Total points in 12 random cards in 8-deck shoe?
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5 members have voted
October 5th, 2019 at 8:01:11 PM
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If there is a heaven, in the unlikely event I'm sent there, I hope there are compilers and spreadsheets that can handle an unlimited number of digits. However, for now, I'm limited to integers as large as 2^64. However, I think others do have access to software I don't that are not so limited.
That said, here is the question at hand. Take an 8-deck shoe. Cards are scored as follows:
A = 1
2-10 = pip value
J = 11
Q = 12
K = 13
What is the number of combination for any given total of 12 random cards, chosen without replacement?
Unfortunately, the combinations ran a little over 2^64, so I had to revert to a decimal.
Can anyone provide the EXACT number of combinations for any total. If so, how did you do it?
That said, here is the question at hand. Take an 8-deck shoe. Cards are scored as follows:
A = 1
2-10 = pip value
J = 11
Q = 12
K = 13
What is the number of combination for any given total of 12 random cards, chosen without replacement?
Unfortunately, the combinations ran a little over 2^64, so I had to revert to a decimal.
Can anyone provide the EXACT number of combinations for any total. If so, how did you do it?
| Total | Combinations |
|---|---|
| 156 | 225,792,840 |
| 155 | 4,128,783,360 |
| 154 | 36,126,854,400 |
| 153 | 209,311,365,120 |
| 152 | 925,616,009,760 |
| 151 | 3,373,898,151,936 |
| 150 | 10,623,140,027,904 |
| 149 | 29,809,235,896,320 |
| 148 | 76,197,335,731,008 |
| 147 | 180,296,163,767,296 |
| 146 | 399,724,519,660,032 |
| 145 | 838,212,685,748,224 |
| 144 | 1,674,991,374,949,480 |
| 143 | 3,208,902,130,674,680 |
| 142 | 5,922,867,556,960,760 |
| 141 | 10,575,845,958,791,100 |
| 140 | 18,331,035,981,153,100 |
| 139 | 30,930,773,414,340,600 |
| 138 | 50,930,223,409,649,600 |
| 137 | 82,003,429,211,543,500 |
| 136 | 129,336,417,589,173,000 |
| 135 | 200,122,672,056,249,000 |
| 134 | 304,176,175,625,480,000 |
| 133 | 454,676,126,820,014,000 |
| 132 | 669,055,131,415,173,000 |
| 131 | 970,038,813,588,301,000 |
| 130 | 1,386,839,163,709,630,000 |
| 129 | 1,956,496,319,319,710,000 |
| 128 | 2,725,353,970,931,820,000 |
| 127 | 3,750,642,161,501,160,000 |
| 126 | 5,102,128,424,591,150,000 |
| 125 | 6,863,784,020,935,050,000 |
| 124 | 9,135,397,420,885,390,000 |
| 123 | 12,034,052,413,826,400,000 |
| 122 | 15,695,374,428,937,700,000 |
| 121 | 20,274,436,431,451,800,000 |
| 120 | 25,946,206,540,362,800,000 |
| 119 | 32,905,414,042,970,200,000 |
| 118 | 41,365,710,559,273,000,000 |
| 117 | 51,558,009,555,994,300,000 |
| 116 | 63,727,901,432,043,100,000 |
| 115 | 78,132,062,984,093,600,000 |
| 114 | 95,033,609,735,335,800,000 |
| 113 | 114,696,376,221,781,000,000 |
| 112 | 137,378,153,142,167,000,000 |
| 111 | 163,322,958,869,565,000,000 |
| 110 | 192,752,475,839,657,000,000 |
| 109 | 225,856,836,660,953,000,000 |
| 108 | 262,784,999,186,317,000,000 |
| 107 | 303,635,000,181,527,000,000 |
| 106 | 348,444,421,949,181,000,000 |
| 105 | 397,181,440,164,700,000,000 |
| 104 | 449,736,842,333,641,000,000 |
| 103 | 505,917,411,150,574,000,000 |
| 102 | 565,441,055,054,571,000,000 |
| 101 | 627,934,037,529,866,000,000 |
