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IXL Software
Guest
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 Posted: Sun Apr 10, 2005 4:15 am Post subject: Reducing The Odds |
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It has often been said here and elsewhere that the only way to improve or
reduce the odds against a player winning a lottery jackpot is to purchase
more tickets (chances). Is that really so?
The reasoning goes something like this:
If I buy 1 ticket on a 649 lottery draw, that ticket has odds of
13,983,816:1 of matching the jackpot numbers.
If I buy 10 tickets for the very same draw, my overall odds now become
1,398,381.6:1. If I buy 1000 tickets for the very same draw, my overall odds
now become 13,983.816:1...and so on.
This logic is essentially saying that I can have a 1,000% improvement of the
odds in my favour by covering only a very tiny percentage (0.00715%) of the
possible outcomes. Don't those numbers look just a little out of whack...in
fact extremely disproportionate?
Consider this: it is entirely possible to purchase 13,983,815 different
tickets and *still* not win the jackpot! You will of course have a hell of a
lot of smaller prizes...but not the big one. Imagine the embarrassment.
Assuming that the minimum match of winning numbers must be at least 3, it is
theoretically possible to purchase 13,723,192 tickets and not win so much as
a goddamn
penny! Incredible as it may seem, that's over 98% coverage of all possible
outcomes with nothing to show for it. I have no idea of how one could go
about purposely trying to win nothing on such a large wager. In this case,
losing everything seems more daunting a task than winning anything. Strange
game...is it not?
Do we begin to see how this "more tickets" logic breaks down pretty rapidly?
This is why I believe that the common basic assumption is incorrect. You
simply
cannot use the aggregate total of chances to properly calculate the overall
odds. You end up with a distorted picture that is out of phase with reality.
I believe that the correct way to interpret the odds is to say that each
ticket in play has a *discrete and equal chance*. In other words, if you
play
1,000 tickets, you have 1,000 *separate (but equal)* chances of 1 in
13,983,816 at the
jackpot...not an aggregate chance of 1 in 13,983.816.
The difference in interpretations is subtle and difficult to adequately
describe but I'm hoping that at least a few people out there can understand
what I'm driving at. The implications of one being true over the other are
huge...if given but a little thought...something that is generally
conspicuous by its absence around these parts.
Note that using an analogy such as a mixture of red and blue marbles in a
jar would be inappropriate for the purpose of counter-argument. That would
be like comparing the probabilities or odds between 2 similar but very
different card games such as Poker and Bridge...even though they both use
the exact same deck of 52 cards...or Chess and Checkers...even though they
both use the exact same playing board and number of playing pieces.
TRUE REDUCTION OF ODDS
========================
The only way to truly reduce the player's odds is to reduce the number of
possible outcomes. The only way to accomplish this is by artificial means
that are commonly called "guessing". That's why it's called a game of
chance...or gambling on an unknown outcome.
Does such a thing exist? The answer is conditionally Yes. Here are a few
examples:
We all enjoy a natural reduction of odds that is conditional on a simple
assumption. The assumption is that the exact same 6 winning numbers will not
be randomly drawn within (or even beyond) the period of a human lifetime at
a rate of 2 draws per week. In practical terms, this means that you can
subtract the number of actual results that have already been drawn from the
total of possible outcomes. In the case of the Canadian 649 lottery, there
will have been 2,214 draw results by the time this is posted. Based on that
assumption, this means that the effective number of outcomes for draw 2,215
will be 13,981,602. Not a *big* reduction by any means...but a reduction
nonetheless for as long as the conditional assumption remains true. To my
mind at least, there is little use in playing lines that have already been
drawn.
Another example is the application of certain criteria that will either
accept or reject any combination of 6 numbers for consideration as worthy
lines to play. These criteria are most often referred to as "filters".
One of the most basic filters is the *sum of the line*. This sum ranges from
a minimum of 21 to a maximum of 279. Once the number of combinations for
each of those sums is calculated, it is easy to plot the results on a graph.
The resulting graph represents the classic "bell" curve that is the classic
statistician's bread & butter. In the case of a 649 lottery, the sums peak
at 150 with 165,772 lines that sum to that total. The remaining sums fall
off equally and perfectly symmetrically on either side of that sum. This is
not mere coincidence. I have seen many subscribers here reject this fact as
either useless or meaningless. They are entitled to that opinion, but I have
never seen even *1* of those proponents offer any clear evidence or
mathematical proof to support their belief. In stark contrast to that
glaring deficiency, I submit the following evidence in support of my claim:
If a player simply restricts their played lines to a sum between 100-199,
this results in 12,169,389 lines that pass the filter. This results in a
nearly 13% reduction in eligible lines and consequently a nearly 15%
improvement of the odds in the players' favour. Notice that this is very
much a clearly *positive* improvement over the concept of merely purchasing
more tickets as described above. Simple arithmetic shows that about 87% of
all the possible lines are covered.
Practical "real" results show that in the Canadian 649, 1,919 of 2,213 draws
to date (86.71%) have had a sum that conforms to this requirement. In fact,
the last 18 consecutive draws have produced results that conform to this
requirement. For the UK649, 842 of 969 draws to date (86.89%) have obeyed
this simple requirement. Up until the most recent draw, 26 previous
consecutive draws fell within the requirement. Would anyone care to reject a
15% improvement of odds for somewhere between 8 or 9 out of every 10 draws?
If so...why? Kindly describe your reasoning with the same detail that I have
attempted here. The possibility always exists that I am totally mistaken.
I'll be the 1st to accept that possibility and will gladly acknowledge any
contrary opinion. Teach me something that I don't already know...I beg of
you. This place offers so little intellectual stimulation other than the
easily predictable and inevitable ego conflicts that prevail here.
I have further examples to offer, but I'll see what the reaction is before
saying anything further. Is it wrong to identify such a strong correlation
between the theoretical and the actual? I invite anyone to show proof that
my line of reasoning is faulty for whatever reason. Keep it clean and try to
stick to facts rather than personality.
Would you rather read material of this kind or the kind of garbage that
small minds produce when they actually have nothing at all to say that will
benefit anyone other than their own perverse needs? In the end, you get the
kind of group that you both make and deserve. |
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Nik Barker
Guest
|
| Posted: Sun Apr 10, 2005 8:10 am Post subject: Re: Reducing The Odds |
|
|
IXL Software wrote:
| Quote: | It has often been said here and elsewhere that the only way to
improve or
reduce the odds against a player winning a lottery jackpot is to
purchase
more tickets (chances). Is that really so?
