7craps
7craps
Joined: Jan 23, 2010
  • Threads: 17
  • Posts: 1644
December 21st, 2018 at 7:14:32 PM permalink
Quote: Wizard

If the question is how long will it take for every number to appear in double-zero roulette, the answer is 160.6602765, on average.
This is the sum of the inverse of every integer from 1 to 38.

agree that is step 1
gp > c=38;
gp > a=sum(k=1,c,1/k);
Quote: Wizard

You're right. I forgot to say to multiply by 38.

using a calculator as in pari/gp (online version right here)
https://pari.math.u-bordeaux.fr/gp.html
(19:07) gp > c=38;
(19:07) gp > a=sum(k=1,c,1/k);
(19:07) gp > b=a*c;
(19:07) gp > b
%4 = 2053580969474233/12782132672400
(19:07) gp > c=38.;
(19:07) gp > a=sum(k=1,c,1/k);
(19:07) gp > b=a*c;
(19:07) gp > b
%8 = 160.66027650522331312865836875179452468
winsome johnny (not Win some johnny)
masterj
masterj
Joined: Dec 19, 2018
  • Threads: 2
  • Posts: 11
January 10th, 2019 at 12:29:56 AM permalink
Quote: mustangsally

the OP questions 37. Where it came from

that is just 1/p where p=1/37

handy tables
0 Roulette (155.4586903)

# of numbersaverage # of spinscumulative sum
111
21.0277777782.027777778
31.0571428573.084920635
41.0882352944.173155929
51.1212121215.29436805
61.156256.45061805
71.1935483877.644166437
81.2333333338.877499771
91.27586206910.15336184
101.32142857111.47479041
111.3703703712.84516078
121.42307692314.2682377
131.4815.7482377
141.54166666717.28990437
151.60869565218.89860002
161.68181818220.58041821
171.76190476222.34232297
181.8524.19232297
191.94736842126.13969139
202.05555555628.19524694
212.17647058830.37171753
222.312532.68421753
232.46666666735.1508842
242.64285714337.79374134
252.84615384640.63989519
263.08333333343.72322852
273.36363636447.08686488
283.750.78686488
294.11111111154.897976
304.62559.522976
315.28571428664.80869028
326.16666666770.97535695
337.478.37535695
349.2587.62535695
3512.3333333399.95869028
3618.5118.4586903
3737155.4586903

The average is not the mode (The "mode" is the value that occurs most often)
or median (The "median" is the "middle" value or close to 50%)
median = spin 147 @ 0.501522154
mode = 133 @ 0.0106293156

00 Roulette (160.6602765)
# of numbersaverage # of spinscumulative sum
111
21.0270270272.027027027
31.0555555563.082582583
41.0857142864.168296868
51.1176470595.285943927
61.1515151526.437459079
71.18757.624959079
81.2258064528.85076553
91.26666666710.1174322
101.31034482811.42777702
111.35714285712.78491988
121.40740740714.19232729
131.46153846215.65386575
141.5217.17386575
151.58333333318.75719908
161.65217391320.409373
171.72727272722.13664572
181.8095238123.94616953
191.925.84616953
20227.84616953
212.11111111129.95728064
222.23529411832.19257476
232.37534.56757476
242.53333333337.1009081
252.71428571439.81519381
262.92307692342.73827073
273.16666666745.9049374
283.45454545549.35948285
293.853.15948285
304.22222222257.38170508
314.7562.13170508
325.42857142967.56027651
336.33333333373.89360984
347.681.49360984
359.590.99360984
3612.66666667103.6602765
3719122.6602765
3838160.6602765

median = spin 152 @ 0.501599171
mode = 138 @ 0.010333952

still interesting one brings up this question
Sally




One more question:
On the single 0 Roulette if we get 36 out of 37 numbers and start to bet the open number then it is exactly the same if I bet a random number?
Because on average you need 37 spins that the last open number shows up.
I know that this open number can not show up in the next x spins but it should show up very often on average 155 spins. Right or wrong?
7craps
7craps
Joined: Jan 23, 2010
  • Threads: 17
  • Posts: 1644
January 10th, 2019 at 9:02:17 AM permalink
Quote: masterj

One more question:
On the single 0 Roulette if we get 36 out of 37 numbers and start to bet the open number then it is exactly the same if I bet a random number?