| 100 | 692,930,608,646,902,000,000 |
| 99 | 759,875,275,848,309,000,000 |
| 98 | 828,127,869,827,542,000,000 |
| 97 | 896,971,465,737,049,000,000 |
| 96 | 965,623,115,097,711,000,000 |
| 95 | 1,033,247,231,547,180,000,000 |
| 94 | 1,098,971,361,130,320,000,000 |
| 93 | 1,161,903,957,936,980,000,000 |
| 92 | 1,221,153,687,878,860,000,000 |
| 91 | 1,275,849,700,278,110,000,000 |
| 90 | 1,325,162,245,345,500,000,000 |
| 89 | 1,368,322,977,053,450,000,000 |
| 88 | 1,404,644,269,407,700,000,000 |
| 87 | 1,433,536,888,657,070,000,000 |
| 86 | 1,454,525,407,107,490,000,000 |
| 85 | 1,467,260,812,125,590,000,000 |
| 84 | 1,471,529,856,918,220,000,000 |
| 83 | 1,467,260,812,125,600,000,000 |
| 82 | 1,454,525,407,107,490,000,000 |
| 81 | 1,433,536,888,657,070,000,000 |
| 80 | 1,404,644,269,407,700,000,000 |
| 79 | 1,368,322,977,053,450,000,000 |
| 78 | 1,325,162,245,345,500,000,000 |
| 77 | 1,275,849,700,278,110,000,000 |
| 76 | 1,221,153,687,878,860,000,000 |
| 75 | 1,161,903,957,936,980,000,000 |
| 74 | 1,098,971,361,130,320,000,000 |
| 73 | 1,033,247,231,547,180,000,000 |
| 72 | 965,623,115,097,710,000,000 |
| 71 | 896,971,465,737,047,000,000 |
| 70 | 828,127,869,827,541,000,000 |
| 69 | 759,875,275,848,307,000,000 |
| 68 | 692,930,608,646,901,000,000 |
| 67 | 627,934,037,529,864,000,000 |
| 66 | 565,441,055,054,572,000,000 |
| 65 | 505,917,411,150,574,000,000 |
| 64 | 449,736,842,333,641,000,000 |
| 63 | 397,181,440,164,700,000,000 |
| 62 | 348,444,421,949,181,000,000 |
| 61 | 303,635,000,181,527,000,000 |
| 60 | 262,784,999,186,317,000,000 |
| 59 | 225,856,836,660,953,000,000 |
| 58 | 192,752,475,839,657,000,000 |
| 57 | 163,322,958,869,565,000,000 |
| 56 | 137,378,153,142,167,000,000 |
| 55 | 114,696,376,221,781,000,000 |
| 54 | 95,033,609,735,335,800,000 |
| 53 | 78,132,062,984,093,600,000 |
| 52 | 63,727,901,432,043,100,000 |
| 51 | 51,558,009,555,994,300,000 |
| 50 | 41,365,710,559,273,100,000 |
| 49 | 32,905,414,042,970,200,000 |
| 48 | 25,946,206,540,362,800,000 |
| 47 | 20,274,436,431,451,800,000 |
| 46 | 15,695,374,428,937,700,000 |
| 45 | 12,034,052,413,826,400,000 |
| 44 | 9,135,397,420,885,390,000 |
| 43 | 6,863,784,020,935,050,000 |
| 42 | 5,102,128,424,591,150,000 |
| 41 | 3,750,642,161,501,160,000 |
| 40 | 2,725,353,970,931,820,000 |
| 39 | 1,956,496,319,319,710,000 |
| 38 | 1,386,839,163,709,630,000 |
| 37 | 970,038,813,588,301,000 |
| 36 | 669,055,131,415,173,000 |
| 35 | 454,676,126,820,014,000 |
| 34 | 304,176,175,625,480,000 |
| 33 | 200,122,672,056,249,000 |
| 32 | 129,336,417,589,173,000 |
| 31 | 82,003,429,211,543,500 |
| 30 | 50,930,223,409,649,600 |
| 29 | 30,930,773,414,340,600 |
| 28 | 18,331,035,981,153,100 |
| 27 | 10,575,845,958,791,100 |
| 26 | 5,922,867,556,960,760 |
| 25 | 3,208,902,130,674,680 |
| 24 | 1,674,991,374,949,480 |
| 23 | 838,212,685,748,224 |
| 22 | 399,724,519,660,032 |
| 21 | 180,296,163,767,296 |
| 20 | 76,197,335,731,008 |
| 19 | 29,809,235,896,320 |
| 18 | 10,623,140,027,904 |
| 17 | 3,373,898,151,936 |
| 16 | 925,616,009,760 |
| 15 | 209,311,365,120 |
| 14 | 36,126,854,400 |
| 13 | 4,128,783,360 |
| 12 | 225,792,840 |
| Total | 47,778,959,505,588,100,000,000 |
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 5th, 2019 at 8:23:07 PM
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7 x 12 = 84.