The reasoning goes something like this:
If I buy 1 ticket on a 649 lottery draw, that ticket has odds of
13,983,816:1 of matching the jackpot numbers.
If I buy 10 tickets for the very same draw, my overall odds now
become
1,398,381.6:1. If I buy 1000 tickets for the very same draw, my
overall odds
now become 13,983.816:1...and so on.
This logic is essentially saying that I can have a 1,000% improvement
of the
odds in my favour by covering only a very tiny percentage (0.00715%)
of the
possible outcomes. Don't those numbers look just a little out of
whack...in
fact extremely disproportionate?
Consider this: it is entirely possible to purchase 13,983,815
different
tickets and *still* not win the jackpot! You will of course have a
hell of a
lot of smaller prizes...but not the big one. Imagine the
embarrassment.
Assuming that the minimum match of winning numbers must be at least
3, it is
theoretically possible to purchase 13,723,192 tickets and not win so
much as
a goddamn
penny! Incredible as it may seem, that's over 98% coverage of all
possible
outcomes with nothing to show for it. I have no idea of how one could
go
about purposely trying to win nothing on such a large wager. In this
case,
losing everything seems more daunting a task than winning anything.
Strange
game...is it not?
Do we begin to see how this "more tickets" logic breaks down pretty
rapidly?
This is why I believe that the common basic assumption is incorrect.
You
simply
cannot use the aggregate total of chances to properly calculate the
overall
odds. You end up with a distorted picture that is out of phase with
reality.
I believe that the correct way to interpret the odds is to say that
each
ticket in play has a *discrete and equal chance*. In other words, if
you
play
1,000 tickets, you have 1,000 *separate (but equal)* chances of 1 in
13,983,816 at the
jackpot...not an aggregate chance of 1 in 13,983.816.
The difference in interpretations is subtle and difficult to
adequately
describe but I'm hoping that at least a few people out there can
understand
what I'm driving at. The implications of one being true over the
other are
huge...if given but a little thought...something that is generally
conspicuous by its absence around these parts.
Note that using an analogy such as a mixture of red and blue marbles
in a
jar would be inappropriate for the purpose of counter-argument. That
would
be like comparing the probabilities or odds between 2 similar but
very
different card games such as Poker and Bridge...even though they both
use
the exact same deck of 52 cards...or Chess and Checkers...even though
they
both use the exact same playing board and number of playing pieces.
TRUE REDUCTION OF ODDS
========================
The only way to truly reduce the player's odds is to reduce the
number of
possible outcomes. The only way to accomplish this is by artificial
means
that are commonly called "guessing". That's why it's called a game of
chance...or gambling on an unknown outcome.
Does such a thing exist? The answer is conditionally Yes. Here are a
few
examples:
We all enjoy a natural reduction of odds that is conditional on a
simple
assumption. The assumption is that the exact same 6 winning numbers
will not
be randomly drawn within (or even beyond) the period of a human
lifetime at
a rate of 2 draws per week. In practical terms, this means that you
can
subtract the number of actual results that have already been drawn
from the
total of possible outcomes. In the case of the Canadian 649 lottery,
there
will have been 2,214 draw results by the time this is posted. Based
on that
assumption, this means that the effective number of outcomes for draw
2,215
will be 13,981,602. Not a *big* reduction by any means...but a
reduction
nonetheless for as long as the conditional assumption remains true.
To my
mind at least, there is little use in playing lines that have already
been
drawn.
Another example is the application of certain criteria that will
either
accept or reject any combination of 6 numbers for consideration as
worthy
lines to play. These criteria are most often referred to as
"filters".
One of the most basic filters is the *sum of the line*. This sum
ranges from
a minimum of 21 to a maximum of 279. Once the number of combinations
for
each of those sums is calculated, it is easy to plot the results on a
graph.
The resulting graph represents the classic "bell" curve that is the
classic
statistician's bread & butter. In the case of a 649 lottery, the sums
peak
at 150 with 165,772 lines that sum to that total. The remaining sums
fall
off equally and perfectly symmetrically on either side of that sum.
This is
not mere coincidence. I have seen many subscribers here reject this
fact as
either useless or meaningless. They are entitled to that opinion, but
I have
never seen even *1* of those proponents offer any clear evidence or
mathematical proof to support their belief. In stark contrast to
that
glaring deficiency, I submit the following evidence in support of my
claim:
If a player simply restricts their played lines to a sum between
100-199,
this results in 12,169,389 lines that pass the filter. This results
in a
nearly 13% reduction in eligible lines and consequently a nearly 15%
improvement of the odds in the players' favour. Notice that this is
very
much a clearly *positive* improvement over the concept of merely
purchasing
more tickets as described above. Simple arithmetic shows that about
87% of
all the possible lines are covered.
Practical "real" results show that in the Canadian 649, 1,919 of
2,213 draws
to date (86.71%) have had a sum that conforms to this requirement. In
fact,
the last 18 consecutive draws have produced results that conform to
this
requirement. For the UK649, 842 of 969 draws to date (86.89%) have
obeyed
this simple requirement. Up until the most recent draw, 26 previous
consecutive draws fell within the requirement. Would anyone care to
reject a
15% improvement of odds for somewhere between 8 or 9 out of every 10
draws?
If so...why? Kindly describe your reasoning with the same detail that
I have
attempted here. The possibility always exists that I am totally
mistaken.
I'll be the 1st to accept that possibility and will gladly
acknowledge any
contrary opinion. Teach me something that I don't already know...I
beg of
you. This place offers so little intellectual stimulation other than
the
easily predictable and inevitable ego conflicts that prevail here.
I have further examples to offer, but I'll see what the reaction is
before
saying anything further. Is it wrong to identify such a strong
correlation
between the theoretical and the actual? I invite anyone to show proof
that
my line of reasoning is faulty for whatever reason. Keep it clean and
try to
stick to facts rather than personality.
Would you rather read material of this kind or the kind of garbage
that
small minds produce when they actually have nothing at all to say
that will
benefit anyone other than their own perverse needs? In the end, you
get the
kind of group that you both make and deserve.
|
Paul
The only problem I can see with your question/analysis/ponderings
above, is the way you end it:
"...or the kind of garbage small minds produce..."
There were a zillion different ways to end that post and even make a
similar point, at the end that is, but you chose one of arrogance, of
talking down to the rest.
So while I find your post interesting in many aspects, it's
disappointing to have to start mine with the above critique.
Anyway having said that I'll continue.
I don't think there's any argument that there are 13,983,816 possible
outcomes before each and every draw takes place.
