Re: Lotto - Gaps - probability, HELP
From: djura (djura-12_at_gawab.com)
Date: 02/10/05
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Date: Thu, 10 Feb 2005 15:46:12 +0100
On 9 Feb 2005 04:46:49 -0800, matt271829-news@yahoo.co.uk wrote:
>
>djura wrote:
>> On 8 Feb 2005 11:57:09 -0800, matt271829-news@yahoo.co.uk wrote:
>>
>> ;))
>> You're not lost at all, that's my feeling.
>> - start with the follow gaps:
>>
>> A A A A A
>> all gaps equal.
>> - only (1) one gaps combination.
>>
>> I'll choose (by statistical survey) A=4,
>> so there are
>> (36-(4+4+4+4+4))x1=36-20=16 Lotto combination.
>>
>> 1 5 9 13 17 21
>> 2 6 10 14 18 22
>> 3 7 11 15 19 23
>> 4 8 12 16 20 24
>> 5 9 13 17 21 25
>> 6 10 14 18 22 26------ OK, 5 balls caught
>> 7 11 15 19 23 27
>> 8 12 16 20 24 28
>> 9 13 17 21 25 29
>> 10 14 18 22 26 30----- 6
>> 11 15 19 23 27 31
>> 12 16 20 24 28 32
>> 13 17 21 25 29 33
>> 14 18 22 26 30 34------ 5
>> 15 19 23 27 31 35
>> 16 20 24 28 32 36
>>
>> Well, what's the next step?
>> Write these 16 combinations on the tickets ;)
>>
>> Winning balls dropped out from the mixer like this:
>> 10 14 18 22 26 30
>> see above.
>
>I understand how you've arrived at the 16 Lotto combinations listed.
>That bit's fine.
>
>GIVEN that you've highlighted "10 14 18 22 26 30" as "all 6", I also
>understand how you've selected the two "all 5" combinations. (Though
>"all 5" is a horrible way of describing it. "All" is the wrong word.)
>
It is for simulation purposes, from a hat ;).
I could choose any other.
But, what is the essence:
- I wouldn't do that if I knew (by a formulae, pattern)
how to calculate exact number of Lotto combinations
with (6 only one), 5, 4, 3 numbers caught for a given
gaps A, B, C, D, E...
1. When I statistically choose 5 gaps (A, B, C, D, E)
and create a system (in the way you understood),
OK., let's say - simulate or whatever you like and that's the point ):
a) There is 1 Lotto comb. with 6 balls caught.
(this is for shure ;)
b) How many Lotto combinations will have 5
numbers caught?
c) How many Lotto combinations will have 4
numbers caught?
d) How many Lotto combinations will have 3
numbers caught?
I know these numbers vary (odd or even gaps numbers)
as you noticed, choosing the one with odd numbers ;)
(1 5 9 13 17 21) in the case gaps are even :)>>
- but it's not relevant at this moment.
(a little question. What about 3 even - 2 odd, or vice verse?)
Anyway, the guarantee is 'rock solid';
there must be min. 1 Lotto comb. with 6 balls caught,
1 with 5 balls caught, 1 with 4 balls caught and
1 with 3 balls caught. OK?
>What I DON'T understand is WHY you have chosen "10 14 18 22 26 30" to
see above.
>highlight as "all 6". This makes a difference. If you'd chosen "1 5 9
> 13 17 21" as "all 6" then there would be only ONE "all 5" instead of
>the two we have above? This seems to imply that your question does not
>have a well-defined (single) answer for a given sequence of gaps.
>
>> --------------------------------
>>
>> But, suppose I choose for gaps ABBBB.
>> "4 the same"
>> There are altogether 5 gaps combination:
>>
>> ABBBB
>> BABBB
>> BBABB
>> BBBAB
>> BBBBA
>>
>> (I call it 'diagonal' :))
>>
>> I'll choose (by statistical survey) A=1, B=4
>> so there are
>> (36-(1+4+4+4+4))x5=(36-17)x5=135 Lotto combination.
>>
>> Group-1: ABBBB (1, 4, 4, 4, 4)
>> 1 2 6 10 14 18
>> 2 3 7 11 15 19
>> ......................... cut
>> 19 20 24 28 32 36
>>
>> Group-2: BABBB (4, 1, 4, 4, 4)
>> 1 5 6 10 14 18
>> 2 6 7 11 15 19
>> ......................... cut
>> 19 23 24 28 32 36
>>
>> ------------------------ cut (group)
>>
>> Group-5: BABBB (4, 4, 4, 4, 1)
>> 1 5 9 13 17 18
>> 2 6 10 14 18 19
>> ......................... cut
>> 19 23 27 31 35 36
>>
>
>This is all fine ... I understand how you are tabulating the lottery
>combinations matching a given sequence of gaps.
>
>> ==========================
>> Question:
>>
>> If I catch all 5 gaps (ABCDE), is it possible
>> to calculate, how many my Lotto
>> combinations will have 5, 4, 3 shoots?
>> - OK., there will be 1 with all 6 .)
>
>But in your earlier 4,4,4,4,4 example there were SIXTEEN potential "all
>6's". Why are you now saying there is ONE with "all 6"? Same question
>as before I guess ... where are you getting that special ONE
>combination from?
What's nice with this system:
- I do not like to think about the numbers in the play.
All 36 play.
- As about the guarantee, it's rock solid but VARIES.
(nobody knows the final epilogue :)
- To open another thread (lucky me)
take care there's one, very nice trap:
The guarantee changes unexpectedly
if sum(A+B)<C
sum(A+B+C)<D,
.... etc.
especially as I like to have A=1.
Well, hope, as there are a lot of math skilful people,
"moving all the time blue, red, green balls into
N boxes" TO TRY this problem
(it's not trivial anyway).
Thank you.
-- Gramophone free design - no mechanics, pure silicon!
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