Your Winning prospects If You Have to Leave the Casino in, 100, rounds. By Shalosh B. Ekhad Suppose that you have, 50, dollars, and you enter a casino where your pobability of winning a round is , 3/5 You owe, 500, dollars to a loan shark, who would kill you if you don't return the debt by , 100, rounds. any lesser amount would do you no good. Suppose you follow the strategy below, where the j-th entry tells you what you would stake if you currently have j dollars . [1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 32, 32, 32, 32, 32, 33, 33, 33, 33, 33, 34, 34, 34, 34, 34, 35, 35, 35, 35, 35, 36, 36, 36, 36, 36, 37, 37, 37, 37, 37, 38, 38, 38, 38, 38, 39, 39, 39, 39, 39, 40, 40, 40, 40, 40, 41, 41, 41, 41, 41, 42, 42, 42, 42, 42, 43, 43, 43, 43, 43, 44, 44, 44, 44, 44, 45, 45, 45, 45, 45, 46, 46, 46, 46, 46, 47, 47, 47, 47, 47, 48, 48, 48, 48, 48, 49, 49, 49, 49, 49, 50, 50, 50, 50, 50, 51, 51, 51, 51, 51, 52, 52, 52, 52, 52, 53, 53, 53, 53, 53, 54, 54, 54, 54, 54, 55, 55, 55, 55, 55, 56, 56, 56, 56, 56, 57, 57, 57, 57, 57, 58, 58, 58, 58, 58, 59, 59, 59, 59, 59, 60, 60, 60, 60, 60, 61, 61, 61, 61, 61, 62, 62, 62, 62, 62, 63, 63, 63, 63, 63, 64, 64, 64, 64, 64, 65, 65, 65, 65, 65, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 68, 68, 68, 68, 68, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 71, 71, 71, 71, 71, 72, 72, 72, 72, 72, 73, 73, 73, 73, 73, 74, 74, 74, 74, 74, 75, 75, 75, 75, 75, 76, 76, 76, 76, 76, 77, 77, 77, 77, 77, 78, 78, 78, 78, 78, 79, 79, 79, 79, 79, 80, 80, 80, 80, 80, 81, 81, 81, 81, 81, 82, 82, 82, 82, 82, 83, 83, 83, 83, 83, 84, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1] Your probability of staying alive, i.e. leaving the casino as a winner with, 500, dollars. is 0.6121761907 If you exit a loser, the polynomial whose coeff. of s^r tells you the probab\ ility of exiting after exatly r rounds is 49 71 42 0.0004581280217 s + 0.0004112008920 s + 0.0004163076229 s 35 76 97 + 0.0003060217074 s + 0.0003918114168 s + 0.0002957814309 s 92 82 48 + 0.0003165620910 s + 0.0003685502432 s + 0.0003550798870 s 27 83 29 + 0.0002828220348 s + 0.0003493416497 s + 0.0003254959458 s 57 -5 13 85 + 0.0003790598741 s + 0.6710886400 10 s + 0.0003557830637 s -5 14 15 34 + 0.8053063680 10 s + 0.00001771674010 s + 0.0003195664449 s 99 90 16 + 0.0002880642806 s + 0.0003150111518 s + 0.00004831838208 s 64 30 89 + 0.0004034206754 s + 0.0001951677035 s + 0.0003531903234 s 17 56 18 + 0.00002126008812 s + 0.0004396016955 s + 0.00009926528415 s 37 98 51 + 0.0002917548731 s + 0.0003204519239 s + 0.0004488406750 s 84 44 36 + 0.0003492958685 s + 0.0003913780958 s + 0.0003793978080 s 19 65 79 + 0.00003024344171 s + 0.0004150109693 s + 0.0003428556418 s 77 72 20 + 0.0003515496448 s + 0.0003717053943 s + 0.0001409938120 s 58 43 93 + 0.0004510200227 s + 0.0003705061298 