Your chance of matching that outcome are written variously as:
1 in 13,983,816
13,983,816:1
13,983,816/1
Assuming that only one draw takes place each time, the '1' in the above
notations refers to the assumption that you have purchased 1 ticket for
that draw. That's why the odds are 'to 1'
Your point is one I have also struggled with, and in the same manner,
in that it doesn't seem quite right, there's something that just keeps
niggling me about it.
However, I believe that the numbers don't lie. Let's suppose I increase
my tickets to 2.
*My* odds for that draw are now 2 in 13,983,816. Is this not the same
as me buying 1 ticket in a different lottery somewhere that only has
6,991,908 possible outcomes?
Another way I found to justify to myself that despite that niggling
feeling, the more tickets answer is correct, is this:
If in a 6/49 lotto I were to purchase 6,991,908 tickets (each with a
different combination) I would have purchased 50% of the possible
outcomes. *My* odds for the ensuing draw would be now 6,991,908 in
13,983,816 or 1 in 2. If I have 50% of the possible outcomes then that
is the same as 'purchasing heads' where the possible outcomes are
either 'heads' or 'tails'.
So my conclusion to the above would be this. If it is true that when I
buy just 1 ticket my odds for the game are 1 in 13,983,816 AND if it is
also true that if I were to buy 6,991,908 tickets then my odds for the
game are 1 in 2, then it must be true that in all circumstances where I
were to purchase a number of tickets between 1 and 6,991,908 there will
be a corresponding correlating effect on *my* odds for that game.
I think part of the reason it often doesn't sound quite right is
because of the 'size' of the odds. In such circumstances I think the
best thing to do is to look at an example that operates in exactly the
same way, but is easier to handle mentally.
So we could imagine that there is a lottery or game with 4 possible
outcomes. If I decide to play and choose 1 of those outcomes *my* odds
for that game are 1 in 4. If I 'buy more tickets', ie I decide to play
and choose 2 out of the possible 4 outcomes then I think it quickly
becomes evident that *my* odds for that game are now 1 in 2, my odds
must be 1 in 2 since I have covered 50% of the possible outcomes.
One reason why I think the above argument seems unreasonable at first
glance in the case of a 6/49 lottery is because of the large numbers.
If we follow the above example: I decide to play and purchase 1 ticket;
*my* odds for that game are 1 in 13,983,816. If, instead, I decided to
purchase two different tickets for that game then *my* odds are 2 in
13,983,816 which can be written as 1 in 6,991,908. It seems unjust
almost, to have purchased just 1 more ticket has slashed *my* odds for
the game in half...and the word 'half' is what causes the mental
quandry because it conjures up notions of 'half = 50%...50% = 1 in 2'
and we start to think, "That can't be right!"
That is why, by reducing the problem to a managable size (the imagining
of a lottery/game with 4 possible outcomes) we can see that it is, in
fact, correct. If it is correct for a game with only 4 possible
outcomes, then it must be correct for game with millions of possible
outcomes.
Anyway, I'll stop there, feel free to comment of course.
Ta
Nik |
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Robert Perkis
Guest
|
| Posted: Sun Apr 10, 2005 8:40 am Post subject: Re: Reducing The Odds |
|
|
IXL Software wrote:
| Quote: |
It has often been said here and elsewhere that the only way to improve or
reduce the odds against a player winning a lottery jackpot is to purchase
more tickets (chances). Is that really so?
The reasoning goes something like this:
If I buy 1 ticket on a 649 lottery draw, that ticket has odds of
13,983,816:1 of matching the jackpot numbers.
If I buy 10 tickets for the very same draw, my overall odds now become
1,398,381.6:1. If I buy 1000 tickets for the very same draw, my overall odds
now become 13,983.816:1...and so on.
This logic is essentially saying that I can have a 1,000% improvement of the
odds in my favour by covering only a very tiny percentage (0.00715%) of the
possible outcomes. Don't those numbers look just a little out of whack...in
fact extremely disproportionate?
Consider this: it is entirely possible to purchase 13,983,815 different
tickets and *still* not win the jackpot! You will of course have a hell of a
lot of smaller prizes...but not the big one. Imagine the embarrassment.
Assuming that the minimum match of winning numbers must be at least 3, it is
theoretically possible to purchase 13,723,192 tickets and not win so much as
a goddamn
penny! Incredible as it may seem, that's over 98% coverage of all possible
outcomes with nothing to show for it. I have no idea of how one could go
about purposely trying to win nothing on such a large wager. In this case,
losing everything seems more daunting a task than winning anything. Strange
game...is it not?
Do we begin to see how this "more tickets" logic breaks down pretty rapidly?
This is why I believe that the common basic assumption is incorrect. You
simply
cannot use the aggregate total of chances to properly calculate the overall
odds. You end up with a distorted picture that is out of phase with reality.
I believe that the correct way to interpret the odds is to say that each
ticket in play has a *discrete and equal chance*. In other words, if you
play
1,000 tickets, you have 1,000 *separate (but equal)* chances of 1 in
13,983,816 at the
jackpot...not an aggregate chance of 1 in 13,983.816.
The difference in interpretations is subtle and difficult to adequately
describe but I'm hoping that at least a few people out there can understand
what I'm driving at. The implications of one being true over the other are
huge...if given but a little thought...something that is generally
conspicuous by its absence around these parts.
Note that using an analogy such as a mixture of red and blue marbles in a
jar would be inappropriate for the purpose of counter-argument. That would
be like comparing the probabilities or odds between 2 similar but very
different card games such as Poker and Bridge...even though they both use
the exact same deck of 52 cards...or Chess and Checkers...even though they
both use the exact same playing board and number of playing pieces.
TRUE REDUCTION OF ODDS
========================
The only way to truly reduce the player's odds is to reduce the number of
possible outcomes. The only way to accomplish this is by artificial means
that are commonly called "guessing". That's why it's called a game of
chance...or gambling on an unknown outcome.
Does such a thing exist? The answer is conditionally Yes. Here are a few
examples:
We all enjoy a natural reduction of odds that is conditional on a simple
assumption. The assumption is that the exact same 6 winning numbers will not
be randomly drawn within (or even beyond) the period of a human lifetime at
a rate of 2 draws per week. In practical terms, this means that you can
subtract the number of actual results that have already been drawn from the
total of possible outcomes. In the case of the Canadian 649 lottery, there
will have been 2,214 draw results by the time this is posted. Based on that
assumption, this means that the effective number of outcomes for draw 2,215
will be 13,981,602. Not a *big* reduction by any means...but a reduction
nonetheless for as long as the conditional assumption remains true. To my
mind at least, there is little use in playing lines that have already been
drawn.
