{"text_format":"1","workbook":"xlsx","n_sheets":2,"sheets":["Model","Simulations"],"not_rendered":{"charts":0,"images":0,"macros":0,"external_links":0,"defined_names":12,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Model","index":0,"n_rows":90,"n_cols":7,"rows_kept":90,"cut":false,"hidden":false,"merged":[]}
["Roulette: Double-Up Strategy"]
["There are 38 possible outcomes, two are double zero, 18 are black and 18 are red."]
["If you bet either black or red your chances of winning an amount equal to your bet is"]
["18/38. If you win you keep your bet and receive an additional amount equal to your"]
["bet. If you lose you receive nothing and lose your bet. This can be modeled as:"]
[]
["In the double-up strategy your  bet doubles until you win. When you eventually win"]
["a bet you will have total winnings equal to the starting bet."]
[]
[null,"Starting Amount",1000]
[null,"Starting Bet",10]
["Bet Number","Bankroll Before Bet","Amount Bet: Stop After 1st Bet","Win or Lose","Change in Bankroll","Bankroll After Bet",{"$f":"\"=999 if Bankroll <\"&C10","v":"=999 if Bankroll <1000"}]
[]
[{"$f":"1+A13","v":1},{"$f":"C10","v":1000},{"$f":"$C$11","v":10},{"$f":"IF(RAND()<18/38,\"Win\",\"Lose\")","v":"Lose"},{"$f":"IF(D14=\"Win\",C14,-C14)","v":-10},{"$f":"B14+E14","v":990},{"$f":"IF(F14>$C$10,A14,999)","v":999}]
[{"$f":"1+A14","v":2},{"$f":"F14","v":990},{"$f":"IF(F14>$C$10,0,2*C14)","v":20},{"$f":"IF(RAND()<18/38,\"Win\",\"Lose\")","v":"Win"},{"$f":"IF(D15=\"Win\",C15,-C15)","v":20},{"$f":"B15+E15","v":1010},{"$f":"IF(F15>$C$10,A15,999)","v":2}]
[{"$f":"1+A15","v":3},{"$f":"F15","v":1010},{"$f":"IF(F15>$C$10,0,2*C15)","v":0},"Lose",{"$f":"IF(D16=\"Win\",C16,-C16)","v":0},{"$f":"B16+E16","v":1010},3]
[4,1010,0,"Win",0,1010,4]
[5,1010,0,"Lose",0,1010,5]
[6,1010,0,"Win",0,1010,6]
[7,1010,0,"Win",0,1010,7]
[8,1010,0,"Lose",0,1010,8]
[9,1010,0,"Lose",0,1010,9]
[10,1010,0,"Lose",0,1010,10]
[11,1010,0,"Win",0,1010,11]
[12,1010,0,"Win",0,1010,12]
[13,1010,0,"Win",0,1010,13]
[14,1010,0,"Lose",0,1010,14]
[15,1010,0,"Win",0,1010,15]
[16,1010,0,"Win",0,1010,16]
[17,1010,0,"Win",0,1010,17]
[18,1010,0,"Lose",0,1010,18]
[19,1010,0,"Win",0,1010,19]
[20,1010,0,"Win",0,1010,20]
[21,1010,0,"Win",0,1010,21]
[22,1010,0,"Win",0,1010,22]
[23,1010,0,"Lose",0,1010,23]
[24,1010,0,"Win",0,1010,24]
[25,1010,0,"Lose",0,1010,25]
[26,1010,0,"Lose",0,1010,26]
[27,1010,0,"Lose",0,1010,27]
[28,1010,0,"Lose",0,1010,28]
[29,1010,0,"Win",0,1010,29]
[30,1010,0,"Lose",0,1010,30]
[31,1010,0,"Win",0,1010,31]
[32,1010,0,"Lose",0,1010,32]
[33,1010,0,"Lose",0,1010,33]
[34,1010,0,"Win",0,1010,34]
[35,1010,0,"Lose",0,1010,35]
[36,1010,0,"Win",0,1010,36]
[37,1010,0,"Lose",0,1010,37]
[38,1010,0,"Lose",0,1010,38]