October 5th, 2019 at 9:43:14 PM
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the concept is called 'arbitrary precision' and free stuff I use is Pari/Gp and (for windows) Precise CalculatorQuote: WizardHowever, I think others do have access to software I don't that are not so limited.
for example:
my Excel's combin(416,12) = 47,778,959,505,588,400,000,000
pari/gp: gp > binomial(416,12)
%1 = 47778959505588340858920
pcalc: 416nCr12
47 778 959 505 588 340 858 920
no problem there
C++ has
C++ BigInt Class (never used it, but know some that have and they never complained about using it)
https://en.wikipedia.org/wiki/List_of_arbitrary-precision_arithmetic_software
try starting there and I am certain one will come by and show their results. I just do not have time to look at it
winsome johnny (not Win some johnny)
October 5th, 2019 at 9:52:42 PM
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Well, you have used combination math to calculate each of those numbers - call them x(n) -in the table. Go back to the formulas that you used, and express each and any of the numbers x(n) as a product of two large numbers, i.e.,
x(n) = A * B where A and B are both large numbers for which all the digits can be calculated on your spreadsheet.
Then, for any given A and B, simply multiply the two numbers by hand, this will give you all the digits.
x(n) = A * B where A and B are both large numbers for which all the digits can be calculated on your spreadsheet.
Then, for any given A and B, simply multiply the two numbers by hand, this will give you all the digits.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
October 6th, 2019 at 12:34:07 PM
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A standard 10 inch slide rule will give you the answer to 3 digits. Make an 80 inch one and you’ll get 24 digits.
It’s all about making that GTA
October 6th, 2019 at 3:26:17 PM
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Microsoft .NET has a BigInteger class that allows for unlimited precision integers.
It is not loaded by default; in Visual Studio, you have to add the System.Numerics namespace manually (through the "Add Reference" option in the menu).
It is not loaded by default; in Visual Studio, you have to add the System.Numerics namespace manually (through the "Add Reference" option in the menu).
October 7th, 2019 at 5:57:29 AM
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Thanks all for your suggestions.
I had a look at this, but don't trust myself to implement it properly.
I think I'll have to just get past this for now and continue living in small-number purgatory.
I'm still using Visual Studio 2005. I am long overdue to get a new computer. Any suggestions on a more modern C++ compiler that can handle integers of unlimited size?
Quote: ThatDonGuyMicrosoft .NET has a BigInteger class that allows for unlimited precision integers.
I had a look at this, but don't trust myself to implement it properly.
I think I'll have to just get past this for now and continue living in small-number purgatory.
I'm still using Visual Studio 2005. I am long overdue to get a new computer. Any suggestions on a more modern C++ compiler that can handle integers of unlimited size?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 7th, 2019 at 6:31:49 PM
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yes.Quote: WizardCan anyone provide the EXACT number of combinations for any total. If so, how did you do it?
