Your Winning prospects If You Have to Leave the Casino in, 100, rounds. By Shalosh B. Ekhad Suppose that you have, 200, 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 0.8909105601 If you exit a loser, the polynomial whose coeff. of s^r tells you the probab\ ility of exiting after exatly r rounds is 57 50 -5 32 0.00004665095981 s + 0.00003045556217 s + 0.3956687773 10 s -5 31 53 -6 25 + 0.5569284278 10 s + 0.00004127378255 s + 0.2701737564 10 s 74 46 94 + 0.00004944590535 s + 0.00003075478109 s + 0.00005605537073 s 81 95 38 + 0.00005756101397 s + 0.00006643431521 s + 0.00001027032810 s -6 23 88 51 + 0.1709960484 10 s + 0.00006443973521 s + 0.00003454649675 s 99 65 87 + 0.00006209046288 s + 0.00004145831182 s + 0.00005615372008 s 58 100 91 + 0.00003716097173 s + 0.00006081508582 s + 0.00006322400208 s 61 68 -5 26 + 0.00004290309220 s + 0.00005659978667 s + 0.2155690183 10 s 79 80 -5 33 + 0.00006091319356 s + 0.00005946531818 s + 0.9163994431 10 s 47 40 54 + 0.00002045958962 s + 0.00001575880694 s + 0.00002880299993 s 71 78 75 + 0.00005698629818 s + 0.00005456274545 s + 0.00006419637533 s 89 82 96 + 0.00005957523777 s + 0.00006391400203 s + 0.00005619980349 s 84 -5 34 72 + 0.00006651744672 s + 0.4297777076 10 s + 0.00005088863182 s 41 48 -5 27 + 0.00001508858250 s + 0.00003141967341 s + 0.1170205757 10 s 98 73 62 + 0.00005813300712 s + 0.00006188941392 s + 0.00005117978607 s -7 19 55 69 + 0.2748779069 10 s + 0.00004554498304 s + 0.00005082757340 s 76 86 83 + 0.00005073784661 s + 0.00006659206669 s + 0.00005493483176 s 52 35 -7 20 + 0.00002910704900 s + 0.00001246892367 s + 0.3298534883 10 s 90 -5 28 42 + 0.00006114259535 s + 0.2955304184 10 s + 0.00002202829646 s 49 56 -5 24 + 0.00002710772199 s + 0.00003143405559 s + 0.1181772690 10 s 63 -6 21 70 + 0.00004105900860 s + 0.1121501860 10 s + 0.00005378306627 s 92 97 -5 36 + 0.00005795909098 s + 0.00006497407092 s + 0.6119117707 10 s -5 29 -5 30 59 + 0.2934084259 10 s + 0.3551046756 10 s + 0.00004526244613 s 43 44 -6 22 + 0.00001487911223 s + 0.00002748978288 s + 0.4037406697 10 s 45 67 85 + 0.00001609987823 s + 0.00004507663954 s + 0.00005431300806 s 77 60 93 + 0.00006359693518 s + 0.00004428735016 s + 0.00006581055451 s 64 37 66 + 0.00005603914808 s + 0.00001452812262 s + 0.00005778965991 s 39 + 0.00001516965136 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 57 50 32 5 0.004789297914 s + 0.008169393900 s + 0.01732802490 s + 0.07776000000 s 31 53 25 + 0.006667319878 s + 0.001322302726 s + 0.01937976127 s 74 8 9 + 0.004502432891 s + 0.05598720000 s + 0.02239488000 s 46 10 94 + 0.004415598004 s + 0.06270566400 s + 0.002655925823 s 81 11 95 + 0.003736182337 s + 0.02149908480 s + 0.001002842971 s 12 38 23 + 0.05052284928 s + 0.005589304845 s + 0.03150712326 s 88 13 51 + 0.002667952858 s + 0.004557805978 s + 0.002809380637 s 99 14 65 + 0.002318211835 s + 