[39,1010,0,"Lose",0,1010,39]
[40,1010,0,"Lose",0,1010,40]
[41,1010,0,"Win",0,1010,41]
[42,1010,0,"Win",0,1010,42]
[43,1010,0,"Win",0,1010,43]
[44,1010,0,"Win",0,1010,44]
[45,1010,0,"Lose",0,1010,45]
[46,1010,0,"Win",0,1010,46]
[47,1010,0,"Win",0,1010,47]
[48,1010,0,"Win",0,1010,48]
[49,1010,0,"Lose",0,1010,49]
[50,1010,0,"Win",0,1010,50]
[null,"Sum of Bets",{"$f":"SUM(C14:C63)","v":30},null,null,"Number of Bets",{"$f":"MIN(G14:G63)","v":2}]
[]
[null,null,null,null,"Final Tally of Amount Won (Lost)",{"$f":"F63-B14","v":10}]
[null,null,null,null,"Maximum Bet",{"$f":"MAX(C14:C63)","v":20}]
[null,"Total of Bets","# Total Bets","Bets",null,"Expected Frequency"]
[1,{"$f":"$C$11","v":10},{"$f":"FREQUENCY(DataTableValues,B69:B89)","v":4684},{"$f":"C11","v":10},null,{"$f":"18/38*10000","v":4736.8421052631575}]
[{"$f":"1+A69","v":2},{"$f":"SUM($D$69:D70)","v":30},2556,{"$f":"2*D69","v":20},null,{"$f":"F69*(20/38)","v":2493.0747922437668}]
[3,{"$f":"SUM($D$69:D71)","v":70},1325,{"$f":"2*D70","v":40},null,{"$f":"F70*(20/38)","v":1312.1446274967193}]
[4,{"$f":"SUM($D$69:D72)","v":150},653,80,null,690.60243552458905]
[5,{"$f":"SUM($D$69:D73)","v":310},401,160,null,363.47496606557314]
[6,{"$f":"SUM($D$69:D74)","v":630},189,320,null,191.30261371872268]
[7,{"$f":"SUM($D$69:D75)","v":1270},91,640,null,100.68558616774878]
[8,{"$f":"SUM($D$69:D76)","v":2550},43,1280,null,52.992413772499354]
[9,{"$f":"SUM($D$69:D77)","v":5110},28,2560,null,27.890744090789131]
[10,{"$f":"SUM($D$69:D78)","v":10230},13,5120,null,14.679338995152174]
[11,{"$f":"SUM($D$69:D79)","v":20470},8,10240,null,7.7259678921853538]
[12,{"$f":"SUM($D$69:D80)","v":40950},4,20480,null,4.0662988906238704]
[13,{"$f":"SUM($D$69:D81)","v":81910},4,40960,null,2.1401573108546685]
[{"$f":"1+A81","v":14},{"$f":"SUM($D$69:D82)","v":163830},0,81920,null,1.1263985846603517]
[15,{"$f":"SUM($D$69:D83)","v":327670},0,163840,null,0.59284136034755353]
[16,{"$f":"SUM($D$69:D84)","v":655350},0,327680,null,0.31202176860397551]
[17,{"$f":"SUM($D$69:D85)","v":1310710},1,655360,null,0.16422198347577657]
[18,{"$f":"SUM($D$69:D86)","v":2621430},0,1310720,null,8.6432622881987664E-2]
[19,{"$f":"SUM($D$69:D87)","v":5242870},0,2621440,null,4.5490854148414556E-2]
[20,{"$f":"SUM($D$69:D88)","v":10485750},0,5242880,null,2.3942554814955028E-2]
[21,{"$f":"SUM($D$69:D89)","v":20971510},0,10485760,null,1.2601344639450014E-2]
[null,"Other",0,null,null,{"$f":"SUM(F69:F89)","v":9999.9859985059538}]

{"sheet":"Simulations","index":1,"n_rows":1002,"n_cols":12,"rows_kept":1002,"cut":false,"hidden":false,"merged":[]}
[null,null,"Data Table: Simulated Values of Formula Cell"]
["Formula Cell-->",{"$f":"Model!C64","v":30},1,2,3,4,5,6,7,8,9,10]
