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Random Questions

Topic closed. 17 replies. Last post 1 year ago by DCTreybil.

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Lincoln, California
United States
Member #167130
June 27, 2015
256 Posts
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Posted: October 25, 2015, 12:37 pm - IP Logged

Concerning hot/cold numbers:

I have a simulator that relates to this idea.

The simulator sets up a series of 10,000,000 flags based on odds.

For example, if odds of 2 : 1 are used, 5,000,000 flags are set in random positions.

Then I count the number of consecutive flags set starting at each of the 10,000,000 positions.

I tried pasting the output here, but it becomes unreadable.

Upshot is, you get 0 hits in a row 5,000,000 times.  This is because 5,000,000 flags do not get set.  This is exactly 1/2.

In this run of the simulator  1 hit in a row 2,500,114 occurs times.  Notice this does not come out exactly even.  Random simulations "shimmer" around ideal results.  They are close, but seldom exact.  This is very close to 1/4th.

In this run of the simulator 2 hits in a row 1,249,741 occur times.  Again, not exactly even, but it comes out very close to 1/8th.

Last but not least, in this run of the simulator, 3 hits in a row occur  625,099 times.  This is very close to 1/16th.

Consider the ratios just mentioned -  1/2, 1/4, 1/8, 1/16 - What are they?  The denominators are all powers of 2.  And 2 : 1 was the odds used.

I bet if I ran the simulator with odds of 3 : 1, the fractions would likely be 1/3, 1/9, 1/27, and 1/81.

So, concerning hot and cold numbers - Sequential occurrences of events happen less frequently as the number of sequential occurrences increases.  If hot numbers were more likely to happen, what would keep hot numbers from becoming the only numbers that ever happen?  And what would ensure that cold numbers did not stop happening?

As I contemplate the results of this simulator, I have to come down on the side that says current results do not depend on previous results.

Very interesting approach.  Could you elaborate more on the Flags?

Your conclusion is the same as the one in my gut.  The workouts I have done seam to produce the results I want to see.  It also seams that with most of the number tricks I have tried history shows that those tricks produce no better % of hits than the bare odds. 

Still, WE keep going.  It just occurred to me that a focus on the Random Generator is the answer.  The random generator is tasked with producing a stream of numbers without producing any reliable trends.  I wonder if the generator has to correct itself when it produces short bursts of trends and if it is possible to spot them? 

Well on WE go.  I keep going because I enjoy the search more than playing the game (probably because I am not winning much yet). 

Knowledge is success, even when the answer is Negative.

    DCTreybil's avatar - actuarial I_w_caption_II_sized.jpg
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    Member #169613
    October 24, 2015
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    Posted: October 25, 2015, 2:03 pm - IP Logged

    First, on your thought that knowledge is success . . .  If you can see the universe in a grain of sand, why not in a hand of cards?  Check out Sting's "Shape of My Heart" on YouTube.  The lyrics to the first verse are of great interest to me.  Based on your last statement, you might enjoy that, too.

    Concerning the flags.  In a computer program, you can easily create an array of 10,000,000 elements.  A single statement does it.  Each of those elements can be a flag.  Each flag can be set (1) or reset (0).  To simulate 2 : 1 odds, you set 5,000,000 of the elements to 1.  Then you see how many time n flags in a row are set.  You profile that.

    And that's where the counts come from.  And those counts are what the odds for each value of n are based on.

    FWIW, to simulate 3 : 1 odds, only 3,333,333 flags are set.  The rest of the process is the same.

      DCTreybil's avatar - actuarial I_w_caption_II_sized.jpg
      New Member

      United States
      Member #169613
      October 24, 2015
      11 Posts
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      Posted: October 25, 2015, 7:01 pm - IP Logged

      Ok, I found a way to get this table in here so you could read it:

      0.500 = odds as decimal fraction (0 < odds < 1)
      1.999 : 1 = odds as ratio (###.### : 1)
      .0 = elapsed time

      . . . AT . . . . AT & ABOVE . .AT & BELOW . . . RATIO ODDS

      . 0 .5,000,092 . 5,000,092 .10,000,000 . . . . . . . . 1.99996
      . 1 .2,500,114 . 7,500,206 . .4,999,908 . . . . . . . . 3.99982
      . 2 .1,249,741 . 8,749,947 . .2,499,794 . . . . . . . . 8.00166
      . 3 . . 625,099 . 9,375,046 . .1,250,053 . . . . . . . 15.99747
      . 4 . . 312,475 . 9,687,521 . . . 624,954 . . . . . . . 32.00256
      . 5 . . 156,410 . 9,843,931 . . . 312,479 . . . . . . . 63.93453
      . 6 . . . 78,195 . 9,922,126 . . . 156,069 . . . . . . 127.88541
      . 7 . . . 39,038 . 9,961,164 . . . .77,874 . . . . . ..  256.16066
      . 8 . . . 19,353 . 9,980,517 . . . .38,836 . . . . . . .516.71575
      . 9 . . . . 9,629 . 9,990,146 . . . .19,483 . . . . . 1,038.52944
      10 . . . . 4,839 . 9,994,985 . . . . .9,854 . . . . . 2,066.54267
      11 . . . . 2,466 . 9,997,451 . . . . .5,015 . . . . . 4,055.15004
      12 . . . . 1,266 . 9,998,717 . . . . .2,549 . . . . . 7,898.89415
      13 . . . . . .634 . 9,999,351 . . . . .1,283 . . . . 15,772.87066
      14 . . . . . .321 . 9,999,672 . . . . . .649 . . . . 31,152.64798
      15 . . . . . .172 . 9,999,844 . . . . . .328 . . . . 58,139.53488
      16 . . . . . . .75 . 9,999,919 . . . . . .156 . . . 133,333.33333
      17 . . . . . . .42 . 9,999,961 . . . . . . .81 . . . 238,095.23810
      18 . . . . . . .21 . 9,999,982 . . . . . . .39 . . . 476,190.47619
      19 . . . . . . . .9 . 9,999,991 . . . . . . .18 . .1,111,111.11111
      20 . . . . . . . .4 . 9,999,995 . . . . . . . 9 . . 2,500,000.00000
      21 . . . . . . . .2 . 9,999,997 . . . . . . . 5 . . 5,000,000.00000
      22 . . . . . . . .1 . 9,999,998 . . . . . . . 3 . 10,000,000.00000
      23 . . . . . . . .1 . 9,999,999 . . . . . . . 2 . 10,000,000.00000
      24 . . . . . . . .1 10,000,000 . . . . . . . 1 . 10,000,000.00000


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