{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["4 Dice Game","6 Dice Game","Notes"],"not_rendered":{"charts":0,"images":0,"macros":1,"external_links":0,"defined_names":1,"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":"4 Dice Game","index":0,"n_rows":64,"n_cols":16,"rows_kept":64,"cut":false,"hidden":false,"merged":[[57,0,57,5],[46,0,46,5],[27,0,27,5],[0,0,0,5]]}
["4 Dice",null,null,null,null,null,null,null,null,null,"GAME"]
["outcome","points","number of ways","probability","weighted points","possible points",null,"Current points","Number of Dice","2 farkles already?","Simulation"]
["farkle",0,204,{"$f":"C3/(6^4)","v":0.15740740740740741},{"$f":"B3*D3","v":0},{"$f":"IF(J3=\"Y\",(-$H$3-300)*D3,-$H$3*D3)","v":-78.703703703703709},null,500,4,"n","Dice #",1,2,3,4]
["4 of a kind (1)",2000,1,{"$f":"C4/(6^4)","v":7.716049382716049E-4},{"$f":"B4*D4","v":1.5432098765432098},{"$f":"D4*($H$3+B4)","v":1.9290123456790123},null,null,null,null,"Dice Value",2,2,5,5]
["4 of a kind (2)",400,1,7.716049382716049E-4,0.30864197530864196,0.69444444444444442,null,"Expected points",null,100,131.25]
["4 of a kind (3)",600,1,7.716049382716049E-4,0.46296296296296291,0.84876543209876543,null,{"$f":"IF(I3=4,$F$26,IF(I3=3,$F$45,IF(I3=2,$F$56,IF(I3=1,$F$64,0))))","v":486.11111111111109},null,150,66.67]
["4 of a kind (4)",800,1,7.716049382716049E-4,0.61728395061728392,1.0030864197530864,null,null,null,200]
["4 of a kind (5)",1000,1,7.716049382716049E-4,0.77160493827160492,1.1574074074074074,null,"Game","points"]
["4 of a kind (6)",1200,1,7.716049382716049E-4,0.92592592592592582,1.3117283950617282,null,1,200,null,3100]
["3 of a kind (1)",1010,20,1.5432098765432098E-2,15.586419753086419,23.302469135802468,null,2,200]
["3 of a kind (2)",230,20,1.5432098765432098E-2,3.5493827160493825,11.265432098765432,null,3,0,null,null,1,5,5,"x","I can pick up all 3 and bank"]
["3 of a kind (3)",330,20,1.5432098765432098E-2,5.0925925925925926,12.808641975308641,null,4,500,null,null,null,null,null,null,"Picking up a 1 has highest expected, but it can't beat guaranteed 200"]
["3 of a kind (4)",430,20,1.5432098765432098E-2,6.6358024691358022,14.351851851851851,null,5,400,null,50,5,5,"x",null,"If I pick up both, I can't bank"]
["3 of a kind (5)",520,20,1.5432098765432098E-2,8.0246913580246915,15.74074074074074,null,6,0,null,null,null,null,null,null,"If I only pick up 1, I have a better chance to survive than to pick up both"]
["3 of a kind (6)",630,20,1.5432098765432098E-2,9.7222222222222214,17.438271604938272,null,7,0,null,null,null,null,null,null,"Even though both situations are unfavorable"]
["Axxx (no straight)",100,240,0.18518518518518517,18.518518518518519,111.1111111111111,null,8,450]
["Aaxx",200,96,7.407407407407407E-2,14.814814814814813,51.851851851851848,null,9,300]
["AA5x",250,48,3.7037037037037035E-2,9.2592592592592595,27.777777777777775,null,10,0]
["A5xx",150,{"$f":"144+48","v":192},0.14814814814814814,22.222222222222221,96.296296296296291,null,"total",{"$f":"SUM(I9:I18)","v":2050}]
["5xxx (no straight)",50,240,0.18518518518518517,9.2592592592592595,101.85185185185185]
