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Kon-Fu-Sed

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Multi-million spins statistics
January 19, 2009, 02:27:22 PM
Hi all,

I happened to see that someone had posted statistics from a multimillion spins investigation on "another" board.

Because I like you people here so much, I post these tables so that you don't have to do the same kind of boring and time-consuming tests again, just because your amount of spins isn't 12M...

And NO; I didn't run some thousands of billions of spins to get to these figures: I used my calculator ;D
Very simple.

Please compare these figures to tests that you have seen or done!

(The "50/50" values are true 50% chance - like coin-tossing)


SINGLE ZERO TABLES

How many trials do we need, MATHEMATICALLY, to find a sequence of AT LEAST length X?

X                    50/50             "Even"              Cl/Dz             DblStr
    2:                   3                  3                  8                 37
    3:                   7                  7                 28                233
    4:                  15                 16                 89              1,445
    5:                  31                 35                277              8,916
    6:                  63                 74                858             54,991
    7:                 127                154              2,648            339,118
    8:                 255                317              8,167          2,091,238
    9:                 511                654             25,186         12,895,976
   10:               1,023              1,345             77,660         79,525,192
   11:               2,047              2,767            239,454        490,405,361
   12:               4,095              5,689            738,320      3,024,166,401
   13:               8,191             11,696          2,276,491     18,649,026,147
   14:              16,383             24,043          7,019,184    115,002,327,911
   15:              32,767             49,423         21,642,486    709,181,022,129
   16:              65,535            101,592         66,731,001  4,373,282,969,801
   17:             131,071            208,830        205,753,922                   
   18:             262,143            429,264        634,407,931                   
   19:             524,287            882,377      1,956,091,122                   
   20:           1,048,575          1,813,778      6,031,280,963                   
   21:           2,097,151          3,728,322     18,596,449,640                   
   22:           4,194,303          7,663,775     57,339,053,061                   
   23:           8,388,607         15,753,316    176,795,413,608                   
   24:          16,777,215         32,381,819    545,119,191,962                   
   25:          33,554,431         66,562,629  1,680,784,175,221                   
   26:          67,108,863        136,823,183  5,182,417,873,600                   
   27:         134,217,727        281,247,655                                     
   28:         268,435,455        578,120,181                                     
   29:         536,870,911      1,188,358,151                                     
   30:       1,073,741,823      2,442,736,201                                     



How many trials do we need, MATHEMATICALLY, to find a sequence of AT LEAST length X?

X                   Corner             SngStr              Split             Single
    2:                  84                151                341              1,368
    3:                 790              1,875              6,330             50,652
    4:               7,319             23,136            117,134          1,874,160
    5:              67,717            285,365          2,166,997         69,343,956
    6:             626,397          3,519,513         40,089,474      2,565,726,408
    7:           5,794,180         43,407,350        741,655,289     94,931,877,132
    8:          53,596,182        535,357,330     13,720,622,865  3,512,479,453,920
    9:         495,764,692      6,602,740,424    253,831,523,036                   
   10:       4,585,823,413     81,433,798,580  4,695,883,176,188                   
   11:      42,418,866,580  1,004,350,182,499                                     
   12:     392,374,515,880                                                         
   13:   3,629,464,271,903                                                         


... and the opposite:

How long sequences can we expect, MATHEMATICALLY, in X trials?

X        50/50   "Even"    Cl/Dz   DblStr   Corner   SngStr    Split   Single
1,000        9        9        6        3        3        2        2        1
5,000       12       11        7        4        3        3        2        2
  10K       13       12        8        5        4        3        3        2
  50K       15       15        9        5        4        4        3        2
 100K       16       15       10        6        5        4        3        3
 500K       18       18       11        7        5        5        4        3
   1M       19       19       12        7        6        5        4        3
   5M       22       21       13        8        6        6        5        4
  10M       23       22       14        8        7        6        5        4
  12M       23       22       14        8        7        6        5        4
  15M       23       22       14        9        7        6        5        4
  20M       24       23       14        9        7        6        5        4
  25M       24       23       15        9        7        6        5        4
  50M       25       24       15        9        7        7        6        4
 100M       26       25       16       10        8        7        6        5
1000M       29       28       18       11        9        8        7        5




DOUBLE ZERO TABLES

How many trials do we need, MATHEMATICALLY, to find a sequence of AT LEAST length X?