I would agree. 1/37
Quote: masterj

Because on average you need 37 spins that the last open number shows up.

still in agreement
Quote: masterj

I know that this open number can not show up in the next x spins

still in agreement. still sleeping
Quote: masterj

but it should show up very often on average 155 spins. Right or wrong?

wrong. not in agreement. The 155 is for ALL 37 numbers to show up, in no particular order before one starts to collect them.

with only 1 number being hunted down we can use the geometric distribution to see the probabilities associated with capturing that last elusive number.
after 155 spins we could still have a 1 in 70 chance that last number is still sleeping

gp > p=1/37;
gp > q=1-p;
gp > sum(k=1,155,a=q^(k-1.)*p)
%3 = 0.98569063411562596101969728657385450278
gp > 1-%3
%4 = 0.014309365884374038980302713426145497223
gp > 1/%4
%5 = 69.884298722979005501155771181951345195


200 spins data
spin Xprob on Xcumulativeprob no showno show 1 in
10.0270270270.0270270270.9729729731.03
20.0262965670.0533235940.9466764061.06
30.0255858490.0789094430.9210905571.09
40.0248943390.1038037820.8961962181.12
50.0242215190.1280253010.8719746991.15
60.0235668840.1515921850.8484078151.18
70.0229299410.1745221260.8254778741.21
80.0223102130.1968323390.8031676611.25
90.0217072340.2185395730.7814604271.28
100.0211205520.2396601250.7603398751.32
110.0205497260.2602098510.7397901491.35
120.0199943280.280204180.719795821.39
130.0194539410.2996581210.7003418791.43
140.0189281590.318586280.681413721.47
150.0184165870.3370028670.6629971331.51
160.0179188410.3549217080.6450782921.55
170.0174345480.3723562570.6276437431.59
180.0169633440.3893196010.6106803991.64
190.0165048760.4058244770.5941755231.68
200.0160587980.4218832750.5781167251.73
210.0156247760.4375080510.5624919491.78
220.0152024850.4527105360.5472894641.83
230.0147916070.4675021430.5324978571.88
240.0143918340.4818939770.5181060231.93
250.0140028650.4958968430.5041031571.98
260.013624410.5095212520.4904787482.04
270.0132561820.5227774350.4772225652.10
280.0128979070.5356753420.4643246582.15
290.0125493150.5482246570.4517753432.21
300.0122101440.5604348010.4395651992.27
310.0118801410.5723149420.4276850582.34
320.0115590560.5838739980.4161260022.40
330.0112466490.5951206460.4048793542.47
340.0109426850.6060633310.3939366692.54
350.0106469370.6167102680.3832897322.61
360.0103591820.627069450.372930552.68
370.0100792040.6371486540.3628513462.76
380.0098067930.6469554480.3530445522.83
390.0095417450.6564971920.3435028082.91
400.009283860.6657810520.3342189482.99
410.0090329450.6748139960.3251860043.08
420.0087888110.6836028070.3163971933.16
430.0085512750.6921540830.3078459173.25
440.008320160.7004742430.2995257573.34
450.0080952910.7085695330.2914304673.43
460.0078764990.7164460330.2835539673.53
470.0076636210.7241096530.2758903473.62
480.0074564960.7315661490.2684338513.73
490.0072549690.7388211180.2611788823.83
500.0070588890.7458800070.2541199933.94
510.0068681080.7527481150.2472518854.04
520.0066824830.7594305980.2405694024.16
530.0065018760.7659324740.2340675264.27
540.0063261490.7722586230.2277413774.39
550.0061551720.7784137960.2215862044.51
560.0059888160.7844026120.2155973884.64
570.0058269560.7902295680.2097704324.77
580.0056694710.7958990390.2041009614.90
590.0055162420.8014152820.1985847185.04
600.0053671550.8067824360.1932175645.18
610.0052220960.8120045320.1879954685.32
620.0050809590.8170854910.1829145095.47
630.0049436350.8220291260.1779708745.62
640.0048100240.826839150.173160855.77
650.0046800230.8315191730.1684808275.94
660.0045535360.8360727090.1639272916.10
670.0044304670.8405031760.1594968246.27
680.0043107250.8448139010.1551860996.44
690.0041942190.849008120.150991886.62
700.0040808620.8530889820.1469110186.81
710.0039705680.857059550.142940457.00
720.0038632550.8609228050.1390771957.19
730.0037588430.8646816480.1353183527.39
740.0036572530.8683389010.1316610997.60
750.0035584080.8718973090.1281026917.81
760.0034622350.8753595440.1246404568.02
770.0033686610.8787282050.1212717958.25
780.0032776160.8820058210.1179941798.47
790.0031890320.8851948530.1148051478.71
800.0031028420.8882976950.1117023058.95
810.0030189810.8913166760.1086833249.20
820.0029373870.8942540630.1057459379.46
830.0028579980.8971120610.1028879399.72
840.0027807550.8998928160.1001071849.99
850.00270560.9025984160.09740158410.27
860.0026324750.9052308910.09476910910.55
870.0025613270.9077922190.09220778110.85
880.0024921020.9102843210.08971567911.15
890.0024247480.9127090690.08729093111.46
900.0023592140.9150682830.08493171711.77
910.0022954520.9173637350.08263626512.10