["55xx",100,96,7.407407407407407E-2,7.4074074074074066,44.444444444444443]
["55Ax",200,48,3.7037037037037035E-2,7.4074074074074066,25.925925925925924]
["AA55",300,6,4.6296296296296294E-3,1.3888888888888888,3.7037037037037033]
[]
[]
["Totals",null,{"$f":"SUM(C3:C23)","v":1296},{"$f":"SUM(D3:D23)","v":1},{"$f":"SUM(E3:E23)","v":143.51851851851856},{"$f":"SUM(F3:F23)","v":486.11111111111109}]
[]
["3 Dice"]
["outcome","points","number of ways","probability","weighted points","possible points"]
["farkle",0,60,{"$f":"C30/(6^3)","v":0.27777777777777779},{"$f":"B30*D30","v":0},{"$f":"IF(J3=\"Y\",(-$H$3-300)*D30,-$H$3*D30)","v":-138.88888888888889}]
["3 of a kind (1)",1000,1,{"$f":"C31/(6^3)","v":4.6296296296296294E-3},4.6296296296296298,{"$f":"D31*($H$3+B31)","v":6.9444444444444438}]
["3 of a kind (2)",200,1,4.6296296296296294E-3,0.92592592592592582,{"$f":"D32*($H$3+B32)","v":3.2407407407407405}]
["3 of a kind (3)",300,1,4.6296296296296294E-3,1.3888888888888888,3.7037037037037033]
["3 of a kind (4)",400,1,4.6296296296296294E-3,1.8518518518518516,4.1666666666666661]
["3 of a kind (5)",500,1,4.6296296296296294E-3,2.3148148148148149,4.6296296296296298]
["3 of a kind (6)",600,1,4.6296296296296294E-3,2.7777777777777777,5.0925925925925926]
["Axx",100,48,0.22222222222222221,22.222222222222221,133.33333333333331]
["Aax",200,12,5.5555555555555552E-2,11.111111111111111,38.888888888888886]
["AA5",250,3,1.3888888888888888E-2,3.4722222222222219,10.416666666666666]
["A5x",150,24,0.1111111111111111,16.666666666666664,72.222222222222214]
["5xx",50,48,0.22222222222222221,11.111111111111111,122.22222222222221]
["55x",100,12,5.5555555555555552E-2,5.5555555555555554,33.333333333333329]
["55A",200,3,1.3888888888888888E-2,2.7777777777777777,9.7222222222222214]
[]
["Totals",null,{"$f":"SUM(C30:C43)","v":216},{"$f":"SUM(D30:D43)","v":1.0000000000000002},86.805555555555557,{"$f":"SUM(F30:F43)","v":309.02777777777777}]
[]
["2 Dice"]
["outcome","points","number of ways","probability","weighted points","possible points"]
["farkle",0,16,{"$f":"C49/(6^2)","v":0.44444444444444442},{"$f":"B49*D49","v":0},{"$f":"IF(J3=\"Y\",(-$H$3-300)*D49,-$H$3*D49)","v":-222.2222222222222}]
["Ax",100,8,{"$f":"C50/(6^2)","v":0.22222222222222221},22.222222222222221,{"$f":"D50*($H$3+B50)","v":133.33333333333331}]
["AA",200,1,2.7777777777777776E-2,5.5555555555555554,19.444444444444443]
["5x",50,8,0.22222222222222221,11.111111111111111,122.22222222222221]
[55,100,1,2.7777777777777776E-2,2.7777777777777777,16.666666666666664]
["A5",150,2,5.5555555555555552E-2,8.3333333333333321,36.111111111111107]
[]
["Totals",null,{"$f":"SUM(C49:C54)","v":36},{"$f":"SUM(D49:D54)","v":1},{"$f":"SUM(E49:E54)","v":50},{"$f":"SUM(F49:F54)","v":105.55555555555554}]
[]
["1 Dice"]
["outcome","points","number of ways","probability","weighted points","possible points"]
["farkle",0,4,{"$f":"C60/(6^1)","v":0.66666666666666663},{"$f":"B60*D60","v":0},{"$f":"IF(J3=\"Y\",(-$H$3-300)*D60,-$H$3*D60)","v":-333.33333333333331}]
["A",100,1,{"$f":"C61/(6^1)","v":0.16666666666666666},{"$f":"B61*D61","v":16.666666666666664},{"$f":"D61*($H$3+B61)","v":100}]