0.05522684903 s + 0.003970994598 s 87 15 58 + 0.001488487840 s + 0.006336210272 s + 0.002928655429 s 100 91 61 + 0.0009775193628 s + 0.0009478938031 s + 0.006036743128 s 68 26 79 + 0.004302370311 s + 0.008739140070 s + 0.003604638086 s 16 80 33 + 0.01382408352 s + 0.001544589115 s + 0.002358485960 s 47 40 54 + 0.003732144346 s + 0.005369550000 s + 0.008507115589 s 71 17 78 + 0.001514993082 s + 0.02446231226 s + 0.001781006866 s 75 89 82 + 0.001291721500 s + 0.001376593617 s + 0.0008532378056 s 96 18 84 + 0.001438856035 s + 0.01399233364 s + 0.0008208465511 s 34 72 41 + 0.01873523863 s + 0.004990532671 s + 0.01112144998 s 48 27 98 + 0.007714086765 s + 0.007651227016 s + 0.001185723016 s 73 62 19 + 0.0008728175128 s + 0.001279074343 s + 0.03142113052 s 55 69 76 + 0.001706397177 s + 0.002231924321 s + 0.002033615530 s 86 83 52 + 0.001734953774 s + 0.003937269490 s + 0.008594607412 s 35 20 90 + 0.002571087709 s + 0.01352172204 s + 0.002937273045 s 28 42 49 + 0.01701159932 s + 0.002206266696 s + 0.004022168975 s 56 24 63 + 0.003041058314 s + 0.004061899560 s + 0.006756314467 s 21 70 92 + 0.02752694242 s + 0.004645439212 s + 0.003130371275 s 97 36 29 + 0.001863725767 s + 0.005307009429 s + 0.008686650858 s 30 59 43 + 0.01776744138 s + 0.006092173139 s + 0.01290732099 s 44 22 45 + 0.001836888821 s + 0.004753738232 s + 0.007545614703 s 67 85 77 + 0.002219573352 s + 0.002414483534 s + 0.002860644202 s 60 93 64 + 0.002703801090 s + 0.0006566595648 s + 0.001108059720 s 37 66 39 + 0.009310376596 s + 0.002621949569 s + 0.01189634607 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 .1470831316e-3*t+.2202736630e-3*t^126+.1807936080e-5*t^397+.1104965649e-5*t^391 +.6699192286e-4*t^30+.3371451100e-5*t^401+.1761405315e-4*t^251+.3988182186e-3*t ^200+.1999783024e-2*t^55+.2005868070e-2*t^56+.2168441946e-2*t^57+.7093572794e-3 *t^58+.1447249377e-2*t^59+.2223736894e-3*t^60+.5952851315e-3*t^61+.2601205272e-\ 3*t^62+.3464758370e-3*t^63+.1793080083e-3*t^64+.9963178404e-4*t^65+.4999676991e\ -4*t^66+.1346008950e-3*t^67+.1033351628e-3*t^68+.8770968554e-4*t^69+.3860077690\ e-4*t^70+.3944408453e-3*t^2+.6581183562e-3*t^3+.5527774144e-3*t^4+.7664963165e-\ 3*t^5+.1774587187e-3*t^6+.7554633206e-3*t^7+.7697511527e-3*t^8+.8624632251e-3*t ^9+.5432750629e-3*t^10+.6323158061e-3*t^11+.1646485298e-3*t^12+.5915495750e-3*t ^13+.1158582334e-2*t^14+.1513635853e-2*t^15+.6856855782e-3*t^16+.4202983568e-3* t^17+.1289881407e-3*t^18+.3444265132e-3*t^19+.3762313458e-3*t^20+.6767194341e-3 *t^21+.7268804236e-3*t^22+.2020503039e-2*t^23+.9586441134e-3*t^24+.1054631976e-\ 2*t^25+.6076225747e-3*t^26+.3817159939e-3*t^27+.2159584296e-3*t^28+.1078631321e\ -3*t^29+.3001424355e-3*t^31+.3293848509e-3*t^32+.4463745603e-3*t^33+.9018033185\ e-3*t^34+.1568869494e-2*t^35+.6289996208e-3*t^36+.1634152834e-2*t^37+.