I use a generating function in pari/gp
b=(prod(i=1, 13, 1 + x*y^i))^32;
print(b)
took a few seconds to complete (i have not learned how to just get the coefficient of x^12
it returns x^1 to x^416)
to write to a text file
so a text file works for me
results
y^156 is the sum of 156
+ 225792840*y^156
+ 4128783360*y^155
+ 36126854400*y^154
+ 209311365120*y^153
+ 925616009760*y^152
+ 3373898151936*y^151
+ 10623140027904*y^150
+ 29809235896320*y^149
+ 76197335731008*y^148
+ 180296163767296*y^147
+ 399724519660032*y^146
+ 838212685748224*y^145
+ 1674991374949480*y^144
+ 3208902130674688*y^143
+ 5922867556960768*y^142
+ 10575845958791168*y^141
+ 18331035981153120*y^140
+ 30930773414340608*y^139
+ 50930223409649664*y^138
+ 82003429211543552*y^137
+ 129336417589173856*y^136
+ 200122672056249344*y^135
+ 304176175625480960*y^134
+ 454676126820014080*y^133
+ 669055131415173288*y^132
+ 970038813588301824*y^131
+ 1386839163709634048*y^130
+ 1956496319319717888*y^129
+ 2725353970931822208*y^128
+ 3750642161501161472*y^127
+ 5102128424591154688*y^126
+ 6863784020935055360*y^125
+ 9135397420885393056*y^124
+ 12034052413826405376*y^123
+ 15695374428937774848*y^122
+ 20274436431451837440*y^121
+ 25946206540362835400*y^120
+ 32905414042970269696*y^119
+ 41365710559273110016*y^118
+ 51558009555994372096*y^117
+ 63727901432043160000*y^116
+ 78132062984093763584*y^115
+ 95033609735335922432*y^114
+ 114696376221781665792*y^113
+ 137378153142167576000*y^112
+ 163322958869565643776*y^111
+ 192752475839657541120*y^110
+ 225856836660953043968*y^109
+ 262784999186317858568*y^108
+ 303635000181527090176*y^107
+ 348444421949183178496*y^106
+ 397181440164700567552*y^105
+ 449736842333643290048*y^104
+ 505917411150573856768*y^103
+ 565441055054573899776*y^102
+ 627934037529867206656*y^101
+ 692930608646904309728*y^100
+ 759875275848307115008*y^99
+ 828127869827542576640*y^98
+ 896971465737048110080*y^97
+ 965623115097710930408*y^96
+ 1033247231547180078080*y^95
+ 1098971361130330388224*y^94
+ 1161903957936987926528*y^93
+ 1221153687878866101472*y^92
+ 1275849700278120556544*y^91
+ 1325162245345502497792*y^90
+ 1368322977053461135360*y^89
+ 1404644269407710191808*y^88
+ 1433536888657081828352*y^87
+ 1454525407107492726528*y^86
+ 1467260812125610382336*y^85
+ 1471529856918235043336*y^84
+ 1467260812125610382336*y^83
+ 1454525407107492726528*y^82
+ 1433536888657081828352*y^81
+ 1404644269407710191808*y^80
+ 1368322977053461135360*y^79
+ 1325162245345502497792*y^78
+ 1275849700278120556544*y^77
+ 1221153687878866101472*y^76
+ 1161903957936987926528*y^75
+ 1098971361130330388224*y^74
+ 1033247231547180078080*y^73
+ 965623115097710930408*y^72
+ 896971465737048110080*y^71
+ 828127869827542576640*y^70
+ 759875275848307115008*y^69
+ 692930608646904309728*y^68
+ 627934037529867206656*y^67
+ 565441055054573899776*y^66
+ 505917411150573856768*y^65
+ 449736842333643290048*y^64
+ 397181440164700567552*y^63
+ 348444421949183178496*y^62
+ 303635000181527090176*y^61
+ 262784999186317858568*y^60
+ 225856836660953043968*y^59
+ 192752475839657541120*y^58
+ 163322958869565643776*y^57
+ 137378153142167576000*y^56
+ 114696376221781665792*y^55
+ 95033609735335922432*y^54
+ 78132062984093763584*y^53
+ 63727901432043160000*y^52
+ 51558009555994372096*y^51
+ 41365710559273110016*y^50
+ 32905414042970269696*y^49
+ 25946206540362835400*y^48
+ 20274436431451837440*y^47
+ 15695374428937774848*y^46
+ 12034052413826405376*y^45
+ 9135397420885393056*y^44
+ 6863784020935055360*y^43
+ 5102128424591154688*y^42
+ 3750642161501161472*y^41
+ 2725353970931822208*y^40
+ 1956496319319717888*y^39
+ 1386839163709634048*y^38
+ 970038813588301824*y^37
+ 669055131415173288*y^36
+ 454676126820014080*y^35
+ 304176175625480960*y^34
+ 200122672056249344*y^33
+ 129336417589173856*y^32
+ 82003429211543552*y^31
+ 50930223409649664*y^30
+ 30930773414340608*y^29
+ 18331035981153120*y^28
+ 10575845958791168*y^27
+ 5922867556960768*y^26
+ 3208902130674688*y^25
+ 1674991374949480*y^24
+ 838212685748224*y^23
+ 399724519660032*y^22
+ 180296163767296*y^21
+ 76197335731008*y^20
+ 29809235896320*y^19
+ 10623140027904*y^18
+ 3373898151936*y^17
+ 925616009760*y^16
+ 209311365120*y^15
+ 36126854400*y^14
+ 4128783360*y^13
+ 225792840*y^12
I know this does NOT help you out with the process
I am a terrible teacher, I just know why it works and how to do it in pari/gp
good luck
back to wsop.com
if you like
I could save the complete text file (I deleted it already) that shows all the ways for drawing 1 to 416 inclusive from 8 decks
Last edited by: 7craps on Oct 7, 2019
winsome johnny (not Win some johnny)
October 7th, 2019 at 7:16:22 PM
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Thanks for the offer, but I really want to do this myself.
