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Fingers and Toes, Here We Go!

Topic closed. 16 replies. Last post 6 years ago by RL-RANDOMLOGIC.

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time*treat's avatar - radar

United States
Member #13130
March 30, 2005
2171 Posts
Offline
Posted: February 19, 2011, 8:32 am - IP Logged

Fingers and Toes, Here We Go!

Number systems adopted by people over the centuries have been based most often on the number of fingers and toes humans have evolved, but not all.  Notable exceptions are the modern ones based on binary digits which are useful in the world of on/off conditions in electronic computers.  For computational efficiency, before computers, a base Twelve system would have been a better choice for us than Ten. This article discusses the Base Twelve or Duodecimal system as well as the peoples who have and still use it.  If you're interested, you can find similar information on other systems.

http://en.wikipedia.org/wiki/Duodecimal

"Languages using duodecimal number systems are uncommon. Languages in the Nigerian Middle Belt such as Janji, Gbiri-Niragu (Kahugu), the Nimbia dialect of Gwandara[1]; the Chepang language of Nepal[2] and the Mahl language of Minicoy Island in India are known to use duodecimal numerals. In fiction, J. R. R. Tolkien's Elvish languages used duodecimal."

For purposes of discussion, I've adopted the tradition of using our familiar base TEN numerals, [0,1,2,3,4,5,6,7,8,9] to represent the same number of objects for all the bases listed, except for the Roman System. For non-Roman bases larger than TEN, I will use [A,B,C,D,E,F,G,H,J,K] to count beyond 9 with a single digit.  Also, when there is a possibility of confusion, I will append the BASE of a number in parenthesis (using base TEN digits.)

The (5,39(10)) Lotto is preferred by many of the proponents of lottery selection systems based on the counting of digits.  Therefore, I've compiled a table of what the Labels for each of the 39(10) objects in this game would look like in systems of various BASES.

BASE   BASE     BASE  BASE   BASE   BASE     BASE   ROMAN
TEN    TWO      FOUR  EIGHT TWELVE SIXTEEN *TWENTY NUMERALS

01     000001     001     01     01      01       01      I
02     000010     002     02     02      02       02      II
03     000011     003     03     03      03       03      III
04     000100     010     04     04      04       04      IV
05     000101     011     05     05      05       05      V
06     000110     012     06     06      06       06      VI
07     000111     013     07     07      07       07      VII
08     001000     020     10     08      08       08      VIII
09     001001     021     11     09      09       09      IX
10     001010     022     12     0A      0A       0A      X
11     001011     023     13     0B      0B       0B      XI
12     001100     030     14     10      0C       0C      XII
13     001101     031     15     11      0D       0D      XIII
14     001110     032     16     12      0E       0E      XIV
15     001111     033     17     13      0F       0F      XV
16     010000     100     20     14      10       0G      XVI
17     010001     101     21     15      11       0H      XVII
18     010010     102     22     16      12       0J      XVIII
19     010011     103     23     17      13       0K      XIX
20     010100     110     24     18      14       10      XX
21     010101     111     25     19      15       11      XXI
22     010110     112     26     1A      16       12      XXII
23     010111     113     27     1B      17       13      XXIII
24     011000     120     30     20      18       14      XXIV
25     011001     121     31     21      19       15      XXV
26     011010     122     32     22      1A       16      XXVI
27     011011     123     33     23      1B       17      XXVII
28     011100     130     34     24      1C       18      XXVIII
29     011101     131     35     25      1D       19      XXIX
30     011110     132     36     26      1E       1A      XXX
31     011111     133     37     27      1F       1B      XXXI
32     100000     200     40     28      20       1C      XXXII
33     100001     201     41     29      21       1D      XXXIII
34     100010     202     42     2A      22       1E      XXXIV
35     100011     203     43     2B      23       1F      XXXV
36     100100     210     44     30      24       1G      XXXVI
37     100101     211     45     31      25       1H      XXXVII
38     100110     212     46     32      26       1J      XXXVIII
39     100111     213     47     33      27       1K      XXXIX

* Yup'ik of South Alaska.

--------------------------
I think this is enough to digest for the time being.  I hope you will ask yourself questions regarding what the information above should indicate to anyone counting digits to choose lottery numbers.  Keep in mind that the ping pong balls will NOT be aware of what base was used to prepare their label, and consequently, will be clueless regarding what digits they are wearing!  Another pertinent question might be, "How will the distribution of frequency counts of digits change for the 575757(10) combinations of 5?"  This is important, as digit selection proponents select and reject sets based on this distribution.

Remember, if we had evolved with 3 or 4 fingers, we very likely would be using a 6, 8, or 12(10) based number system today, rather than TEN!  Smile

Whatever means used to label the ping-pong balls (for those states that still use real machines) [1,2,3,_ ... or Ralph, Norton, Trixie, _____ ... or Blonde, Blue, Brown, ______... or Short Line, B & O, Reading, ____________], people will devise a system to look for patterns, and try to make their play do better than random.

Unless and until it demonstrates a better payout than the Digit Counters' Way (base 10) compared to what they are currently using, at best it will serve as an amusing distraction.

In neo-conned Amerika, bank robs you.
Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

    RL-RANDOMLOGIC's avatar - usafce

    United States
    Member #59354
    March 13, 2008
    3972 Posts
    Offline
    Posted: February 19, 2011, 3:34 pm - IP Logged

    I assume  this game pays for matching 2-3-4 of the correct letters in the name.

    Bob, Bill, Ernie, George, Betty, Barney,Wilma,Fred,Ethel,Lucy,Ricky

     

    a = 2,  b = 5,  c = 1, d = 1, e = 9, f = 1, g = 2,  i= 4, k=1, l=5, m=1,

    n=2, o=2, r=5, t=3, u=1, w=1,  y=4.

     

    My six letter choices are  e-b-r-l-i-y

    RL