s + 0.0003255237173 s 96 21 61 + 0.0003228108335 s + 0.00007373091330 s + 0.0003803044470 s 86 78 38 + 0.0003316208866 s + 0.0003928922338 s + 0.0004181410777 s 70 31 75 + 0.0003641219629 s + 0.0003372582897 s + 0.0003688821152 s 68 45 41 + 0.0003664298640 s + 0.0004147483907 s + 0.0003263786892 s 22 55 52 + 0.0001597477145 s + 0.0003993765406 s + 0.0003857108840 s 100 66 59 + 0.0003123817928 s + 0.0003807112880 s + 0.0003722058222 s 23 73 80 + 0.0001403984429 s + 0.0003907064051 s + 0.0003845271465 s 50 39 62 + 0.0003622254182 s + 0.0002967843144 s + 0.0004278700698 s 46 69 32 + 0.0003672099597 s + 0.0004242044365 s + 0.0002528345324 s 28 24 53 + 0.0001638905709 s + 0.0001626733501 s + 0.0004258253864 s 87 94 91 + 0.0003579823047 s + 0.0003205018057 s + 0.0003414954906 s 60 67 25 + 0.0004461327277 s + 0.0004254791190 s + 0.0002153492171 s 33 74 40 + 0.0003258288866 s + 0.0003830933452 s + 0.0004291626149 s 81 63 47 + 0.0003433117786 s + 0.0003974222520 s + 0.0004466553341 s 95 26 54 + 0.0003090800467 s + 0.0001594113226 s + 0.0004150609297 s 88 + 0.0003195596209 s If you exit a winner, the polynomial whose coeff. of s^r tells you the proba\ bility of exiting after exatly r rounds is 49 71 42 35 0.004552851928 s + 0.007976312013 s + 0.01379443030 s + 0.01626246445 s 76 97 92 + 0.002561201990 s + 0.007179354106 s + 0.003640346377 s 82 48 27 + 0.007917494973 s + 0.01490943543 s + 0.001250443608 s 83 29 57 + 0.003785060330 s + 0.003262087008 s + 0.01475357837 s 13 85 14 + 0.001306069402 s + 0.002787160113 s + 0.0005224277606 s 15 34 99 + 0.003761479877 s + 0.005811554344 s + 0.005075796419 s 90 16 64 + 0.004692284628 s + 0.0001253826626 s + 0.01216709390 s 30 89 17 + 0.005190342142 s + 0.003701138541 s + 0.007723572013 s 56 18 37 + 0.002810595181 s + 0.0003911939072 s + 0.01876463075 s 98 51 84 + 0.002678558883 s + 0.01046313241 s + 0.008901203339 s 44 36 19 + 0.01546909914 s + 0.002532299821 s + 0.004519794220 s 65 79 77 + 0.003475382907 s + 0.006857178936 s + 0.01033404815 s 72 20 58 + 0.004646737635 s + 0.004548682385 s + 0.003039408906 s 43 93 96 + 0.006205917850 s + 0.007273506153 s + 0.002264854593 s 21 61 86 + 0.002631230403 s + 0.005430918995 s + 0.009110587366 s 78 38 70 + 0.002965560196 s + 0.002530187597 s + 0.005883349302 s 31 75 68 + 0.01116580319 s + 0.01071785896 s + 0.01062353678 s 45 41 22 + 0.004272352313 s + 0.005691832055 s + 0.009728956361 s 55 52 100 + 0.01437022455 s + 0.005740653631 s + 0.004267201761 s 66 59 23 + 0.01281691201 s + 0.009150536988 s + 0.004140020767 s 73 80 50 + 0.01004965324 s + 0.005478466842 s + 0.006743165670 s 39 62 46 + 0.01103670672 s + 0.01083047234 s + 0.01690427701 s 69 32 28 + 0.004308512314 s + 0.005635216781 s + 0.01592417972 s 24 53 87 + 0.01236316417 s + 0.01353557705 s + 0.002407597796 s 94 91 60 + 0.002925789226 s + 