[null,1,10,310,10,10,30,10,30,70,10,10]
["Dummy1",2,10,30,10,30,30,10,10,70,10,10]
["Dummy2",3,70,30,30,10,70,30,30,30,10,70]
[{"$f":"MAX(C3:L1002)","v":1310710},4,10,310,30,10,10,10,30,10,10,30]
[{"$f":"MIN(C3:L1002)","v":10},5,30,30,150,10,150,10,10,150,10,30]
[null,6,10,10,30,10,10,30,70,70,30,30]
[null,7,10,1270,70,30,70,10,150,30,10,10]
[null,8,70,70,10,10,30,10,10,10,30,30]
[null,9,10,70,10,30,630,10,30,150,30,10]
[null,10,30,150,70,150,70,10,310,10,30,70]
[null,11,10,10,10,70,70,150,30,30,70,70]
[null,12,310,10,70,10,30,10,70,630,30,10]
[null,13,10,10,10,30,30,10,10,10,70,10]
[null,14,10,10,30,10,10,70,5110,70,30,10]
[null,15,150,30,150,70,10,10,30,10,310,70]
[null,16,30,10,30,10,30,1270,70,10,150,30]
[null,17,30,310,630,30,310,10,70,630,150,1270]
[null,18,70,30,10,150,30,10,70,10,630,10]
[null,19,10,10,30,70,70,10,10,10,30,10]
[null,20,10,150,70,10,70,30,10,10,10,10]
[null,21,10,10,10,30,10,30,10,5110,10,10]
[null,22,70,10,30,70,1270,310,10,70,10,30]
[null,23,70,30,10,630,30,70,70,10,70,10]
[null,24,10,70,10,310,30,30,10,150,70,10]
[null,25,30,30,10,10,10,30,30,630,30,630]
[null,26,150,10,30,10,30,150,10,10,10,30]
[null,27,70,150,10,30,10,30,10,10,30,70]
[null,28,70,30,70,10,30,70,30,30,30,70]
[null,29,1270,10,70,70,30,10,30,10,10,30]
[null,30,10,10,10,10,70,30,70,150,10,70]
[null,31,10,10,70,30,30,30,150,30,150,30]
[null,32,310,10,10,10,1270,10230,150,150,30,30]
[null,33,10,30,10,30,30,10,630,10,10,10]
[null,34,30,10,310,10,30,30,1270,30,310,30]
[null,35,10,10,70,10,30,70,630,10,30,150]
[null,36,10,10,630,70,310,30,10,10,30,10]
[null,37,10,70,10,30,10,10,10,10,30,10]
[null,38,70,150,30,30,70,310,10,10,10,30]
[null,39,10,10,10,10,30,70,10230,10,10,150]
[null,40,10,10,10,30,30,30,70,30,10,10]
[null,41,10,150,30,10,10,10,70,10,10,150]
[null,42,150,10,70,310,150,10,30,70,70,10]
[null,43,10,10,10,70,10,150,10,30,10,10]
[null,44,5110,30,30,10,10,30,10,30,10,10]
[null,45,10,70,310,30,70,10,630,310,10,70]
[null,46,10,310,10,10,10,10,70,30,10,10]
[null,47,30,10,30,10,30,10,310,70,310,30]
[null,48,30,10,70,10,70,70,310,150,310,70]
[null,49,10,10,10,10,310,30,10,150,30,10]
[null,50,30,10,30,10,10,10,10,10,10,10]
[null,51,30,30,30,10,70,30,30,10,10,70]
[null,52,30,310,10,310,70,10,10,30,81910,10]
[null,53,310,10,70,10,70,10,10,10,30,10]
[null,54,30,10,10,10,10,150,70,10,10,10]
[null,55,30,10,10,10,30,70,10,10,150,30]
[null,56,30,1270,10,30,10,30,30,30,10,10]
[null,57,30,10,30,30,30,10,30,30,630,10]
[null,58,10,30,70,10,70,10,10,70,10,30]
[null,59,10,150,150,70,70,150,30,30,70,30]
[null,60,30,10,30,630,30,10,10,30,30,10]
[null,61,10,10,10,30,10,10,10,150,30,10]
[null,62,310,10,10,310,310,10,10,10,70,70]
[null,63,30,10,30,10,10,30,70,30,310,10]
[null,64,10,30,30,310,10,10,70,70,30,30]