X                    50/50            "Even"               Cl/Dz             DblStr
    2:                   3                  3                  9                 39
    3:                   7                  8                 30                253
    4:                  15                 18                 99              1,607
    5:                  31                 40                317             10,188
    6:                  63                 87              1,007             64,533
    7:                 127                185              3,192            408,719
    8:                 255                393             10,110          2,588,562
    9:                 511                831             32,018         16,394,232
   10:               1,023              1,757            101,395        103,830,144
   11:               2,047              3,711            321,088        657,590,920
   12:               4,095              7,835          1,016,781      4,164,742,499
   13:               8,191             16,543          3,219,811     26,376,702,500
   14:              16,383             34,925         10,196,071    167,052,449,175
   15:              32,767             73,732         32,287,561  1,057,998,844,780
   16:              65,535            155,659        102,243,946  6,700,659,350,280
   17:             131,071            328,614        323,772,499                   
   18:             262,143            693,743      1,025,279,584                   
   19:             524,287          1,464,571      3,246,718,687                   
   20:           1,048,575          3,091,873     10,281,275,844                   
   21:           2,097,151          6,527,289     32,557,373,510                   
   22:           4,194,303         13,779,833    103,098,349,450                   
   23:           8,388,607         29,090,761    326,478,106,596                   
   24:          16,777,215         61,413,830  1,033,847,337,557                   
   25:          33,554,431        129,651,422  3,273,849,902,267                   
   26:          67,108,863        273,708,558                                     
   27:         134,217,727        577,829,180                                     
   28:         268,435,455      1,219,861,604                                     
   29:         536,870,911      2,575,263,388                                     
   30:       1,073,741,823      5,436,667,154                                     



How many trials do we need, MATHEMATICALLY, to find a sequence of AT LEAST length X?

X                   Corner             SngStr              Split             Single
    2:                  89                159                360              1,443
    3:                 856              2,031              6,858             54,871
    4:               8,144             25,741            130,320          2,085,135
    5:              77,377            326,069          2,476,098         79,235,167
    6:             735,090          4,130,227         47,045,880      3,010,936,383
    7:           6,983,371         52,316,223        893,871,738    114,415,582,591
    8:          66,342,042        662,672,173     16,983,563,040  4,347,792,138,495
    9:         630,249,408      8,393,847,545    322,687,697,778                   
   10:       5,987,369,391    106,322,068,924  6,131,066,257,800                   
   11:      56,880,009,226  1,346,746,206,390                                     
   12:     540,360,087,661                                                         
   13:   5,133,420,832,794                                                         


... and the opposite:

How long sequences can we expect, MATHEMATICALLY, in X trials?

X        50/50   "Even"    Cl/Dz   DblStr   Corner   SngStr    Split   Single
1,000        9        9        5        3        3        2        2        1
5,000       12       11        7        4        3        3        2        2
  10K       13       12        7        4        4        3        3        2
  50K       15       14        9        5        4        4        3        2
 100K       16       15        9        6        5        4        3        3
 500K       18       17       11        7        5        5        4        3
   1M       19       18       11        7        6        5        4        3
   5M       22       20       13        8        6        6        5        4
  10M       23       21       13        8        7        6        5        4
  12M       23       21       14        8        7        6        5        4
  15M       23       22       14        8        7        6        5        4
  20M       24       22       14        9        7        6        5        4
  25M       24       22       14        9        7        6        5        4
  50M       25       23       15        9        7        6        6        4
 100M       26       24       15        9        8        7        6        5
1000M       29       27       17       11        9        8        7        5


If you've got a calculator... WHY spend time doing boring multimillion spins tests?
The end results are the same... Aren't they?

Regards,
KFS
If s**t can happen, s**t will happen.

bliss

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Re: Multi-million spins statistics
January 19, 2009, 03:46:42 PM
Nice work KFS.  :)

One thing though, do you think this would be better off in the reference section? It's bound to come in useful in the future, and if left here it will be buried...

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kompressor

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Re: Multi-million spins statistics
January 20, 2009, 12:36:13 AM
if i'm looking for a sequence of 5....i look at greater than 4 ??

thanks

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Kon-Fu-Sed

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Re: Multi-million spins statistics
January 20, 2009, 07:35:41 AM
Hi Bliss, kompressor, and all,


@ Bliss:
Yes, you are right. I wasn't sure...
So I followed the instruction: "If unsure; post it here..."