0.005926902734 s + 0.006895800020 s 67 25 33 + 0.002529871319 s + 0.003506080376 s + 0.01526805595 s 74 40 81 + 0.003810366471 s + 0.007821884442 s + 0.004491771492 s 63 47 95 + 0.004981984877 s + 0.002375568567 s + 0.007712864602 s 26 54 88 + 0.01511241898 s + 0.005057912651 s + 0.007418618235 s If you quit the casion after, 100, rounds without being either a winner or lo\ ser, the polynomial whose coeff. of t^r tells you the exact probability of having r dollars is .7151588050e-3*t+.2205208849e-3*t^126+.1850862016e-4*t^463+.5353018739e-3*t^64+ .1428577976e-5*t^451+.6027225867e-2*t^50+.2919995981e-3*t^84+.9086952659e-4*t^ 417+.1248452743e-3*t^419+.1284417063e-2*t^56+.1033537625e-2*t^57+.2901315485e-3 *t^58+.7584140020e-3*t^59+.1619255704e-3*t^60+.5829626812e-3*t^61+.2936100229e-\ 3*t^62+.6591461199e-3*t^63+.4220715407e-3*t^65+.3343723607e-3*t^66+.1123538617e\ -2*t^67+.1337638221e-2*t^68+.1792269328e-2*t^69+.1172671134e-2*t^70+.3511249579\ e-2*t^71+.1627072287e-2*t^72+.2109802474e-2*t^73+.1873733799e-2*t^2+.3419918116\ e-2*t^3+.2614665883e-2*t^4+.2913131515e-2*t^5+.8189364422e-3*t^6+.4897418956e-2 *t^7+.2692410806e-2*t^8+.2565133291e-2*t^9+.1971894153e-2*t^10+.4783158298e-2*t ^11+.1831535216e-2*t^12+.3702237510e-2*t^13+.3594705352e-2*t^14+.2356067861e-2* t^15+.1745501559e-2*t^16+.2033545144e-2*t^17+.1133557610e-2*t^18+.4966495825e-2 *t^19+.4876685642e-2*t^20+.4781098310e-2*t^21+.2250730009e-2*t^22+.2810092410e-\ 2*t^23+.8103728276e-3*t^24+.1443574039e-2*t^25+.1284795205e-2*t^26+.1612592421e\ -2*t^27+.1921212434e-2*t^28+.1878022789e-2*t^29+.1324066450e-2*t^30+.7089318218\ e-2*t^31+.5398619328e-2*t^32+.4183392655e-2*t^33+.3666054488e-2*t^34+.\ 2270566677e-2*t^35+.5692584379e-3*t^36+.1099259372e-2*t^37+.1331579437e-2*t^38+ .1220874873e-2*t^39+.6733209829e-3*t^40+.9693827864e-3*t^41+.2401442288e-3*t^42 +.1422537759e-2*t^43+.9295349514e-3*t^44+.2029793542e-2*t^45+.2422141650e-2*t^ 46+.6043881019e-2*t^47+.1925291577e-2*t^48+.4205434620e-2*t^49+.3628858966e-2*t ^51+.3338342310e-2*t^52+.2207849932e-2*t^53+.7981598301e-3*t^54+.1939575245e-2* t^55+.3948712190e-3*t^133+.3158740288e-3*t^134+.2759645395e-3*t^135+.2347853130\ e-3*t^136+.1541028947e-3*t^137+.1329345574e-4*t^138+.2783551406e-3*t^139+.\ 1205943990e-3*t^140+.1317520533e-3*t^141+.1931287017e-3*t^142+.2785994682e-3*t^ 143+.2596123908e-4*t^144+.1069212206e-3*t^145+.1793236547e-3*t^146+.1895510217e\ -3*t^147+.1659440268e-3*t^148+.2531108937e-3*t^149+.3101481846e-4*t^150+.\ 3347893848e-3*t^151+.1165673574e-3*t^152+.2250753348e-3*t^153+.3768309854e-3*t^ 154+.5531527636e-3*t^155+.1284506133e-3*t^156+.3936603107e-3*t^157+.4608152885e\ -3*t^158+.3157260222e-3*t^159+.8521986106e-3*t^160+.7530264351e-3*t^161+.\ 3208551598e-3*t^162+.1307159624e-2*t^163+.1431069606e-2*t^164+.1504077074e-2*t^ 165+.2633122460e-3*t^166+.2349813198e-2*t^167+.6873295169e-3*t^168+.1621872898e\ -2*t^169+.1999589092e-2*t^170+.3829332331e-2*t^171+.3186945630e-2*t^172+.