Another example is the application of certain criteria that will either
accept or reject any combination of 6 numbers for consideration as worthy
lines to play. These criteria are most often referred to as "filters".
One of the most basic filters is the *sum of the line*. This sum ranges from
a minimum of 21 to a maximum of 279. Once the number of combinations for
each of those sums is calculated, it is easy to plot the results on a graph.
The resulting graph represents the classic "bell" curve that is the classic
statistician's bread & butter. In the case of a 649 lottery, the sums peak
at 150 with 165,772 lines that sum to that total. The remaining sums fall
off equally and perfectly symmetrically on either side of that sum. This is
not mere coincidence. I have seen many subscribers here reject this fact as
either useless or meaningless. They are entitled to that opinion, but I have
never seen even *1* of those proponents offer any clear evidence or
mathematical proof to support their belief. In stark contrast to that
glaring deficiency, I submit the following evidence in support of my claim:
If a player simply restricts their played lines to a sum between 100-199,
this results in 12,169,389 lines that pass the filter. This results in a
nearly 13% reduction in eligible lines and consequently a nearly 15%
improvement of the odds in the players' favour. Notice that this is very
much a clearly *positive* improvement over the concept of merely purchasing
more tickets as described above. Simple arithmetic shows that about 87% of
all the possible lines are covered.
Practical "real" results show that in the Canadian 649, 1,919 of 2,213 draws
to date (86.71%) have had a sum that conforms to this requirement. In fact,
the last 18 consecutive draws have produced results that conform to this
requirement. For the UK649, 842 of 969 draws to date (86.89%) have obeyed
this simple requirement. Up until the most recent draw, 26 previous
consecutive draws fell within the requirement. Would anyone care to reject a
15% improvement of odds for somewhere between 8 or 9 out of every 10 draws?
If so...why? Kindly describe your reasoning with the same detail that I have
attempted here. The possibility always exists that I am totally mistaken.
I'll be the 1st to accept that possibility and will gladly acknowledge any
contrary opinion. Teach me something that I don't already know...I beg of
you. This place offers so little intellectual stimulation other than the
easily predictable and inevitable ego conflicts that prevail here.
I have further examples to offer, but I'll see what the reaction is before
saying anything further. Is it wrong to identify such a strong correlation
between the theoretical and the actual? I invite anyone to show proof that
my line of reasoning is faulty for whatever reason. Keep it clean and try to
stick to facts rather than personality.
Would you rather read material of this kind or the kind of garbage that
small minds produce when they actually have nothing at all to say that will
benefit anyone other than their own perverse needs? In the end, you get the
kind of group that you both make and deserve.
|
In a 6/49 game when you work with a group of 18 numbers
the odds of having all 6 winning numbers among your 18
drop to only 1 in 753. Now doesn't that seem like a
ridiculous change from 1 in 13.9 million to 1 in 753?
Robert Perkis
Keep on wheeling.  |
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|
|
Nick UK
Guest
|
| Posted: Sun Apr 10, 2005 12:25 pm Post subject: Re: Reducing The Odds |
|
|
"IXL Software" wrote..
| Quote: |
Teach me something that I don't already know...
|
Here is something you obviously don't know. It also represents some good
advice for you..
*Never* accuse anyone of criminal intent unless you can produce absolute
*proof* that will back up your accusation. If you cannot produce the
evidence, then do the decent thing and withdraw it - unconditionally.
| Quote: | I invite anyone to show proof that my line of reasoning is faulty for
whatever reason. Keep it clean and try to
stick to facts rather than personality.
|
I invite you to provide proof of your accusation. You lack reasoning. You
did not keep things clean. You soiled things with your dirty, filthy,
unfounded accusation.
| Quote: | Would you rather read material of this kind or the kind of garbage that
small minds produce when they actually have nothing at all to say that
will benefit anyone other than their own perverse needs? In the end, you
get the kind of group that you both make and deserve.
|
Eh? What was that? "the kind of group you both make and deserve"?
'er, do you mean the kind of group like this?..
| Quote: | Shall I tell everyone the *true* story about your clumsy attempt to
fraudulently obtain a software unlock code?
Paul McCoy.
|
and this..
| Quote: | Don't try to press this any further or I'll be forced to
nail your arse to the wall.
Paul McCoy.
|
and this..
| Quote: | If you want to air dirty laundry in public, you can expect to be
taken to the cleaners.
Paul McCoy.
|
and this..
| Quote: | If your aim is to turn this into a juvenile pissing contest, I guarantee
that you will live to regret it.
|
and this..
| Quote: | It's a pretty long stretch for me to stoop to your level, but I can manage
it if necessary. Get out while you still can. One warning is all you get.
Now slither back under your rock and stay there.
Paul McCoy.
|
and this..
| Quote: | Next time I need advice from an idiot, I'll be sure to call on you.
Paul McCoy.
|
and this..
| Quote: | Any further garbage like this from you will be treated with zero
tolerance. No more warnings.
Paul McCoy.
|
and this..
| Quote: | Get out while you still can. One warning is all you get. Paul McCoy.
|
A little reminder..
"the kind of group you both make and deserve"?
POT-KETTLE-BLACK?
Rounding off with this heart-rending Oscar winning performance..
| Quote: | Let me tell you now that I am some f***ing upset by what I have read.
Seeing my name dragged through the mud and Christ-knows what kind of shit
is unwarranted and absolutely intolerable.
Paul McCoy.
|
You'd better get used to it and learn to tolerate it. What you are now
getting in this newsgroup (and will continue to get) is what you *deserve*.
It will not stop until you withdraw your false accusation - unconditionally!
Your stomach-churning arrogance knows no limits or bounds.
Nick. |
|
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|
|
erce
Guest
|
| Posted: Sun Apr 10, 2005 1:30 pm Post subject: Re: Reducing The Odds |
|
|
IXL Software wrote:
| Quote: | I believe that the correct way to interpret the odds is to say that
each
ticket in play has a *discrete and equal chance*. In other words, if
you
play
1,000 tickets, you have 1,000 *separate (but equal)* chances of 1 in
13,983,816 at the
jackpot...not an aggregate chance of 1 in 13,983.816.
|
so if you buy 13983816 different tickets your chances are not 13983816
in 13983816 but you have 13983816 equal 1 in 13983816 chances of
winning
| Quote: | If a player simply restricts their played lines to a sum between
100-199,
this results in 12,169,389 lines that pass the filter. This results
in a
nearly 13% reduction in eligible lines and consequently a nearly 15%
improvement of the odds in the players' favour. Notice that this is
very
much a clearly *positive* improvement over the concept of merely
purchasing
more tickets as described above. Simple arithmetic shows that about
87% of
all the possible lines are covered.
|
harry bets on all the horses in a race and you bet on the horses with
short odds
either of you millionnaires yet?
erce |
|
| Back to top |
|
|
erce
Guest
|
| Posted: Sun Apr 10, 2005 1:35 pm Post subject: Re: Reducing The Odds |
|
|
Nick UK wrote:
| Quote: | "IXL Software" wrote..