[null,65,310,10,10,10,150,10,10,10,30,10]
[null,66,10,10,30,30,10,10,10,10,10,150]
[null,67,70,30,10,10,630,10,150,10,30,10]
[null,68,30,10,10,30,30,10,10,10,10,30]
[null,69,10230,30,30,30,70,10,10,310,10,30]
[null,70,10,10,70,10,30,10,150,30,30,10]
[null,71,70,10,10,30,10,10,30,10,30,10]
[null,72,70,10,30,10,10,30,70,10,10,10]
[null,73,310,10,10,10,30,150,30,630,150,10]
[null,74,30,10,70,310,10,30,70,10,70,10]
[null,75,10,10,30,70,30,30,10,10,10,10]
[null,76,10,10,150,10,10,10,30,10,10,10]
[null,77,10,70,630,10,30,10,30,150,70,10]
[null,78,10,30,70,10,1270,10,30,30,10,10]
[null,79,30,10,10,10,10,10,10,30,30,70]
[null,80,150,10,30,310,630,30,10,10,10,10]
[null,81,30,10,2550,150,10,10,10,10,10,10]
[null,82,630,10,10,70,30,10,10,30,310,150]
[null,83,10,10,30,30,10,10,10,10,150,30]
[null,84,10,10,10,10,30,10,70,10,30,30]
[null,85,10,10,30,1310710,30,10,10,30,30,10]
[null,86,70,10,30,10,10,70,10,70,1270,30]
[null,87,10,10,10,10,10,150,310,310,70,70]
[null,88,70,10,70,10,10,10,150,10,30,10]
[null,89,30,30,10,10,70,10,10,70,10,30]
[null,90,150,70,10,10,10,10,70,10,10,30]
[null,91,10,30,70,30,30,10,70,310,70,30]
[null,92,70,150,30,70,30,10,10,70,70,10]
[null,93,150,10,10,10,10,10,30,70,30,10]
[null,94,10,10,10,310,70,30,10,10,150,30]
[null,95,70,30,150,10,10,70,10,10,70,10]
[null,96,630,150,30,10,10,150,30,70,10,30]
[null,97,10,10,10,30,30,10,10,70,30,70]
[null,98,10,30,30,70,70,30,10,30,10,10]
[null,99,30,30,10,70,30,150,10230,10,10,70]
[null,100,150,30,30,10,310,10,150,70,10,10]
[null,101,70,1270,10,10,10,10,10,70,30,10]
[null,102,30,10,20470,70,10,70,10,10,10,310]
[null,103,10,30,10,10,10,1270,10,10,30,30]
[null,104,10,30,10,10,30,10,30,30,10,30]
[null,105,10,30,10,10,10,150,10,10,10,10]
[null,106,10,70,70,10,30,70,10,10,70,30]
[null,107,10,20470,310,30,70,10,10,30,30,10]
[null,108,1270,10,10,30,30,70,70,1270,10,10]
[null,109,10,30,70,10,30,10,10,10,30,30]
[null,110,10,10,70,10,30,10,10,30,30,10]
[null,111,10,10,630,30,30,70,10,30,10,10]
[null,112,70,150,30,10,10,150,10,10,10,30]
[null,113,70,150,70,30,70,30,10,10,30,10]
[null,114,150,10,10,30,10,10,10,30,10,70]
[null,115,30,10,30,10,10,10,10,10,70,30]
[null,116,310,30,70,10,70,10,10,30,10,10]
[null,117,30,10,70,10,310,10,30,10,10,630]
[null,118,10,10,70,30,30,10,70,150,30,70]
[null,119,310,70,1270,10,30,10,70,70,30,30]
[null,120,10,70,10,30,10,630,10,70,70,10]
[null,121,70,150,150,10,10,310,10,10,70,30]
[null,122,30,10,30,30,10,30,10,630,150,70]
[null,123,310,30,10,10,30,30,30,10,10,70]
[null,124,30,10,10,10,10,10,30,70,30,10]
[null,125,30,10,10,10,10,10,10,70,30,70]
[null,126,30,10,30,1270,70,10,10,10,10,10]
[null,127,10,150,150,30,150,10,10,30,10,10]
[null,128,310,10,310,10,10,10,30,10,10,70]