\ 1684309264e-2*t^38+.1260943480e-2*t^39+.4416576473e-3*t^40+.3388604500e-3*t^41+ .7405976645e-4*t^42+.2172417532e-3*t^43+.8401713809e-4*t^44+.1154433733e-3*t^45 +.1821154569e-3*t^47+.1263099973e-3*t^49+.2866566941e-3*t^50+.2233961110e-3*t^ 51+.5555681110e-3*t^52+.6869185619e-3*t^53+.4211803117e-3*t^54+.4478815588e-4*t ^112+.3984992215e-4*t^113+.2990084749e-4*t^114+.9290702536e-4*t^115+.4188121911\ e-4*t^116+.6281924236e-4*t^117+.1124576833e-3*t^118+.2332884454e-3*t^119+.\ 7402852151e-4*t^120+.2234375125e-3*t^121+.1767328039e-3*t^122+.3855673169e-3*t^ 123+.4865407388e-3*t^124+.7242302480e-3*t^125+.1039459141e-2*t^127+.1194501186e\ -2*t^128+.1593346260e-2*t^129+.1060405437e-2*t^130+.1580105701e-2*t^131+.\ 8920939458e-4*t^132+.1562557754e-2*t^133+.1158307271e-2*t^134+.9556340113e-3*t^ 135+.6846250716e-3*t^136+.3557675583e-3*t^137+.3363013187e-4*t^138+.5464501189e\ -3*t^139+.1870143879e-3*t^140+.1993705266e-3*t^141+.2328762617e-3*t^142+.\ 2570844552e-3*t^143+.2715748337e-4*t^144+.8947236126e-4*t^145+.1148204194e-3*t^ 146+.1104695025e-3*t^147+.7344600151e-4*t^148+.8687852990e-4*t^149+.1075920307e\ -4*t^150+.8002092965e-4*t^151+.2757641784e-4*t^152+.3891036975e-4*t^153+.\ 4881877409e-4*t^154+.5936093781e-4*t^155+.1230011236e-4*t^156+.3372807002e-4*t^ 157+.3221230425e-4*t^158+.2198305536e-4*t^159+.3968617064e-4*t^160+.2922159703e\ -4*t^161+.1279053924e-4*t^162+.3406849631e-4*t^163+.3184153142e-4*t^164+.\ 2767175316e-4*t^165+.5335340509e-5*t^166+.3865528692e-4*t^167+.1112474685e-4*t^ 168+.2501742745e-4*t^170+.5174877164e-4*t^171+.4843991693e-4*t^172+.8551623142e\ -5*t^173+.8317439894e-5*t^174+.4394409740e-4*t^175+.4547207982e-4*t^176+.\ 4293977767e-4*t^177+.6794352528e-4*t^178+.9900137899e-4*t^179+.1426088437e-4*t^ 180+.4698423057e-4*t^181+.1173038135e-3*t^182+.1072086377e-3*t^183+.1066002348e\ -3*t^184+.2395254085e-3*t^185+.5495429894e-4*t^186+.3689333568e-3*t^187+.\ 1724656154e-3*t^188+.4158570955e-3*t^189+.4104262644e-3*t^190+.5222108940e-3*t^ 191+.1134006129e-3*t^192+.9186518822e-3*t^193+.7606593889e-3*t^194+.7315430932e\ -3*t^195+.1052896192e-2*t^196+.1365476225e-2*t^197+.3888682963e-3*t^198+.\ 9019271747e-4*t^71+.2928830165e-4*t^72+.9250808706e-4*t^74+.1066572498e-3*t^75+ .1372134372e-3*t^76+.1506643237e-3*t^77+.5661397772e-4*t^78+.3702391014e-3*t^79 +.1984035127e-3*t^80+.5089686378e-3*t^81+.9212055717e-3*t^82+.1598178396e-2*t^ 83+.5429470171e-3*t^84+.1621097308e-2*t^85+.1864088742e-2*t^86+.1637054748e-2*t ^87+.1189186552e-2*t^88+.1086129548e-2*t^89+.2465424489e-3*t^90+.9797075911e-3* t^91+.4041871246e-3*t^92+.2867406516e-3*t^93+.1860019701e-3*t^94+.3424685071e-3 *t^95+.5097709221e-4*t^96+.8892663535e-4*t^97+.1450860203e-3*t^98+.1530772144e-\ 3*t^99+.8232235022e-4*t^100+.3822953078e-4*t^101+.2070380268e-4*t^102+.\ 7260320741e-4*t^103+.5962521149e-4*t^104+.3021810248e-4*t^105+.4528010439e-4*t^ 106+.6531146972e-4*t^107+.1386335361e-4*t^108+.1742531529e-4*t^109+.4507861218e\ -4*t^110+.6267874765e-4*t^111+.1260109132e-4*t^376+.1138521210e-3*t^314+.