Teach me something that I don't already know...
Here is something you obviously don't know. It also represents some
good
advice for you..
*Never* accuse anyone of criminal intent unless you can produce
absolute
*proof* that will back up your accusation. If you cannot produce
the
evidence, then do the decent thing and withdraw it - unconditionally.
|
if your confident your right stop spamming the newsgroup and sue the
guy
if your not confident stop spamming the newsgroup
erce |
|
| Back to top |
|
|
Colin Fairbrother
Guest
|
| Posted: Sun Apr 10, 2005 1:35 pm Post subject: Re: Reducing The Odds |
|
|
Mr IXL
You are not keeping abreast of developments. Colin has well and truly kicked
the bejesuz out of Odds/Evens and good old Sums.
If you claim to espouse logic then you should be able to follow my charts:
http://www.lottoposter.com/forum_posts.asp?TID=143&PN=1
Run Filterologists
Run Filterologists
Run, Run, Run
Colin he will get you
One by one
You can't hide
It's time to tan your hide
Run Filterologists
Run Filterologists
Run
Colin
ps I thought the article you did on understanding Wheel jargon was pretty
good. |
|
| Back to top |
|
|
Paracelsus
Guest
|
| Posted: Sun Apr 10, 2005 1:41 pm Post subject: Re: Reducing The Odds |
|
|
"IXL Software" <[email protected]> wrote in message
news:[email protected]...
|
| I believe that the correct way to interpret the odds is to say that each
| ticket in play has a *discrete and equal chance*.
<snip>
| We all enjoy a natural reduction of odds that is conditional on a simple
| assumption. The assumption is that the exact same 6 winning numbers will
not
| be randomly drawn within (or even beyond) the period of a human lifetime
at
| a rate of 2 draws per week. In practical terms, this means that you can
| subtract the number of actual results that have already been drawn from
the
| total of possible outcomes. In the case of the Canadian 649 lottery, there
| will have been 2,214 draw results by the time this is posted. Based on
that
| assumption, this means that the effective number of outcomes for draw
2,215
| will be 13,981,602. Not a *big* reduction by any means...but a reduction
| nonetheless for as long as the conditional assumption remains true. To my
| mind at least, there is little use in playing lines that have already been
| drawn.
First you say each combination has an equal chance of being drawn, then you
say the chances of a previous combination being drawn again is practically
zero. What's wrong with this picture?
It looks like a little thought is conspicuously more absent in some parts
than in others.
| Teach me something that I don't already know...I beg of
| you.
That's what they all say. |
|
| Back to top |
|
|
Dick Adams
Guest
|
| Posted: Sun Apr 10, 2005 2:00 pm Post subject: Re: Reducing The Odds |
|
|
[Snipped since everyone has already read it]
If I understood you correctly, you are saying that buying more tickets
does not improve your odds of winning as well as buying more tickets
within the range of sums.
If that is correct, then what your position amounts to is "Buy more
tickets based on filters". I can not imagine disagreeing with that.
Dick - Still The Wizard of Odds and sometimes Taxes too |
|
| Back to top |
|
|
Stig Holmquist
Guest
|
| Posted: Sun Apr 10, 2005 2:05 pm Post subject: Re: Reducing The Odds |
|
|
On Sun, 10 Apr 2005 00:00:40 -0400, "IXL Software"
<[email protected]> wrote:
| Quote: | It has often been said here and elsewhere that the only way to improve or
reduce the odds against a player winning a lottery jackpot is to purchase
more tickets (chances). Is that really so?
The reasoning goes something like this:
If I buy 1 ticket on a 649 lottery draw, that ticket has odds of
13,983,816:1 of matching the jackpot numbers.
If I buy 10 tickets for the very same draw, my overall odds now become
1,398,381.6:1. If I buy 1000 tickets for the very same draw, my overall odds
now become 13,983.816:1...and so on.
This logic is essentially saying that I can have a 1,000% improvement of the
odds in my favour by covering only a very tiny percentage (0.00715%) of the
possible outcomes. Don't those numbers look just a little out of whack...in
fact extremely disproportionate?
Consider this: it is entirely possible to purchase 13,983,815 different
tickets and *still* not win the jackpot! You will of course have a hell of a
lot of smaller prizes...but not the big one. Imagine the embarrassment.
Assuming that the minimum match of winning numbers must be at least 3, it is
theoretically possible to purchase 13,723,192 tickets and not win so much as
a goddamn
penny! Incredible as it may seem, that's over 98% coverage of all possible
outcomes with nothing to show for it. I have no idea of how one could go
about purposely trying to win nothing on such a large wager. In this case,
losing everything seems more daunting a task than winning anything. Strange
game...is it not?
Do we begin to see how this "more tickets" logic breaks down pretty rapidly?
This is why I believe that the common basic assumption is incorrect. You
simply
cannot use the aggregate total of chances to properly calculate the overall
odds. You end up with a distorted picture that is out of phase with reality.
I believe that the correct way to interpret the odds is to say that each
ticket in play has a *discrete and equal chance*. In other words, if you
play
1,000 tickets, you have 1,000 *separate (but equal)* chances of 1 in
13,983,816 at the
jackpot...not an aggregate chance of 1 in 13,983.816.
The difference in interpretations is subtle and difficult to adequately
describe but I'm hoping that at least a few people out there can understand
what I'm driving at. The implications of one being true over the other are
huge...if given but a little thought...something that is generally
conspicuous by its absence around these parts.
Note that using an analogy such as a mixture of red and blue marbles in a
jar would be inappropriate for the purpose of counter-argument. That would
be like comparing the probabilities or odds between 2 similar but very
different card games such as Poker and Bridge...even though they both use
the exact same deck of 52 cards...or Chess and Checkers...even though they
both use the exact same playing board and number of playing pieces.