\ 6925435696e-3*t^173+.6850120683e-3*t^174+.2993457313e-2*t^175+.2241529770e-2*t^ 176+.2002904055e-2*t^177+.2420815406e-2*t^178+.2389845049e-2*t^179+.3646834266e\ -3*t^180+.9114613594e-3*t^181+.1571800921e-2*t^182+.1087414659e-2*t^183+.\ 1196201457e-2*t^185+.2323054044e-3*t^186+.1052544871e-2*t^187+.4308473133e-3*t^ 190+.4164684572e-3*t^191+.6974134237e-4*t^192+.5160425800e-3*t^193+.3449660356e\ -3*t^194+.2406722422e-3*t^195+.2867808998e-3*t^196+.3249241604e-3*t^197+.\ 9968316632e-4*t^198+.2783443762e-3*t^199+.8388291418e-4*t^200+.2035333403e-3*t^ 201+.7278857391e-4*t^202+.2090304496e-3*t^203+.1417128991e-3*t^205+.1708220859e\ -3*t^206+.1841911736e-3*t^207+.4625044340e-4*t^208+.4750714175e-4*t^209+.\ 4371827093e-4*t^210+.1332996640e-3*t^211+.9650683542e-4*t^212+.7587795931e-4*t^ 213+.1250666165e-3*t^214+.1192272193e-3*t^215+.3285591270e-4*t^216+.3435183471e\ -4*t^217+.7255041069e-4*t^218+.1404143348e-3*t^219+.4199301837e-2*t^74+.\ 5720683463e-2*t^75+.4585755327e-2*t^76+.3432789224e-2*t^77+.1504809504e-2*t^78+ .4166207191e-2*t^79+.1264791369e-2*t^80+.2140808079e-2*t^81+.1872011111e-2*t^82 +.1565193262e-2*t^83+.7023490727e-3*t^85+.7118625481e-3*t^86+.4341305092e-3*t^ 87+.3632247734e-3*t^88+.4392152418e-3*t^89+.4693898619e-3*t^91+.2893466695e-3*t ^92+.2514138332e-3*t^93+.1625375268e-3*t^94+.4615211804e-3*t^95+.9012703426e-4* t^96+.1652711031e-3*t^97+.3629815238e-3*t^98+.6133952850e-3*t^99+.5337015951e-3 *t^100+.2663159327e-3*t^101+.1740603896e-3*t^102+.8257411448e-3*t^103+.\ 9316335580e-3*t^104+.6096046118e-3*t^105+.1183210273e-2*t^106+.2234003227e-2*t^ 107+.6407261158e-3*t^108+.9185355672e-3*t^109+.2502811308e-2*t^110+.3708751172e\ -2*t^111+.2913295921e-2*t^112+.2764922337e-2*t^113+.1956745494e-2*t^114+.\ 5218068833e-2*t^115+.1879390102e-2*t^116+.2749004093e-2*t^117+.3121778580e-2*t^ 118+.3781433211e-2*t^119+.9790374396e-3*t^120+.1664193823e-2*t^121+.1394868777e\ -2*t^123+.1115443971e-2*t^124+.9659225285e-3*t^125+.7133597557e-3*t^127+.\ 6014655930e-3*t^129+.2730914094e-3*t^130+.3695953061e-3*t^131+.1825935199e-4*t^ 132+.8567180486e-3*t^251+.6253994492e-3*t^189+.2248130357e-3*t^376+.6430488186e\ -4*t^314+.6950682061e-4*t^220+.7157337003e-4*t^221+.8738275652e-5*t^222+.\ 1773489369e-3*t^223+.3995542718e-4*t^224+.1329647831e-3*t^225+.7785231192e-4*t^ 226+.1880578571e-3*t^227+.3030659520e-4*t^228+.1576669457e-3*t^229+.1049460660e\ -3*t^230+.5330287370e-4*t^231+.2342503552e-3*t^232+.1722264505e-3*t^233+.\ 5764934809e-4*t^234+.1720229549e-3*t^235+.2261946921e-3*t^236+.3497322246e-3*t^ 237+.1681017131e-3*t^238+.4624574145e-3*t^239+.4873623515e-4*t^240+.1759986052e\ -3*t^241+.4574928366e-3*t^242+.3011860998e-3*t^243+.5007832679e-3*t^244+.