\ 1208156372e-2*t^199+.9145196453e-3*t^201+.3072472874e-3*t^202+.7965874891e-3*t^ 203+.1158328700e-3*t^204+.5252933278e-3*t^205+.4903534812e-3*t^206+.4248267220e\ -3*t^207+.1013128237e-3*t^208+.1145809857e-3*t^209+.8756673781e-4*t^210+.\ 2391596503e-3*t^211+.1572170621e-3*t^212+.1191189609e-3*t^213+.1637845054e-3*t^ 214+.1332144362e-3*t^215+.3802767990e-4*t^216+.4332319306e-4*t^217+.7573126135e\ -4*t^218+.1239436063e-3*t^219+.6023920102e-4*t^220+.5590612404e-4*t^221+.\ 9319990989e-5*t^222+.9950669230e-4*t^223+.2408415793e-4*t^224+.5545331582e-4*t^ 225+.3418037259e-4*t^226+.5901454171e-4*t^227+.1126180681e-4*t^228+.4262945442e\ -4*t^229+.2560560498e-4*t^230+.1801776649e-4*t^231+.3849048089e-4*t^232+.\ 2974802682e-4*t^233+.1037287190e-4*t^234+.2685847149e-4*t^235+.2259219111e-4*t^ 236+.3303195778e-4*t^237+.1769357320e-4*t^238+.3411773109e-4*t^239+.5254116966e\ -5*t^240+.1421358975e-4*t^241+.2399327771e-4*t^242+.1984773886e-4*t^243+.\ 2046653850e-4*t^244+.1123406020e-4*t^245+.4455850739e-5*t^246+.2769638605e-4*t^ 247+.2309349601e-4*t^248+.1875058393e-4*t^249+.1355624111e-4*t^250+.6413292062e\ -5*t^252+.8516539975e-5*t^253+.2035043688e-4*t^254+.2319391704e-4*t^255+.\ 1318676053e-4*t^256+.2571465467e-4*t^257+.4837938601e-5*t^258+.2096927375e-4*t^ 259+.1162975059e-4*t^260+.1310324789e-4*t^261+.1853673637e-4*t^262+.3581641303e\ -4*t^263+.1049955319e-4*t^264+.1440149323e-4*t^265+.1833203282e-4*t^266+.\ 1375108297e-4*t^267+.4151571272e-4*t^268+.1516200674e-4*t^269+.4384058571e-5*t^ 270+.4370980450e-4*t^271+.3103197360e-4*t^272+.5856647673e-4*t^273+.2393290152e\ -4*t^274+.8945148662e-4*t^275+.2564137977e-5*t^276+.4386493259e-4*t^277+.\ 2368074616e-4*t^278+.1391937301e-3*t^279+.9644692352e-4*t^280+.6095515504e-4*t^ 281+.1129916200e-5*t^282+.1245501272e-3*t^283+.1684826777e-3*t^284+.2870107903e\ -3*t^285+.1842929222e-3*t^286+.4361762045e-3*t^287+.1004661691e-4*t^288+.\ 8965129836e-4*t^289+.2396559852e-3*t^290+.5259035678e-3*t^291+.2863619261e-3*t^ 292+.5496534914e-3*t^293+.1992071905e-4*t^294+.4855497150e-3*t^295+.3179937389e\ -3*t^296+.6799745140e-3*t^297+.6229675331e-3*t^298+.6205836714e-3*t^299+.\ 8766564347e-4*t^300+.3131863733e-3*t^301+.3998617275e-3*t^302+.3724743073e-3*t^ 303+.1819041128e-3*t^304+.3790415339e-3*t^305+.5681714182e-4*t^306+.3571928732e\ -3*t^307+.2094650712e-3*t^308+.3476462850e-3*t^309+.5514749754e-4*t^310+.\ 1593026815e-3*t^311+.5862817137e-5*t^312+.1261646213e-3*t^313+.1588823485e-3*t^ 315+.1386386319e-3*t^316+.4478538080e-4*t^317+.5223017633e-4*t^318+.6604642015e\ -4*t^319+.6179484502e-4*t^320+.3714508641e-4*t^321+.1015215974e-3*t^322+.\ 5504790221e-4*t^323+.2200784258e-4*t^324+.9254352238e-5*t^325+.5727517525e-4*t^ 326+.8976396361e-4*t^327+.5748166356e-4*t^328+.3533254272e-4*t^329+.1180169887e\ -4*t^330+.1030483286e-3*t^331+.1889420629e-4*t^332+.2529615636e-4*t^333+.