TRUE REDUCTION OF ODDS
========================
The only way to truly reduce the player's odds is to reduce the number of
possible outcomes. The only way to accomplish this is by artificial means
that are commonly called "guessing". That's why it's called a game of
chance...or gambling on an unknown outcome.
Does such a thing exist? The answer is conditionally Yes. Here are a few
examples:
We all enjoy a natural reduction of odds that is conditional on a simple
assumption. The assumption is that the exact same 6 winning numbers will not
be randomly drawn within (or even beyond) the period of a human lifetime at
a rate of 2 draws per week. In practical terms, this means that you can
subtract the number of actual results that have already been drawn from the
total of possible outcomes. In the case of the Canadian 649 lottery, there
will have been 2,214 draw results by the time this is posted. Based on that
assumption, this means that the effective number of outcomes for draw 2,215
will be 13,981,602. Not a *big* reduction by any means...but a reduction
nonetheless for as long as the conditional assumption remains true. To my
mind at least, there is little use in playing lines that have already been
drawn.
Another example is the application of certain criteria that will either
accept or reject any combination of 6 numbers for consideration as worthy
lines to play. These criteria are most often referred to as "filters".
One of the most basic filters is the *sum of the line*. This sum ranges from
a minimum of 21 to a maximum of 279. Once the number of combinations for
each of those sums is calculated, it is easy to plot the results on a graph.
The resulting graph represents the classic "bell" curve that is the classic
statistician's bread & butter. In the case of a 649 lottery, the sums peak
at 150 with 165,772 lines that sum to that total. The remaining sums fall
off equally and perfectly symmetrically on either side of that sum. This is
not mere coincidence. I have seen many subscribers here reject this fact as
either useless or meaningless. They are entitled to that opinion, but I have
never seen even *1* of those proponents offer any clear evidence or
mathematical proof to support their belief. In stark contrast to that
glaring deficiency, I submit the following evidence in support of my claim:
If a player simply restricts their played lines to a sum between 100-199,
this results in 12,169,389 lines that pass the filter. This results in a
nearly 13% reduction in eligible lines and consequently a nearly 15%
improvement of the odds in the players' favour. Notice that this is very
much a clearly *positive* improvement over the concept of merely purchasing
more tickets as described above. Simple arithmetic shows that about 87% of
all the possible lines are covered.
Practical "real" results show that in the Canadian 649, 1,919 of 2,213 draws
to date (86.71%) have had a sum that conforms to this requirement. In fact,
the last 18 consecutive draws have produced results that conform to this
requirement. For the UK649, 842 of 969 draws to date (86.89%) have obeyed
this simple requirement. Up until the most recent draw, 26 previous
consecutive draws fell within the requirement. Would anyone care to reject a
15% improvement of odds for somewhere between 8 or 9 out of every 10 draws?
If so...why? Kindly describe your reasoning with the same detail that I have
attempted here. The possibility always exists that I am totally mistaken.
I'll be the 1st to accept that possibility and will gladly acknowledge any
contrary opinion. Teach me something that I don't already know...I beg of
you. This place offers so little intellectual stimulation other than the
easily predictable and inevitable ego conflicts that prevail here.
I have further examples to offer, but I'll see what the reaction is before
saying anything further. Is it wrong to identify such a strong correlation
between the theoretical and the actual? I invite anyone to show proof that
my line of reasoning is faulty for whatever reason. Keep it clean and try to
stick to facts rather than personality.
Would you rather read material of this kind or the kind of garbage that
small minds produce when they actually have nothing at all to say that will
benefit anyone other than their own perverse needs? In the end, you get the
kind of group that you both make and deserve.
Your discussion of the sum of six drawn numbers is of particular |
interest to me.
In his book "Lottery Numbers, Past, Present and Future" H. Schneider
also examined the sum and recommended the range 82-243 based on only
50 draws from each of two past 6/49 games. He clearly did not
recognize that the range should be symmetrical around the mean 150
in the long run.
Eight years ago I wrote an article in "Lotto World" (Apr.'97) on
p.40-43 about how to predict the std.dev. for the sum in any lotto
game and outlined ranges for 40-80% certainty. The std.dev. for the
6/49 game will be 32.8 and the std. normal table can be used to
select any desired range, since the data form a nearly perfect
Gaussian curve.
How many sums did you find outside the 100-199 range and were any
outside 82-243?
There is a second statistic abou the sums that has long intrigued me.
Each sum of six has a mean with its own std.dev. There seems to be
no known formula for predicting the mean std.dev. for each sumof any
lotto, but its value is likely to be around 13.5 for 6/49 with a range
from 6 to 21 based on data from Schneider.
If you have all 6/49 data on a spreadsheet perhaps you could also
calculate the std.dev. for the sum of each set of six and tell us
their mean, range and variance. Such data can then be used as an
additional filter. The smallest value will be 1.87 for the set
1-2-3-4-5-6 and all sets with six consequtive numbers, of which there
must be 43 sets, while the largest will be 25.21 for 1-2-3-47-48-49 of
wich there is only one set, and thus the distribution is not normal,
but close.
Note that the set 1-2-3-47-48-49 has a sum of 150 but the most extreme
std.dev. and the sets 22-23-24-25-26-27 and 23-24-25-26-27-28 have
sums clost to 150,( 147 and 153 resp), but the lowest std.dev. Thus
sum is not a sufficient filter, but needs to be supplemented with s.d.
Stig Holmquist |
|
| Back to top |
|
|
Nick UK
Guest
|
| Posted: Sun Apr 10, 2005 4:30 pm Post subject: Re: Reducing The Odds |
|
|
"erce" wote something that sounded like..
| Quote: |
if your confident your right stop spamming the newsgroup and sue the
guy
if your not confident stop spamming the newsgroup
erce
|
Neither of your two sentences (above) make grammatical sense. However, if I
put in the required commas and full stops, I think what you are trying to
say is this..
<If you're confident you are right, then stop spamming the newsgroup and sue
the guy.>
<If you're not confident, then stop spamming the newsgroup.>
If indeed that is what you are trying to say, then I suggest you..
(1) Explain 'confident' and in what context are you using the word?
(2) Before you accuse me of 'spamming' this ng, look up the word 'spam' and
learn what it is.
(3) Take a short course in elementary English before attempting to subscribe
to any newsgroup.
Nick. |
|
| Back to top |
|
|
John Griffin
Guest
|
| Posted: Sun Apr 10, 2005 4:55 pm Post subject: Re: Reducing The Odds |
|
|
Stig Holmquist <[email protected]> wrote:
| Quote: | On Sun, 10 Apr 2005 00:00:40 -0400, "IXL Software"
[email protected]> wrote:
...