@ kompressor:
Yes, you have to be looking for greater than four.
Five is greater than four, right? ;)

How shall I explain this?
I wish I was a teacher...


If you have 35 roulette-results there should (mathematically and in average) be at least one sequence there of length 5.

But we cannot say for certain that it is broken by the opposite or a zero at that exact length.
The sequence MAY be 6 or 7 long.
We can only say "for certain" (math certainty, that is ;)) that there will be at least five of the same.
(Mathematically and in average...)

The thing is, that if you look at enough 35-spins samples you will - sooner or later - find one sample that contains 35 of the same...
(I wrote sooner or later ;) - maybe you have to check a "few" billions of samples before you find it. But it will be there...)


Anywayzzz... I understand what you are saying...
So I have - as you may see - changed the headings and indices to what I hope will be more clear.


Best regards,
KFS
If s**t can happen, s**t will happen.

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kompressor

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Re: Multi-million spins statistics
January 20, 2009, 05:29:56 PM
good lord kon-fu...


FULL TRIO (TERA TNT)


"...All Even-money bets balance out closely after +/- 100 spins. (The Law of averages)
The average is 55/45. Nine out of ten times the discrepancy between two even-money bets will be
less the 20 i.e. 60/40. YOU WOULD WIN NINE OUT OF TEN TIMES WITH BASICPLAY IF
THERE WERE NO TABLE LIMITS. BUT, the Casinos also need to be profitable. This is why
we developed AdvPlay1 and 2. These two systems combined with BasicPlay will keep your
stakes low ( under the table limit) and bring your count back to one as quick as possible ...."

FULLTRIO.pdf


any statistics endorse that ??

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Kon-Fu-Sed

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Re: Multi-million spins statistics
January 20, 2009, 09:29:55 PM
Hi kompressor,


No.

;)

As I have said before; nothing will really "even out" other than in percent.
And the larger the sample the smaller the difference is ... in percent.

But a small percentage of a large sum is also a large number.
I mean that 5% of 100 is 5 while 0.05% of 100,000 is 50 - ten times more while the percentage was 1/100th.

And so: The larger the sample, the wider is the spread.
IN NUMBERS.
Or, in the down-to-earth term: IN UNITS.


And regarding 100-spins sequences that is talked about...

I ran 1,000,000 such sequences and counted how many "High" numbers (>18) there were in each.
This was for single-zero...

I stopped at some "levels" and output the sums that far.
And this is the result:

[table=,]
High,      10,     50,    100,    500,   1000,   5000,    10K,    50K,   100K,   500K,     1M
   21,       ,       ,       ,       ,       ,       ,       ,       ,       ,       ,      1
   22,       ,       ,       ,       ,       ,       ,       ,       ,       ,       ,     
   23,       ,       ,       ,       ,       ,       ,       ,       ,       ,       ,     
   24,       ,       ,       ,       ,       ,       ,       ,       ,       ,       ,     
   25,       ,       ,       ,       ,       ,       ,       ,       ,       ,      1,      1
   26,       ,       ,       ,       ,       ,       ,       ,       ,       ,       ,   
   27,       ,       ,       ,       ,       ,       ,       ,       ,       ,       ,      5
   28,       ,       ,       ,       ,       ,       ,       ,      1,      1,      4,      9
   29,       ,       ,       ,       ,       ,       ,       ,      4,      6,     22,     36
   30,       ,       ,       ,       ,       ,      1,      1,      4,      6,     33,     82
   31,       ,       ,       ,       ,       ,      1,      3,     10,     16,     67,    129
   32,       ,       ,       ,       ,       ,      3,      5,     20,     34,    146,    300
   33,       ,       ,       ,       ,       ,      1,      6,     26,     59,    286,    594
   34,       ,       ,       ,       ,      1,      2,      6,     46,     97,    512,   1038
   35,       ,       ,       ,       ,      1,      9,     18,     92,    183,    944,   1860
   36,       ,      1,      1,      1,      2,     12,     26,    144,    294,   1513,   3081
   37,       ,       ,       ,      1,      5,     28,     56,    252,    516,   2614,   5270
   38,       ,       ,      1,      2,      6,     48,     89,    422,    816,   4116,   8259
   39,       ,      1,      1,      5,     11,     78,    137,    651,   1291,   6404,  12666
   40,       ,       ,      3,     16,     23,     95,    177,    835,   1696,   8781,  17637
   41,      1,      1,      5,     16,     33,    144,    256,   1267,   2525,  12636,  24978
   42,       ,      1,      2,     12,     32,    188,    385,   1714,   3331,  16490,  33167
   43,       ,      1,      2,     17,     35,    185,    407,   2090,   4167,  21005,  42058
   44,       ,      2,      4,     21,     43,    244,    504,   2618,   5215,  25913,  52038
   45,      1,      4,      7,     40,     77,    330,    618,   3030,   6105,  30657,  61085
   46,      2,      8,     13,     38,     71,    326,    655,   3414,   6865,  34632,  69218
   47,       ,      4,      6,     36,     67,    374,    746,   3845,   7580,  37919,  75505
   48,      1,      3,      8,     44,     82,    407,    770,   3956,   8033,  39607,  78955
   49,      1,      1,      6,     33,     77,    416,    785,   3902,   7889,  39892,  79800
   50,       ,      4,      6,     35,     67,    365,    732,   3793,   7680,  38556,  76966
   51,       ,      3,      5,     32,     60,    350,    711,   3507,   7078,  35357,  70939
   52,      1,      3,      9,     40,     69,    312,    642,   3204,   6362,  31904,  63554
   53,       ,      2,      3,     33,     68,    288,    589,   2855,   5586,  27585,  55099
   54,       ,      3,      6,     21,     52,    233,    455,   2235,   4505,  22323,  44762
   55,      1,      1,      3,     19,     38,    161,    355,   1765,   3478,  17555,  35581
   56,       ,      1,      3,     11,     30,    131,    294,   1378,   2791,  13628,  27162
   57,       ,      1,      1,      9,     18,     90,    189,    998,   1999,  10003,  20011
   58,      2,      4,      4,     11,     20,     80,    154,    724,   1422,   6810,  13780
   59,       ,      1,      1,      5,      6,     41,     90,    485,    956,   4719,   9519
   60,       ,       ,       ,      1,      2,     28,     60,    286,    575,   3013,   6162
   61,       ,       ,       ,       ,      1,     12,     32,    162,    363,   1860,   3765
   62,       ,       ,       ,      1,      2,      8,     18,    117,    225,   1139,   2260
   63,       ,       ,       ,       ,      1,      5,     17,     81,    122,    636,   1305
   64,       ,       ,       ,       ,       ,      2,      7,     35,     69,    344,    660
   65,       ,       ,       ,       ,       ,      1,      2,     16,     33,    204,    387
   66,       ,       ,       ,       ,       ,       ,      1,      9,     15,     91,    170
   67,       ,       ,       ,       ,       ,       ,      1,      4,      8,     45,     76
   68,       ,       ,       ,       ,       ,      1,      1,      3,      4,     16,     40
   69,       ,       ,       ,       ,       ,       ,       ,       ,      3,     11,     18
   70,       ,       ,       ,       ,       ,       ,       ,       ,       ,      4,      7
   71,       ,       ,       ,       ,       ,       ,       ,       ,      1,      2,      3
   72,       ,       ,       ,       ,       ,       ,       ,       ,       ,      1,      1
   73,       ,       ,       ,       ,       ,       ,       ,       ,       ,       ,      1
[/table]

As you can see, the more sequences we investigate (the larger the sample), the wider is the spread of Highs/hits - in NUMBERS.

Please note that there was for example as few as 36 Highs/hits in one sample of only 50, which shows that also low-probability events can happen very early in the chain of events.
Also in your personal chain...
(Take care ;))


Regards,
KFS


If s**t can happen, s**t will happen.

VLSroulette

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Re: Multi-million spins statistics
January 20, 2009, 09:36:41 PM
I happened to see that someone had posted statistics from a multimillion spins investigation on "another" board.

Hi mate that "someone" (poit!) generously gave thumbs-up for us to host such analysis here:
http://vlsroulette.com/reference-area/12-million-rng-spin-stats-shared-by-poit/

:thumbsup:


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Kon-Fu-Sed

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Re: Multi-million spins statistics
January 20, 2009, 09:47:28 PM
Hi Victor,

I saw that and I think that's excellent as anyone now can compare my calculated figures with a true statistics investigation.
His stats include so much more than my figures, but what that data shows is that everything else also conform to math - like the SD, for example.
Check it out - there is no surprise at all in there.