920.0022334130.9195971480.08040285212.44
930.002173050.9217701980.07822980212.78
940.0021143190.9238845170.07611548313.14
950.0020571750.9259416920.07405830813.50
960.0020015760.9279432680.07205673213.88
970.0019474790.9298907470.07010925314.26
980.0018948450.9317855920.06821440814.66
990.0018436330.9336292240.06637077615.07
1000.0017938050.9354230290.06457697115.49
1010.0017453240.9371683530.06283164715.92
1020.0016981530.9388665050.06113349516.36
1030.0016522570.9405187620.05948123816.81
1040.0016076010.9421263630.05787363717.28
1050.0015641520.9436905150.05630948517.76
1060.0015218780.9452123930.05478760718.25
1070.0014807460.9466931390.05330686118.76
1080.0014407260.9481338650.05186613519.28
1090.0014017870.9495356530.05046434719.82
1100.0013639010.9508995540.04910044620.37
1110.0013270390.9522265930.04777340720.93
1120.0012911730.9535177660.04648223421.51
1130.0012562770.9547740430.04522595722.11
1140.0012223230.9559963660.04400363422.73
1150.0011892870.9571856530.04281434723.36
1160.0011571450.9583427980.04165720224.01
1170.001125870.9594686680.04053133224.67
1180.0010954410.960564110.0394358925.36
1190.0010658350.9616299450.03837005526.06
1200.0010370290.9626669730.03733302726.79
1210.0010090010.9636759740.03632402627.53
1220.000981730.9646577040.03534229628.29
1230.0009551970.9656129010.03438709929.08
1240.0009293810.9665422820.03345771829.89
1250.0009042630.9674465450.03255345530.72
1260.0008798230.9683263680.03167363231.57
1270.0008560440.9691824120.03081758832.45
1280.0008329080.970015320.0299846833.35
1290.0008103970.9708257170.02917428334.28
1300.0007884940.9716142110.02838578935.23
1310.0007671830.9723813940.02761860636.21
1320.0007464490.9731278430.02687215737.21
1330.0007262750.9738541180.02614588238.25
1340.0007066450.9745607630.02543923739.31
1350.0006875470.975248310.0247516940.40
1360.0006689650.9759172750.02408272541.52
1370.0006508840.9765681590.02343184142.68
1380.0006332930.9772014520.02279854843.86
1390.0006161770.9778176290.02218237145.08
1400.0005995240.9784171530.02158284746.33
1410.000583320.9790004730.02099952747.62
1420.0005675550.9795680280.02043197248.94
1430.0005522150.9801202430.01987975750.30
1440.0005372910.9806575340.01934246651.70
1450.0005227690.9811803030.01881969753.14
1460.000508640.9816889440.01831105654.61
1470.0004948930.9821838370.01781616356.13
1480.0004815180.9826653550.01733464557.69
1490.0004685040.9831338590.01686614159.29
1500.0004558420.9835897010.01641029960.94
1510.0004435220.9840332220.01596677862.63
1520.0004315350.9844647570.01553524364.37
1530.0004198710.9848846280.01511537266.16
1540.0004085240.9852931520.01470684868.00
1550.0003974820.9856906340.01430936669.88
1560.000386740.9860773740.01392262671.83
1570.0003762870.9864536610.01354633973.82
1580.0003661170.9868197780.01318022275.87
1590.0003562220.9871760.01282477.98
1600.0003465950.9875225950.01247740580.14
1610.0003372270.9878598220.01214017882.37
1620.0003281130.9881879350.01181206584.66
1630.0003192450.988507180.0114928287.01
1640.0003106170.9888177970.01118220389.43
1650.0003022220.9891200190.01087998191.91
1660.0002940540.9894140720.01058592894.47
1670.0002861060.9897001780.01029982297.09
1680.0002783740.9899785520.01002144899.79
1690.000270850.9902494020.009750598102.56
1700.000263530.9905129310.009487069105.41
1710.0002564070.9907693390.009230661108.33
1720.0002494770.9910188160.008981184111.34
1730.0002427350.9912615510.008738449114.44
1740.0002361740.9914977250.008502275117.62
1750.0002297910.9917275160.008272484120.88
1760.0002235810.9919510970.008048903124.24
1770.0002175380.9921686350.007831365127.69
1780.0002116590.9923802930.007619707131.24
1790.0002059380.9925862310.007413769134.88
1800.0002003720.9927866030.007213397138.63
1810.0001949570.992981560.00701844142.48
1820.0001896880.9931712480.006828752146.44
1830.0001845610.9933558090.006644191150.51
1840.0001795730.9935353810.006464619154.69
1850.0001747190.9937101010.006289899158.99
1860.0001699970.9938800980.006119902163.40
1870.0001654030.9940455010.005954499167.94
1880.0001609320.9942064330.005793567172.61
1890.0001565830.9943630160.005636984177.40
1900.0001523510.9945153670.005484633182.33
1910.0001482330.99466360.0053364187.39
1920.0001442270.9948078270.005192173192.60
1930.0001403290.9949481560.005051844197.95
1940.0001365360.9950846930.004915307203.45
1950.0001328460.9952175390.004782461209.10
1960.0001292560.9953467940.004653206214.91
1970.0001257620.9954725570.004527443220.88
1980.0001223630.995594920.00440508227.01
1990.0001190560.9957139760.004286024233.32
2000.0001158380.9958298150.004170185239.80