Your discussion of the sum of six drawn numbers is of
particular
interest to me.
In his book "Lottery Numbers, Past, Present and Future" H.
Schneider also examined the sum and recommended the range
82-243 based on only 50 draws from each of two past 6/49
games. He clearly did not recognize that the range should be
symmetrical around the mean 150 in the long run.
Eight years ago I wrote an article in "Lotto World" (Apr.'97)
on p.40-43 about how to predict the std.dev. for the sum in
any lotto game and outlined ranges for 40-80% certainty. The
std.dev. for the 6/49 game will be 32.8 and the std. normal
table can be used to select any desired range, since the data
form a nearly perfect Gaussian curve.
How many sums did you find outside the 100-199 range and were
any outside 82-243?
There is a second statistic abou the sums that has long
intrigued me. Each sum of six has a mean with its own std.dev.
There seems to be no known formula for predicting the mean
std.dev. for each sumof any lotto, but its value is likely to
be around 13.5 for 6/49 with a range from 6 to 21 based on
data from Schneider. If you have all 6/49 data on a
spreadsheet perhaps you could also calculate the std.dev. for
the sum of each set of six and tell us their mean, range and
variance. Such data can then be used as an additional filter.
The smallest value will be 1.87 for the set 1-2-3-4-5-6 and
all sets with six consequtive numbers, of which there must be
43 sets, while the largest will be 25.21 for 1-2-3-47-48-49 of
wich there is only one set, and thus the distribution is not
normal, but close.
Note that the set 1-2-3-47-48-49 has a sum of 150 but the most
extreme std.dev. and the sets 22-23-24-25-26-27 and
23-24-25-26-27-28 have sums clost to 150,( 147 and 153 resp),
but the lowest std.dev. Thus sum is not a sufficient filter,
but needs to be supplemented with s.d.
Stig Holmquist
|
I'm gonna buy a "Quinto" ticket. What's the sum of 2 of clubs, 5
of clubs, 8 of diamonds, jack of hearts and king of hearts?
Wait...never mind...the sums idea is grossly silly. They draw
balls, not numbers. |
|
| Back to top |
|
|
IXL Software
Guest
|
| Posted: Sun Apr 10, 2005 4:55 pm Post subject: Re: Reducing The Odds |
|
|
"Dick Adams" <[email protected]> wrote in message
news:[email protected]...
| Quote: |
[Snipped since everyone has already read it]
If I understood you correctly, you are saying that buying more tickets
does not improve your odds of winning as well as buying more tickets
within the range of sums.
If that is correct, then what your position amounts to is "Buy more
tickets based on filters". I can not imagine disagreeing with that.
Dick - Still The Wizard of Odds and sometimes Taxes too
|
Oh! Is that what I said? Well I'll be dadburned.
Paul |
|
| Back to top |
|
|
IXL Software
Guest
|
| Posted: Sun Apr 10, 2005 5:00 pm Post subject: Re: Reducing The Odds |
|
|
"Colin Fairbrother" <[email protected]> wrote in message
news:[email protected]...
| Quote: | Mr IXL
You are not keeping abreast of developments. Colin has well and truly
kicked
the bejesuz out of Odds/Evens and good old Sums.
If you claim to espouse logic then you should be able to follow my charts:
http://www.lottoposter.com/forum_posts.asp?TID=143&PN=1
Run Filterologists
Run Filterologists
Run, Run, Run
Colin he will get you
One by one
You can't hide
It's time to tan your hide
Run Filterologists
Run Filterologists
Run
Colin
|
Huh!...and I'm the one that gets accused of arrogance. Sorry bud. I fail to
see what your chart proves about anything at all. The point is...?
| Quote: |
ps I thought the article you did on understanding Wheel jargon was pretty
good.
|
Thank you.
Paul |
|
| Back to top |
|
|
John Griffin
Guest
|
| Posted: Sun Apr 10, 2005 5:00 pm Post subject: Re: Reducing The Odds |
|
|
"IXL Software" <[email protected]> wrote:
| Quote: | It has often been said here and elsewhere that the only way to
improve or reduce the odds against a player winning a lottery
jackpot is to purchase more tickets (chances). Is that really
so?
|
Yes, it has often been said, and yes, it's clearly so.
| Quote: |
The reasoning goes something like this:
If I buy 1 ticket on a 649 lottery draw, that ticket has odds
of 13,983,816:1 of matching the jackpot numbers.
|
Against.
| Quote: | If I buy 10 tickets for the very same draw, my overall odds
now become 1,398,381.6:1. If I buy 1000 tickets for the very
same draw, my overall odds now become 13,983.816:1...and so
on.
This logic is essentially saying that I can have a 1,000%
improvement of the odds in my favour by covering only a very
tiny percentage (0.00715%) of the possible outcomes. Don't
those numbers look just a little out of whack...in fact
extremely disproportionate?
|
Yes--1000 times is 100000%. Other than that, no.
| Quote: | Consider this: it is entirely possible to purchase 13,983,815
different tickets and *still* not win the jackpot! You will of
course have a hell of a lot of smaller prizes...but not the
big one. Imagine the embarrassment.
|
You could write a book and do the talk show circuit.
| Quote: | Assuming that the minimum match of winning numbers must be at
least 3, it is theoretically possible to purchase 13,723,192
tickets and not win so much as a goddamn
penny! Incredible as it may seem, that's over 98% coverage of
all possible outcomes with nothing to show for it. I have no
idea of how one could go about purposely trying to win nothing
on such a large wager. In this case, losing everything seems
more daunting a task than winning anything. Strange game...is
it not?
|
No. That one possible outcome might seem "strange" and make a
good conversation piece, but its probability is well defined.
| Quote: | Do we begin to see how this "more tickets" logic breaks down
pretty rapidly?
|
If you "see" that, don't ever play the lottery.
| Quote: | This is why I believe that the common basic
assumption is incorrect. You simply
cannot use the aggregate total of chances to properly
calculate the overall odds. You end up with a distorted
picture that is out of phase with reality.
|
No. There are 13983816 possible outcomes (ignoring
permutations). If you have one ticket, there is exactly one good
outcome. If you have N, there are exactly N good ones. There is
no mystery.
| Quote: | I believe that the correct way to interpret the odds is to say
that each ticket in play has a *discrete and equal chance*. In
other words, if you play
1,000 tickets, you have 1,000 *separate (but equal)* chances
of 1 in 13,983,816 at the
jackpot...
|
True.
| Quote: | not an aggregate chance of 1 in 13,983.816.
|
Yes - it's an aggregate chance of 1000 in 13983816.
| Quote: | The difference in interpretations is subtle and difficult to
adequately describe but I'm hoping that at least a few people
out there can understand what I'm driving at. The implications
of one being true over the other are huge...if given but a
little thought...something that is generally conspicuous by
its absence around these parts.
|
Irony.