[5,50,1,0.16666666666666666,{"$f":"B62*D62","v":8.3333333333333321},91.666666666666657]
[]
["Totals",null,{"$f":"SUM(C60:C62)","v":6},{"$f":"SUM(D60:D62)","v":0.99999999999999989},{"$f":"SUM(E60:E62)","v":24.999999999999996},{"$f":"SUM(F60:F62)","v":-141.66666666666666}]

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[null,null,null,null,null,null,null,null,1,1,1,1,1,2,{"$f":"calculateScore(I3,J3,K3,L3,M3,N3)","v":3000},{"$f":"IF(O3=0,IF($C$2= \"Y\",-500,0),$A$2+O3)","v":3100},null,1,1,1,1,2,2000,{"$f":"IF(W3=0,IF($C$2= \"Y\",-500,0), $A$2+W3)","v":2100},null,1,1,1,2,1000,{"$f":"IF(AD3=0,IF($C$2= \"Y\",-500,0), $A$2+AD3)","v":1100},null,1,1,2,{"$f":"calculateScore(AG3,AH3,AI3,0,0,0)","v":200},{"$f":"IF(AJ3=0,IF($C$2= \"Y\",-500,0), $A$2+AJ3)","v":300},null,1,2,100,{"$f":"IF(AO3=0,IF($C$2= \"Y\",-500,0), $A$2+AO3)","v":200},null,2,{"$f":"calculateScore(AR3,0,0,0,0,0)","v":0},{"$f":"IF(AS3=0,IF($C$2= \"Y\",-500,0), $A$2+AS3)","v":0}]
["Expected Value",null,null,null,null,null,null,null,1,1,1,1,1,3,3000,3100,null,1,1,1,1,3,2000,2100,null,1,1,1,3,1000,1100,null,1,1,3,{"$f":"calculateScore(AG4,AH4,AI4,0,0,0)","v":200},300,null,1,3,100,200,null,3,{"$f":"calculateScore(AR4,0,0,0,0,0)","v":0},0]
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["Dice Simulator","Dice 1","Dice 2 ","Dice 3","Dice 4","Dice 5","Dice 6",null,1,1,1,1,2,2,2000,2100,null,1,1,1,2,2,1000,1100,null,1,1,2,2,200,300,null,1,2,2,100,200,null,2,2,0,0]
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[null,null,null,null,null,null,null,null,1,1,1,1,2,4,2000,2100,null,1,1,1,2,4,1000,1100,null,1,1,2,4,200,300,null,1,2,4,100,200,null,2,4,0,0]
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["start",null,null,null,null,null,null,null,1,1,1,1,2,6,2000,2100,null,1,1,1,2,6,1000,1100,null,1,1,2,6,200,300,null,1,2,6,100,200,null,2,6,0,0]
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["pick up","reroll","EV",null,null,null,null,null,1,1,1,1,3,2,2000,2100,null,1,1,1,3,2,1000,1100,null,1,1,3,2,200,300,null,1,3,2,100,200,null,3,2,0,0]
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[600,3,600,null,null,null,null,null,1,1,1,1,3,4,2000,2100,null,1,1,1,3,4,1000,1100,null,1,1,3,4,200,300,null,1,3,4,100,200,null,3,4,0,0]
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[750,2,750,null,null,null,null,null,1,1,1,1,3,6,2000,2100,null,1,1,1,3,6,1000,1100,null,1,1,3,6,200,300,null,1,3,6,100,200,null,3,6,0,0]
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{"sheet":"Notes","index":2,"n_rows":10,"n_cols":1,"rows_kept":10,"cut":false,"hidden":false,"merged":[[0,0,0,5],[1,0,1,5],[2,0,2,5],[5,0,5,5]]}
["It is better to pick up one dice than two and reroll more dice"]
["Always roll 6 dice as long as you are under 17000"]
["Roll 5 dice if under 2900 points"]
["Roll 4 dice if under 900"]
["roll 3 if you have 385 or less"]
["Don't roll 2 dice or less if you have more than 300 points"]
[]
["Fun Spots"]
["AA55xx - Taking all is worth 300, taking one and rolling five is worth 310"]
["A222xx - Better to take 100 points and roll five dice"]