This is a math game when you treat number-sequences as number-sequences and the wheel/dealer as an RNG.
That's why we can simply use a calculator instead of running billions of spins to collect stats.

Poit's stats and my calculations show that conclusively, IM(ns ;))HO.


KFS
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Kon-Fu-Sed

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Re: Multi-million spins statistics
January 20, 2009, 10:44:06 PM
Regarding to "even out in the long run"...


Suddenly I thought like this:

Suppose that during 3700 spins one "even" chance hits exactly as expected: 18/37.
That means it hit 1800 times.

Now, suppose we expect  it to "even out" during the next 3700 spins.
So we expect it to hit a total of 3700 times during the total of 7400 spins - that's to even out, right?

Of those 3700 hits we already had 1800 in the first 3700 spins so we expect 1900 hits during the next 3700 spins.

But then the "even" chance has to hit 19/37...

Is there ANY reason why it should?


And it doesn't matter if you think it's going to even out during the next 37 or 37 billions spins: It still has to hit BETTER than 18/37.
Even if it hit AT THE EXPECTED 18/37 before.
Now, think of the necessary hit-rate to even out, if it had hit BELOW 18/37...

The truth is that an "even bet" (or ANY bet) will only "even out" to its NORMAL hit-rate of 18/37 (or whatever) in the long run.

And for the "even" bets, that missing "half/37" is an ever growing number in the long run:
0.5/37 of 3700 = 50 below half
0.5/37 of 37M = 500,000 below half...

To some, this seems to mean to "even out". In the long run.


Just my $0.02 - just a thought of how to explain it...

Never mind.

KFS
If s**t can happen, s**t will happen.

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purple

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Re: Multi-million spins statistics
January 24, 2009, 03:18:44 PM
Hi Kon Fu Sed,
First of all thank you for all your hard work.
Now I'm trying to understand your stats.
What do these extracts from your tables below mean ?

Is it for instance that we need a maximum of 37 spins for a doublestreet to repeat twice?28 spins for a cl/dz to repeat twice? 1368 for a straight up to repeat? That a cl/dz will repeat 4 times within 89 spins?
And what are these long sequences of 10K and 50K? Is it that within 1000 there will be at least 6 repeats of a cl/dz?

Thanks
Purple

SINGLE ZERO TABLES

How many trials do we need, MATHEMATICALLY, to find a sequence of AT LEAST length X?

X                    50/50             "Even"              Cl/Dz             DblStr
    2:                   3                  3                  8                 37
    3:                   7                  7                 28                233
    4:                  15                 16                 89              1,445
    5:                  31                 35                277              8,916


and
How many trials do we need, MATHEMATICALLY, to find a sequence of AT LEAST length X?

X                   Corner             SngStr              Split             Single
    2:                  84                151                341              1,368
    3:                 790              1,875              6,330             50,652
    4:               7,319             23,136            117,134          1,874,160
   

... and the opposite:

How long sequences can we expect, MATHEMATICALLY, in X trials?

X        50/50   "Even"    Cl/Dz   DblStr   Corner   SngStr    Split   Single
1,000        9        9        6        3        3        2        2        1
5,000       12       11        7        4        3        3        2        2
  10K       13       12        8        5        4        3        3        2
  50K       15       15        9        5        4        4        3        2


My best all time favourite roulette book filled with hundreds of pictures is 'The Roulette Winner' by Lee Tutor.

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Kon-Fu-Sed

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Re: Multi-million spins statistics
January 24, 2009, 06:32:39 PM
Hi purple,

Yes.

;)

Or maybe not. :D

Quote

 we need a maximum of 37 spins

Not really maximum...
Mathematically that's what is needed to find a repeating 6/37 bet.

Quote

 Is it that within 1000 there will be at least 6 repeats of a cl/dz?

In 1,000 trials you can expect (mathematically) to find at least one repeat-sequence of a column/dozen (a 12/37 bet) that is at least six long.