The difference is very simple to describe: None.
| Quote: | Note that using an analogy such as a mixture of red and blue
marbles in a jar would be inappropriate for the purpose of
counter-argument. That would be like comparing the
probabilities or odds between 2 similar but very different
card games such as Poker and Bridge...even though they both
use the exact same deck of 52 cards...or Chess and
Checkers...even though they both use the exact same playing
board and number of playing pieces.
|
There is no need for any analogy, because it's too simple. N
mutually exclusive 1/x probabilities add up to N/x. Every
freakin' time, euphemistically speaking.
| Quote: | TRUE REDUCTION OF ODDS
|
Uhoh...
| Quote: | ========================
The only way to truly reduce the player's odds is to reduce
the number of possible outcomes.
|
The only way to reduce the number of possible outcomes is to play
a different game.
| Quote: | The only way to accomplish
this is by artificial means that are commonly called
"guessing". That's why it's called a game of chance...or
gambling on an unknown outcome.
|
You were talking reality before, but now you've switched to
fantasy. Your guess does absolutely nothing to the machine or
its balls.
| Quote: | Does such a thing exist? The answer is conditionally Yes. Here
are a few examples:
We all enjoy a natural reduction of odds that is conditional
on a simple assumption. The assumption is that the exact same
6 winning numbers will not be randomly drawn within (or even
beyond) the period of a human lifetime at a rate of 2 draws
per week. In practical terms, this means that you can subtract
the number of actual results that have already been drawn from
the total of possible outcomes.
|
That was funny. I hope you were trying for comic relief. You
could add some amusement by trying to describe some magic which
transfers probability from one event to the others.
| Quote: | In the case of the Canadian
649 lottery, there will have been 2,214 draw results by the
time this is posted. Based on that assumption, this means
that the effective number of outcomes for draw 2,215 will be
13,981,602. Not a *big* reduction by any means...but a
reduction nonetheless for as long as the conditional
assumption remains true. To my mind at least, there is little
use in playing lines that have already been drawn.
|
True...exactly the same little use as playing any other. However,
if you play all 2214 of those past draws, your chance of hitting
the jackpot is precisely 2214/13983816--the same as you have with
any other 2214 lines.
| Quote: | Another example is the application of certain criteria that
will either accept or reject any combination of 6 numbers for
consideration as worthy lines to play. These criteria are most
often referred to as "filters".
|
"Filters" are for the hobbyist. The lottery gadget does not use
them in selecting numbers. They're worthless except for their
entertainment value, which is admittedly considerable to lots of
people.
| Quote: | One of the most basic filters is the *sum of the line*. This
sum ranges from a minimum of 21 to a maximum of 279. Once the
number of combinations for each of those sums is calculated,
it is easy to plot the results on a graph. The resulting graph
represents the classic "bell" curve that is the classic
statistician's bread & butter. In the case of a 649 lottery,
the sums peak at 150 with 165,772 lines that sum to that
total. The remaining sums fall off equally and perfectly
symmetrically on either side of that sum. This is not mere
coincidence. I have seen many subscribers here reject this
fact as either useless or meaningless. They are entitled to
that opinion, but I have never seen even *1* of those
proponents offer any clear evidence or mathematical proof to
support their belief. In stark contrast to that glaring
deficiency, I submit the following evidence in support of my
claim:
|
Here's the bare essential and irrefutable fact about the sums: If
you want to use one, you have to buy all of its combinations. The
fantasy in the minds of proponents of the sums foolishness is
that the sum is "the thing," and it attracts the draw
proportionally to its number of combinations. "Silly" is the
best word for any belief that a line adding to 150 is somehow
"better" than 44-45-46-47-48-49 or 1-2-3-4-5-6.
| Quote: | If a player simply restricts their played lines to a sum
between 100-199, this results in 12,169,389 lines that pass
the filter. This results in a nearly 13% reduction in eligible
lines and consequently a nearly 15% improvement of the odds in
the players' favour.
|
Bullshit. You can filter all the hell you want, but the machine
will even more mindlessly do its thing without regard to any of
that stuff.
| Quote: | Notice that this is very much a clearly
*positive* improvement over the concept of merely purchasing
more tickets as described above.
|
In your dreams.
| Quote: | Simple arithmetic shows that
about 87% of all the possible lines are covered.
Practical "real" results show that in the Canadian 649, 1,919
of 2,213 draws to date (86.71%) have had a sum that conforms
to this requirement. In fact, the last 18 consecutive draws
have produced results that conform to this requirement. For
the UK649, 842 of 969 draws to date (86.89%) have obeyed this
simple requirement. Up until the most recent draw, 26 previous
consecutive draws fell within the requirement. Would anyone
care to reject a 15% improvement of odds for somewhere between
8 or 9 out of every 10 draws? If so...why? Kindly describe
your reasoning with the same detail that I have attempted
here. The possibility always exists that I am totally
mistaken. I'll be the 1st to accept that possibility and will
gladly acknowledge any contrary opinion. Teach me something
that I don't already know...I beg of you. This place offers so
little intellectual stimulation other than the easily
predictable and inevitable ego conflicts that prevail here.
|
The sums of the results will fit that normal curve you mentioned.
That information is of no value, since it has nothing to do with
any individual result.
| Quote: | I have further examples to offer, but I'll see what the
reaction is before saying anything further. Is it wrong to
identify such a strong correlation between the theoretical and
the actual? I invite anyone to show proof that my line of
reasoning is faulty for whatever reason. Keep it clean and try
to stick to facts rather than personality.
Would you rather read material of this kind or the kind of
garbage that small minds produce when they actually have
nothing at all to say that will benefit anyone other than
their own perverse needs? In the end, you get the kind of
group that you both make and deserve.
|
That was pretty funny. "Keep it objective and impersonal, you
assholes." Okay, it pains me, but I'll try to be polite: You
aren't goofy--only your delusions are.
Suppose 13983816 people have applied all the "filters," chosen
their sets of "likely" numbers and eliminated their ideas of
"unlikely" numbers or whatever and have all thereby "reduced
their odds" and no two have chosen the same six numbers. The
probability that one of them will win is greater than 1.00,
according to the "reduced your odds" misconceptions. |
|
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