Do any forum members have Mathematica?
Do any forum members have Mathematica?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 7th, 2019 at 7:33:13 PM
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cool, at least you can compare your results to mine (the posted one) IF you want, once you complete them.Quote: WizardThanks for the offer, but I really want to do this myself.
I think I did this correctly...
generating function is a simple formula
(complete text file took 'last result computed in 19,875 ms.' )
good luck
added: for the sum=88
Pari :1,404,644,269,407,710,191,808
Wiz: 1,404,644,269,407,700,000,000
also: the code could just count the NUMBER of 'unique combinations'
there are only 2,704,156 of those. from there, the total number of combinations is simple math
... 9657700*x^14 + 5200300*x^13 + 2704156*x^12 + 1352078*x^11 + 646646*x^10 + 293930*x^9 + 125970*x^8 + 50388*x^7 + 18564*x^6 + 6188*x^5 + 1820*x^4 + 455*x^3 + 91*x^2 + 13*x + 1
this part result is from the expansion of this: print((1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30+x^31+x^32)^13)
also added: text file for drawing 0 to 20 cards without replacement. (72 KB in size)
combinations for all sums (y coefficient is the sum and the x coefficient is the number of cards drawn)
they have their own line in notepad++ (line #9 is for draw 12 cards)
https://drive.google.com/open?id=1zEi298vpVtQw-yGA-7OKl-fqYWvJW0Qh
enjoy generating functions
Last edited by: 7craps on Oct 8, 2019
winsome johnny (not Win some johnny)
October 8th, 2019 at 8:12:15 AM
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one assumed this was 8 standard decks of playing cards. could be almost anything.Quote: WizardThat said, here is the question at hand. Take an 8-deck shoe. Cards are scored as follows:
A = 1
2-10 = pip value
J = 11
Q = 12
K = 13
What is the number of combination for any given total of 12 random cards, chosen without replacement?
no one asked the obvious question.
What is this for?
(you may not want to answer)
I could see a side bet for Baccarat but that might only contain 6 cards
and the shoe would have to be shuffled after every draw (no problem online)
of course, this could be just some kid's homework assignment (kids these days)
winsome johnny (not Win some johnny)
October 8th, 2019 at 9:11:37 AM
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Quote: 7crapsWhat is this for?
That was an outstanding post in the last page. So good, I can't think of any good cross talk.
Sorry, this whole thing was for side bets in Super Fan Tan (scroll to the bottom).