\ 1877852974e-4*t^334+.4161506812e-4*t^335+.1035219262e-4*t^336+.2723501603e-4*t^ 337+.2040806522e-4*t^338+.5083327321e-6*t^339+.4618981937e-4*t^340+.2008790695e\ -4*t^341+.9028468170e-5*t^342+.2297414834e-4*t^343+.2375068403e-4*t^344+.\ 3005181790e-4*t^345+.2668425430e-5*t^438+.9275048600e-5*t^346+.8873167767e-5*t^ 347+.7741829559e-6*t^348+.1069381842e-4*t^349+.2107338475e-4*t^350+.1321674862e\ -4*t^351+.3839153418e-4*t^352+.1653917120e-5*t^353+.6156509421e-5*t^354+.\ 1387418283e-4*t^355+.3274595117e-4*t^356+.1394869334e-4*t^357+.1935587409e-4*t^ 358+.1478278114e-4*t^359+.5477793640e-4*t^360+.2931368800e-5*t^361+.1299106680e\ -4*t^362+.9151330748e-5*t^363+.3044866522e-4*t^364+.4874846236e-5*t^365+.\ 7485062995e-5*t^366+.1422391667e-4*t^367+.1247258365e-4*t^369+.1248976479e-4*t^ 370+.1144841472e-4*t^371+.3650692445e-5*t^372+.9683243733e-5*t^373+.1477851810e\ -4*t^374+.6683991730e-5*t^377+.1658100576e-5*t^378+.1017594906e-4*t^379+.\ 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1227389101e-3*t^431+.7232795912e-5*t^432+.5920934224e-5*t^433+.1586430753e-4*t^ 434+.7044324974e-4*t^435+.1255688531e-3*t^436+.1272312423e-3*t^437+.7452012898e\ -4*t^439+.2206776203e-5*t^440+.1625891098e-3*t^441+.3856931525e-4*t^442+.\ 2145203944e-3*t^443+.2947782825e-5*t^444+.1630435209e-3*t^445+.3199912327e-3*t^ 446+.1514467298e-4*t^447+.6731856774e-4*t^448+.1832849057e-3*t^449+.1693140109e\ -5*t^450+.1386712030e-3*t^452+.1414631448e-3*t^453+.3992384185e-5*t^454+.\ 2159216900e-3*t^455+.5611614203e-5*t^456+.1717036437e-3*t^457+.5186510043e-4*t^ 458+.5342133729e-4*t^459+.8590134333e-4*t^460+.3302030448e-5*t^461+.4879849055e\ -5*t^462+.7560411271e-4*t^463+.6232641253e-4*t^464+.1184965195e-3*t^465+.\ 4195001135e-4*t^466+.9426011626e-5*t^467+.2531032861e-5*t^468+.1049734253e-4*t^ 469+.1123552105e-4*t^470+.8005462964e-4*t^471+.6347190338e-4*t^472+.5314172204e\ -4*t^473+.3019865640e-4*t^475+.1648124535e-4*t^476+.9254487285e-5*t^477+.\ 7838770316e-4*t^478+.7388170254e-5*t^479+.9289076887e-5*t^480+.1741368391e-4*t^ 481+.1461942874e-4*t^482+.5268686536e-6*t^483+.4281138412e-4*t^484+.2090681046e\ -4*t^485+.2952314764e-5*t^486+.1848959610e-4*t^487+.3494145390e-4*t^488+.\ 1208911649e-4*t^490+.2186240751e-4*t^491+.5615031969e-4*t^493+.8738559227e-5*t^ 494+.2102537318e-4*t^495+.2483345234e-4*t^496+.4305242492e-4*t^497+.2978601896e\ -5*t^498+.2229653215e-4*t^499+.3897444530e-4*t^73+.1426682457e-5*t^474+.\ 6729716915e-5*t^451+.2414209253e-4*t^169+.1144883084e-3*t^46+.9329924388e-5*t^ 405+.2186611554e-6*t^407+.3643795715e-6*t^489+.2215292322e-5*t^492+.4703150154e\ -4*t^48+.2762069599e-6*t^375+.6938866184e-5*t^420+.5372561055e-5*t^385+.\ 7480792421e-5*t^368 The expected duration of such a game is, 35.52005266 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, 35.52005266 The whole thing took, 12.776, seconds to compute.