hope this helps out
winsome johnny (not Win some johnny)
masterj
masterj
Joined: Dec 19, 2018
  • Threads: 2
  • Posts: 11
January 10th, 2019 at 9:26:54 AM permalink
Hello Johnny,

you mean after 36 numbers showed up there is still a chance to have a 1 in 70 chance that this last number is still sleeping after 155 spins more? This count starts at 0, after the 36 different numbers occured?

masterj
OnceDear
Administrator
OnceDear
Joined: Jun 1, 2014
  • Threads: 43
  • Posts: 3698
January 10th, 2019 at 10:45:22 AM permalink
Quote: masterj

Hello Johnny,

you mean after 36 numbers showed up there is still a chance to have a 1 in 70 chance that this last number is still sleeping after 155 spins more? This count starts at 0, after the 36 different numbers occured?

masterj


Surely if you have calculated the probability of some event happening in 'the next 155 spins' ... let's call it P... and you then watch 154 spins and it either has or has not happened, you don't just say 'Yayyyy the chance of it happening in the next one spin is P'
At every moment in time, there is the past and there is the future. What probability calculations you do for the future will always be starting from scratch. What's happened before has left the room and is no longer part of the calculation.
If you are enjoying the game, you're already winning.
Keyser
Keyser
Joined: Apr 16, 2010
  • Threads: 34
  • Posts: 1819
January 10th, 2019 at 10:56:25 AM permalink
In other words, simply count the number of pockets on the wheel and realize that the ball can land in any one of them.
OnceDear
Administrator
OnceDear
Joined: Jun 1, 2014
  • Threads: 43
  • Posts: 3698
Thanks for this post from:
Keyser
January 10th, 2019 at 11:08:16 AM permalink
Quote: Keyser

In other words, simply count the number of pockets on the wheel and realize that the ball can land in any one of them.

And count it again before every wager. $;o)
If you are enjoying the game, you're already winning.
masterj
masterj
Joined: Dec 19, 2018
  • Threads: 2
  • Posts: 11
January 10th, 2019 at 11:11:32 AM permalink
I agree!
But if 1000 Players start after 36 numbers showed up (average after 118 spins) then the biggest part of this group should hit the last open number at around 155 spins. Is this assumtion right or wrong?
unJon
unJon 
Joined: Jul 1, 2018
  • Threads: 7
  • Posts: 847
Thanks for this post from:
OnceDear
January 10th, 2019 at 11:29:46 AM permalink
Quote: masterj

I agree!
But if 1000 Players start after 36 numbers showed up (average after 118 spins) then the biggest part of this group should hit the last open number at around 155 spins. Is this assumtion right or wrong?



On average, 14.3 people would not have seen the last open number, and 985.7 people would have already seen the last open number.

But make sure you wrap your head around this:

If those same 1000 Players didnít wait for 36 numbers to come up, but instead just immediately all started playing on one random number, then after 155 spins, 985.7 people would have hit that random number at least once and 14.3 people would not yet have hit that random number.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
masterj
masterj
Joined: Dec 19, 2018
  • Threads: 2
  • Posts: 11
January 10th, 2019 at 12:14:11 PM permalink
Let's say 1000 Players start immediately, then the biggest part of these group will get 36 different numbers around 118 spins and 37 different numbers around 155 spins. Right or wrong?

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