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 8th, 2019 at 9:57:55 AM
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thanks.Quote: Wizardthis whole thing was for side bets in Super Fan Tan (scroll to the bottom).
for the '83 to 156' 12 draw sum I get
260625054933788 98333464
260925054933788 00000000 (yours)
using notepad++ and pari/gp
a=(225792840 + 4128783360 + 36126854400 + 209311365120 + 925616009760 + 3373898151936 + 10623140027904 + 29809235896320 + 76197335731008 + 180296163767296 + 399724519660032 + 838212685748224 + 1674991374949480 + 3208902130674688 + 5922867556960768 + 10575845958791168 + 18331035981153120 + 30930773414340608 + 50930223409649664 + 82003429211543552 + 129336417589173856 + 200122672056249344 + 304176175625480960 + 454676126820014080 + 669055131415173288 + 970038813588301824 + 1386839163709634048 + 1956496319319717888 + 2725353970931822208 + 3750642161501161472 + 5102128424591154688 + 6863784020935055360 + 9135397420885393056 + 12034052413826405376 + 15695374428937774848 + 20274436431451837440 + 25946206540362835400 + 2905414042970269696 + 41365710559273110016 + 51558009555994372096 + 63727901432043160000 + 78132062984093763584 + 95033609735335922432 + 114696376221781665792 + 137378153142167576000 + 163322958869565643776 + 192752475839657541120 + 225856836660953043968 + 262784999186317858568 + 303635000181527090176 + 348444421949183178496 + 397181440164700567552 + 449736842333643290048 + 505917411150573856768 + 565441055054573899776 + 627934037529867206656 + 692930608646904309728 + 759875275848307115008 + 828127869827542576640 + 896971465737048110080 + 965623115097710930408 + 1033247231547180078080 + 1098971361130330388224 + 1161903957936987926528 + 1221153687878866101472 + 1275849700278120556544 + 1325162245345502497792 + 1368322977053461135360 + 1404644269407710191808 + 1433536888657081828352 + 1454525407107492726528 + 1467260812125610382336 + 1471529856918235043336 + 1467260812125610382336);
print(a)
How did you get your sums?
you failed to mention that. (not that it really matters, your values are very close - even rounded)
winsome johnny (not Win some johnny)
October 8th, 2019 at 10:38:09 AM
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Quote: 7crapsfor the '83 to 156' 12 draw sum I get
260625054933788 98333464
260925054933788 00000000 (yours)
Are you sure the fourth digit in your number isn't a 9?
Quote:using notepad++ and pari/gp (code)
Thanks! I just found Run PARI/GP in your browser. This seems to allow simple arithmetic calculations with hundreds of digits. I put in your numbers to get the totals I need for the fan tan bets. I also added an acknowledgement section ;-).
As to notepad++, this looks intriguing! I'm very overdue to get a new computer, so hate to install anything onto this one. May I ask for now, what kind of data type do you declare for an integer with LOTS of significant digits?
Quote:How did you get your sums?
I wrote a recursive program in C++. I can share the code if you want.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
October 8th, 2019 at 11:30:57 AM
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Quote: WizardQuote: 7crapsfor the '83 to 156' 12 draw sum I get
260625054933788 98333464
260925054933788 00000000 (yours)
Quote: WizardAre you sure the fourth digit in your number isn't a 9?
260 9 2505493378898333464
yep it is
In pari/gp, (or precise calculator) no need to declare, even for a rational. it always returns exact values for integers up to the limit default (38 digits on win64).Quote: WizardMay I ask for now, what kind of data type do you declare for an integer with LOTS of significant digits?
for example 2^1000 returns all 302 digits without doing anything.
sometimes I forget and the screen keeps going for a rational...
one has to convert that 'exact fraction' to a decimal, very easy
significant digits: for e
simple: \p100
exp(1) returns 100 significant digits
gp > \p100
realprecision = 115 significant digits (100 digits displayed)
gp > exp(1)
%1 = 2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427
I just figured you would use that and the C++ arbitrary precision library. should be easy to use as there are examples on GitHub to follow.Quote: WizardI wrote a recursive program in C++. I can share the code if you want.
Last edited by: 7craps on Oct 8, 2019
winsome johnny (not Win some johnny)
October 8th, 2019 at 11:52:22 AM
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thanksQuote: WizardThanks! I just found Run PARI/GP in your browser. This seems to allow simple arithmetic calculations with hundreds of digits. I put in your numbers to get the totals I need for the fan tan bets. I also added an acknowledgement section ;-).
as to pari/gp (basic version)
many do not like it as it can be very slow for some code (loops and large matrix multiplication) as it it NOT compiled.
there are ways to get around this.
I thought everyone used notepad++ as their text editor.
I was late to use it but it is so versatile
winsome johnny (not Win some johnny)