\ 2639475266e-3*t^245+.1205141104e-3*t^246+.8443649220e-3*t^247+.8972029569e-3*t^ 248+.9570752705e-3*t^249+.3971254223e-3*t^250+.3387422827e-3*t^252+.4567632536e\ -3*t^253+.1141966324e-2*t^254+.1362635678e-2*t^255+.1034014471e-2*t^256+.\ 1967754046e-2*t^257+.2361201938e-3*t^258+.1506948174e-2*t^259+.7559865177e-3*t^ 260+.9104954985e-3*t^261+.1513176403e-2*t^262+.2062985814e-2*t^263+.6018068621e\ -3*t^264+.8905302171e-3*t^265+.1054210248e-2*t^266+.7067865606e-3*t^267+.\ 1688569605e-2*t^268+.5628911649e-3*t^269+.1772404278e-3*t^270+.1159499371e-2*t^ 271+.7532601953e-3*t^272+.1142204949e-2*t^273+.4259462712e-3*t^274+.1055437198e\ -2*t^275+.7102180129e-4*t^276+.4186830131e-3*t^277+.2059861747e-3*t^278+.\ 8364500346e-3*t^279+.4201134285e-3*t^280+.2195705449e-3*t^281+.6488445891e-5*t^ 282+.4299722531e-3*t^283+.3577477077e-3*t^284+.4493526801e-3*t^285+.2843103360e\ -3*t^286+.4599051433e-3*t^287+.1604205841e-4*t^288+.1253674299e-3*t^289+.\ 1505191580e-3*t^290+.2566118127e-3*t^291+.1639854600e-3*t^292+.2172193566e-3*t^ 293+.1385675505e-4*t^294+.1921592784e-3*t^295+.8338029092e-4*t^296+.1826641298e\ -3*t^297+.1656879144e-3*t^298+.1757243126e-3*t^299+.3564421183e-4*t^300+.\ 9337570338e-4*t^301+.9611933975e-4*t^302+.8867612752e-4*t^303+.4952384399e-4*t^ 304+.1475775670e-3*t^305+.1624471742e-4*t^306+.1024367022e-3*t^307+.1032882285e\ -3*t^309+.4327096708e-4*t^310+.1039131435e-3*t^311+.7961514300e-4*t^313+.\ 8100943908e-4*t^315+.7191028226e-4*t^316+.3320796547e-4*t^317+.6090421728e-4*t^ 318+.4775426124e-4*t^319+.2274407128e-4*t^321+.7720170719e-4*t^322+.5817626712e\ -4*t^323+.5706458683e-4*t^326+.6775167139e-4*t^327+.5383240584e-4*t^328+.\ 4178762071e-4*t^329+.9863178928e-4*t^331+.1565750097e-4*t^332+.2635201549e-4*t^ 333+.1654352632e-4*t^334+.6644918933e-4*t^335+.2457175933e-4*t^336+.4228559942e\ -4*t^337+.3032844351e-4*t^338+.5557603095e-4*t^340+.5489403455e-4*t^341+.\ 1380248031e-4*t^342+.7187339902e-4*t^343+.5705274665e-4*t^344+.9997765938e-4*t^ 345+.1785050252e-4*t^346+.1926886845e-4*t^347+.5341797911e-5*t^348+.3554049894e\ -4*t^349+.9306976439e-4*t^350+.4642600791e-4*t^351+.9239534546e-4*t^352+.\ 4824989832e-5*t^353+.1104335619e-4*t^354+.7886455296e-4*t^355+.8920547868e-4*t^ 356+.1144894349e-3*t^357+.1440313893e-3*t^358+.1634067567e-3*t^359+.2748662345e\ -4*t^360+.2438469444e-4*t^361+.9078435760e-4*t^362+.1081589291e-3*t^363+.\ 1450409923e-3*t^364+.7781809041e-4*t^365+.2354571588e-5*t^438+.1726700800e-3*t^ 367+.3695543270e-4*t^368+.2417175973e-3*t^369+.1917559369e-3*t^370+.4016480318e\ -3*t^371+.2212588312e-4*t^372+.8222757480e-4*t^373+.3048942608e-3*t^374+.\ 8029036783e-5*t^375+.2550076272e-3*t^377+.7321487628e-5*t^378+.4912714638e-3*t^ 379+.5144819412e-3*t^380+.1796389389e-3*t^381+.1827632144e-3*t^382+.3183770973e\ -3*t^383+.2745902143e-4*t^384+.3726816381e-3*t^385+.2695812048e-3*t^386+.