You can compare my results (the 12M line above) to the stats posted here:
http://vlsroulette.com/reference-area/12-million-rng-spin-stats-shared-by-poit/

Stats results:
Evens repeats: 22, 22, 22, 21, 21, 23. My calculator says [highlight]22[/highlight]
Dozens/Columns repeats: 18, 14, 14, 14, 13, 16. My calculator says [highlight]14[/highlight]
Double Street repeats: 8, 8, 8, 9, 8, 9, 8, 9, 8, 10, 9. My calculator says [highlight]8[/highlight]
Corner repeats: 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 6, 7, 7, 8, 7, 7, 7, 6, 7, 7, 8, 7. My calculator says [highlight]7[/highlight]
Single Street repeats: 7, 6, 6, 7, 6, 6, 7, 6, 6, 6, 6, 6. My calculator says [highlight]6[/highlight]
Splits repeats: 1 repeats 4 times, 39 repeats 5 times and 20 repeats 6 times. My calculator says [highlight]5[/highlight]
Single numbers: 29 repeats 4 times and 8 repeats 5 times. My calculator says [highlight]4[/highlight]

IMHO, a calculator is useful sometimes.
(One doesn't need to work so hard to get the figures ;))
KFS
If s**t can happen, s**t will happen.

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purple

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Re: Multi-million spins statistics
January 25, 2009, 03:58:33 AM
Hi I'm still trying to get it.

Stats results:
Evens repeats: 22, 22, 22, 21, 21, 23. My calculator says 22

Are you saying that in 1000 spins there will be  about 22 alterations for every even chance (BR, HL, OE), ie 132 alterations in total?) I don't think you're saying that there will be one instance of an even chance repeating 22 times are you?

 Dozens/Columns repeats: 18, 14, 14, 14, 13, 16. My calculator says 14
In 1000 spins On average each column repeated itself at least 13 times, or one instance when a col/doz repeated itself 13 times in a row?Double Street repeats: 8, 8, 8, 9, 8, 9, 8, 9, 8, 10, 9. My calculator says 8
In 1000 spins each street repeated itself at least 8 times, or was there one instance when a street repeated itself 8 times in a row?[/i]

etc for


Corner repeats: 7, 7, 7, 7, 6, 7, 7, 7, 7, 7, 6, 7, 7, 8, 7, 7, 7, 6, 7, 7, 8, 7. My calculator says 7
Single Street repeats: 7, 6, 6, 7, 6, 6, 7, 6, 6, 6, 6, 6. My calculator says 6

Splits repeats: 1 repeats 4 times, 39 repeats 5 times and 20 repeats 6 times.
My calculator says 5 Please explain this
Single numbers: 29 repeats 4 times and 8 repeats 5 times. My calculator says 4
Please explain this

My best all time favourite roulette book filled with hundreds of pictures is 'The Roulette Winner' by Lee Tutor.

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Kon-Fu-Sed

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Re: Multi-million spins statistics
January 25, 2009, 07:26:14 AM
Hi purple,

The repeat-values I showed - for example:
Quote

 [highlight]Evens repeats: 22, 22, 22, 21, 21, 23.[/highlight] My calculator says 22

were copied from the 12-million spins statistics that I gave you the link to: .
http://vlsroulette.com/reference-area/12-million-rng-spin-stats-shared-by-poit/

So they were found in 12 million spins.
The six values are for Low, High, Red, Black, Odd and Even, respectively.

I copied the repeat-values for col/doz, dbl streets, corners, single streets, splits and singles from the same 12 million spins stats.

My calculator values (same example):
Quote

 Evens repeats: 22, 22, 22, 21, 21, 23. [highlight]My calculator says 22[/highlight]

were taken from the table "How long sequences can we expect, MATHEMATICALLY, in X trials?"
This is the X = 12M (12,000,000) line in that table (single zero):

X        50/50   "Even"    Cl/Dz   DblStr   Corner   SngStr    Split   Single
  [highlight]12M[/highlight]
       23       [highlight]22[/highlight]       14        8        7        6        5        4
[/tt]
Showing that in 12 million spins, a 22-repeater of an "even" (18/37) bet will be found (mathematically).
And the rest of the "calculator values" are also found at that line.

I hope this clears things up for you.
KFS
If s**t can happen, s**t will happen.

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Breeze88

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Re: Multi-million spins statistics
February 17, 2009, 01:02:21 PM
HI Kon-Fu-Sed


Now that we know that all chances even out , we should take advantage of this , shouldnt we?


here is a example of how i think we could take advantage of the even out  rule...


so lets say a dozen didnt showed for at least 13 spins and when that dozen shows after the 13th spin we should bet on it , because its rather unlikely that that dozen will go now back to sleep for another long trail because  of the even out rule.. isnt it?

or how often do you see such an extreme event exmpl on doz .:  12122211121221123212122111222112


waht do you think?


cheerz