take a chance of , 1/100, of losing some money then you should insist on playing this game, 4159, times. BTW, the approx. using CLT gives, 4330 If you are willing to take a chance of , 1/1000, of losing some money then you should insist on playing this game, 7369, times. BTW, the approx. using CLT gives, 7640 If you are willing to take a chance of , 1/10000, of losing some money then you should insist on playing this game, 10689, times. BTW, the approx. using CLT gives, 11065 ------------------------------------ Suppose you are offered a bet such that You lose, 10, dollar with probability, 9/10, and you win, 100, dollars with probability, 1/10 The expected gain is one dollar, so if you are rational you should accept th\ is bet. Alas you hate to lose money. If you are willing to take a chance of , 1/10, of losing some money then you should insist on playing this game, 1682, times. BTW, the approx. using CLT gives, 1789 If you are willing to take a chance of , 1/100, of losing some money then you should insist on playing this game, 5675, times. BTW, the approx. using CLT gives, 5894 If you are willing to take a chance of , 1/1000, of losing some money then you should insist on playing this game, 10053, times. BTW, the approx. using CLT gives, 10400 If you are willing to take a chance of , 1/10000, of losing some money then you should insist on playing this game, 14596, times. BTW, the approx. using CLT gives, 15063 ----------------------------- This took, 1610.863, seconds.