\ 8182966015e-3*t^387+.3696382030e-3*t^388+.7925609153e-4*t^389+.1767768847e-4*t^ 390+.7825180427e-4*t^391+.6111359134e-3*t^392+.6530480684e-3*t^393+.7309701899e\ -3*t^394+.4553766563e-3*t^395+.1601672734e-4*t^396+.1152590294e-3*t^397+.\ 9318189381e-3*t^398+.7236824623e-4*t^399+.3268729154e-3*t^400+.2006945155e-3*t^ 401+.6320045715e-6*t^402+.6964067514e-3*t^403+.3723538434e-4*t^404+.3547151672e\ -3*t^405+.2869385219e-3*t^406+.4087891488e-5*t^407+.2089464444e-5*t^408+.\ 3568904572e-3*t^409+.3509758596e-3*t^410+.1298848079e-3*t^411+.4299303586e-3*t^ 412+.2940456116e-3*t^413+.4882454568e-4*t^414+.3552691295e-3*t^415+.1248166922e\ -3*t^416+.2303685324e-4*t^418+.3040103783e-4*t^420+.2425256742e-3*t^421+.\ 1184737443e-3*t^422+.1661075485e-3*t^423+.1258826906e-4*t^424+.7227763212e-4*t^ 425+.3410640982e-4*t^426+.1373260942e-3*t^427+.1615304739e-3*t^428+.1458431525e\ -3*t^429+.2855214883e-3*t^430+.1264153142e-3*t^431+.4402807975e-4*t^432+.\ 1090258921e-3*t^433+.3231137812e-4*t^434+.1268454250e-3*t^435+.7452221727e-4*t^ 436+.6659800939e-4*t^437+.5396061795e-4*t^440+.9973094024e-4*t^441+.9664668462e\ -4*t^442+.6887299737e-4*t^443+.9326245899e-4*t^444+.1195534525e-3*t^445+.\ 1693733015e-3*t^446+.2709048988e-4*t^448+.9758084463e-4*t^449+.6859261520e-4*t^ 450+.6935122172e-4*t^452+.4330751421e-4*t^453+.3420251293e-4*t^454+.4310332048e\ -4*t^455+.1665311874e-3*t^456+.4985935238e-4*t^457+.2805019628e-4*t^458+.\ 7762539429e-4*t^459+.4504461774e-4*t^460+.1828230599e-4*t^461+.6530916623e-4*t^ 462+.9306492330e-4*t^464+.3507083353e-4*t^465+.3643523564e-4*t^466+.1826648292e\ -3*t^468+.4934930231e-4*t^469+.1095494705e-4*t^470+.7053211961e-4*t^471+.\ 4834331439e-4*t^472+.4359135829e-4*t^473+.1009102877e-3*t^474+.1379340983e-4*t^ 475+.9036463314e-4*t^476+.4266520216e-5*t^477+.9247881079e-4*t^478+.8437372526e\ -5*t^479+.4823065619e-5*t^480+.1590947918e-4*t^481+.1218895830e-3*t^482+.\ 2616474434e-4*t^484+.4021172132e-4*t^485+.1220762681e-3*t^486+.1327233824e-4*t^ 487+.6886519883e-4*t^488+.1950356699e-3*t^490+.1927138504e-4*t^491+.1366603336e\ -3*t^492+.3588874524e-4*t^493+.1035193924e-4*t^494+.3319044415e-4*t^495+.\ 2095922308e-4*t^497+.1684413150e-3*t^498+.2683187372e-4*t^499+.3440456242e-4*t^ 320+.6615516613e-6*t^483+.4233172555e-6*t^489+.2095795816e-4*t^496+.1927248658e\ -4*t^324+.7916590986e-3*t^184+.2745815865e-5*t^312+.3941645749e-4*t^447+.\ 6060759663e-3*t^128+.1249669051e-4*t^467+.7613081631e-4*t^308+.3380850079e-3*t^ 188+.2986705468e-4*t^204+.3294613744e-4*t^439+.8090515308e-5*t^325+.8623991148e\ -4*t^90+.1092643550e-2*t^122+.8550055311e-5*t^366+.9389382215e-6*t^339+.\ 1056524956e-4*t^330 The expected duration of such a game is, 71.31831540 If the loan shark unexpectedly disappers, and spares your life, then the exp\ ected gain, if you are also allowed to keep your current capital is, 71.31831540 The whole thing took, 12.235, seconds to compute.