[null,129,10,10,30,10,10,310,10,10,10,30]
[null,130,310,10,30,70,10,10,10,30,30,30]
[null,131,70,70,30,70,70,30,30,10,10,10]
[null,132,10,5110,10,30,30,10,10,10,10,10]
[null,133,10,30,70,10,2550,70,30,30,70,30]
[null,134,10,70,1270,30,10,30,30,10,10,70]
[null,135,70,10,150,150,10,10,70,30,10,70]
[null,136,70,70,10,10,10,10,10,150,1270,70]
[null,137,30,10,30,1270,10,30,2550,150,10,10]
[null,138,10,10,30,30,70,10,70,10,30,10]
[null,139,10,150,30,10,630,10,70,10,30,10]
[null,140,30,10,10,30,10,30,2550,30,70,30]
[null,141,30,10,30,70,310,10,10,10,10,10]
[null,142,70,30,10,10,10,30,30,10,10,150]
[null,143,70,10,30,30,10,30,70,70,10,30]
[null,144,70,30,10,10,10,310,150,10,630,10]
[null,145,10,70,10,30,30,10,150,30,10,10]
[null,146,30,70,70,30,10,30,10,150,10,10]
[null,147,70,10,10,10,30,30,30,30,310,30]
[null,148,30,150,10,150,310,310,10,10,30,630]
[null,149,10,30,10,10,10,10,10,630,70,30]
[null,150,10,30,70,70,70,10,30,30,10,30]
[null,151,310,10,30,2550,30,70,10,30,10,70]
[null,152,30,150,70,70,310,10,70,310,10,10]
[null,153,70,30,10,70,10,10,10,10,310,30]
[null,154,70,10,10,10,30,30,30,30,30,30]
[null,155,70,10,10,1270,30,10,10,150,10,30]
[null,156,30,30,10,10,10,30,150,10,10,10]
[null,157,150,150,150,70,310,10,10,10,30,10]
[null,158,10,10,310,30,70,30,30,30,30,630]
[null,159,30,150,10,310,10,30,70,30,10,70]
[null,160,30,10,10,70,70,30,10,30,10,10]
[null,161,30,70,70,10,30,30,30,10,30,10]
[null,162,150,310,30,630,30,10,10,70,310,30]
[null,163,150,630,10,10,10,30,30,30,10,70]
[null,164,10,10,10,10,10,70,10,10,10,70]
[null,165,10,10,10,10,10,150,30,10,10,150]
[null,166,30,30,30,1270,70,10,70,10,310,10]
[null,167,30,10,70,10,10,150,10,310,10,10]
[null,168,10,10,70,10,10,150,70,10,10,10]
[null,169,30,630,630,70,70,30,70,10,30,70]
[null,170,10,10,30,10,30,10,10,10,70,150]
[null,171,10,10,10,10,30,30,310,30,10,10]
[null,172,30,1270,10,10,10,310,10,70,10,10]
[null,173,10,10,30,30,30,10,10,30,10,30]
[null,174,310,30,10,310,10,310,10,30,150,10]
[null,175,10,10,10,30,10,10,30,10,70,30]
[null,176,10,310,10,10,150,10,10,30,10,10]
[null,177,10,30,10,10,150,70,10,10,10,630]
[null,178,30,30,2550,150,30,70,10,10,10,10]
[null,179,10,10,30,10,30,30,10,10,10,30]
[null,180,10,310,10,630,10,10,30,10,10,10]
[null,181,10,10,10,10,30,30,10,310,10,70]
[null,182,30,70,70,70,5110,30,10,10,150,70]
[null,183,30,70,10,10,10,10,10,10,30,10]
[null,184,310,30,10,30,10,310,630,310,70,630]
[null,185,30,10,10,10,310,70,10,30,10,150]
[null,186,630,70,10,150,30,10,10,10,10,10]
[null,187,10,150,70,10,10,30,10,30,30,310]
[null,188,2550,150,70,30,10,310,150,10,30,310]
[null,189,150,310,70,30,10,30,70,10,70,10]
[null,190,310,30,10,70,70,10,70,70,10,70]
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