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Math Help - [SOLVED] Quick, Simple Question

  1. #1
    statsgirl
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    [SOLVED] Quick, Simple Question

    If you play the same set of numbers in the lottery, say 1 1 1 1 for example, every day over the course of a year, are your chances any better to win than if you play a different or random number every day over the course of a year?


    Some people have told me that it makes sense that, if you play the same number (e.g. 1 1 1 1), you'll be "due" to win eventually. Others, and I myself, believe that you have the same chance in either circumstance.



    Thanks,
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    Grand Panjandrum
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    Quote Originally Posted by statsgirl View Post
    If you play the same set of numbers in the lottery, say 1 1 1 1 for example, every day over the course of a year, are your chances any better to win than if you play a different or random number every day over the course of a year?


    Some people have told me that it makes sense that, if you play the same number (e.g. 1 1 1 1), you'll be "due" to win eventually. Others, and I myself, believe that you have the same chance in either circumstance.



    Thanks,
    If the lottery is run properly it makes no difference to your chance of winning
    if you use the same numbers every time as opposed to changing them. Every
    set of numbers should have an equal chance of winning and the winning
    combination should be be independent from play be play.

    Now if all the other players are changing their numbers to avoid recent wins
    of chasing "hot" numbers or combinations it may be worth considering
    avoiding the popular combinations to maximise your win (by sharing it with
    the fewer other players).

    RonL
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    Quote Originally Posted by statsgirl View Post
    If you play the same set of numbers in the lottery, say 1 1 1 1 for example, every day over the course of a year, are your chances any better to win than if you play a different or random number every day over the course of a year?

    Some people have told me that it makes sense that, if you play the same number (e.g. 1 1 1 1), you'll be "due" to win eventually. Others, and I myself, believe that you have the same chance in either circumstance.

    Thanks,
    the people who say that 1,1,1,1 is less likely to come out are correct to a certain extent if they are working on the basis that it is less likely for an easily recognisable pattern to appear - as opposed to a seemingly random set of numbers.

    While it is true that the numbers 1,1,1,1 and 1,2,3,4 have equal chance of coming out (assuming that there are four [1] balls of course ), there are ways of 'proving' that these are less likely to appear. Instead of looking at the individual numbers, step back and take in the wider picture.

    If you compare how many patterns like this there are that you can recognise to the number of patterns you do not recognise, you will see that the latter is in the majority.


    Another way of looking at is to hypothesise about the numerical difference between each ball:
    For example, "It is less likely that the difference between each ball will be [1/2/3/4/5 etc]" which, of course, is true (I'm not going to provide proofs, unless I get REALLY bored)..

    In other words, you are less likely to win if you use a sequence of numbers like 1,2,3,4; 2,4,6,8; or even 1,2,3,6 (fibonacci sequence if im not mistaken) because the 'steps' between them are all equal or are in some form of set pattern.

    Statistically speaking, very few 6-digit number combinations follow a pattern of some shape or form - you only need to look at the past lottery results to see this.


    Does that make sense?
    In plain English, there are more 'random' sequences of numbers than there are 'patterns' of numbers. Therefore, theoretically speaking, you are more likely to find a seemingly random pattern of numbers.. true?


    My apologies if this appears to be nonsense babbling (its 6.10am and i havent had any sleep lol)
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    Grand Panjandrum
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    Quote Originally Posted by kwah View Post
    Does that make sense?
    In plain English, there are more 'random' sequences of numbers than there are 'patterns' of numbers. Therefore, theoretically speaking, you are more likely to find a seemingly random pattern of numbers.. true?


    My apologies if this appears to be nonsense babbling (its 6.10am and i havent had any sleep lol)
    Its not "nonsense babbling" it's just plain wrong.

    RonL
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    maybe you mis-understood my badly written explanation.

    I'm not disputing the fact that 1,2,3,4,5,6 has the same theoretical chance of appearing as 4,2,9,1,5,7 -- I am looking at the patterns.

    What I was trying to say is that the chance of randomly selecting a series of numbers that a regular person would recognise as a pattern is slimmer than the chances of selecting a series of numbers that we don't recognise.
    eg, the numbers increasing by (un)equal steps (1,2,3,4,5,6) (21,24,27,30,33,36) (1,2,13,14,25,26) in a pattern of some sort.


    I havent checked them myself, but I'm so confident that you will not be able to identify any patterns that a regular lottery player would notice, I'm willing to give $100 to anybody that finds one in the UK National Lottery results found Draw History | The National Lottery
    That lists the last 48 draws, but you can download a full history currently listing 1222 draws dating back almost 13 years from the Lotto Draw History .


    My point is that I HIGHLY DOUBT that it has ever happened.

    Feel free to show me proof / strong evidence otherwise, and I'll graciously retract everything I've said so far - but until then..
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    Quote Originally Posted by kwah View Post
    maybe you mis-understood my badly written explanation.

    I'm not disputing the fact that 1,2,3,4,5,6 has the same theoretical chance of appearing as 4,2,9,1,5,7 -- I am looking at the patterns.

    What I was trying to say is that the chance of randomly selecting a series of numbers that a regular person would recognise as a pattern is slimmer than the chances of selecting a series of numbers that we don't recognise.
    eg, the numbers increasing by (un)equal steps (1,2,3,4,5,6) (21,24,27,30,33,36) (1,2,13,14,25,26) in a pattern of some sort.


    I havent checked them myself, but I'm so confident that you will not be able to identify any patterns that a regular lottery player would notice, I'm willing to give $100 to anybody that finds one in the UK National Lottery results found Draw History | The National Lottery
    That lists the last 48 draws, but you can download a full history currently listing 1222 draws dating back almost 13 years from the Lotto Draw History .


    My point is that I HIGHLY DOUBT that it has ever happened.

    Feel free to show me proof / strong evidence otherwise, and I'll graciously retract everything I've said so far - but until then..
    In a lottery where 6 numbers are selected at random without replacement from
    1 to 49 the probability of 1,2,3,4,5,6 is exactly the same as 9, 14, 23, 33, 32, 47.

    RonL
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    Jeez ... I'm merely trying to state that when people say that 1,2,3,4,5,6 (or similar pattern is less likely to appear than any other combination because they are mistakenly working from the probability of a recognisable pattern Vs. a seemingly random number.

    This is as opposed to the true probability which you keep referring to - In a lottery where 6 numbers are selected at random without replacement from
    1 to 49 the probability of 1,2,3,4,5,6 is exactly the same as 9, 14, 23, 33, 32, 47.


    Do you understand now?! If not, I give up ..
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    Quote Originally Posted by kwah View Post
    Jeez ... I'm merely trying to state that when people say that 1,2,3,4,5,6 (or similar pattern is less likely to appear than any other combination because they are mistakenly working from the probability of a recognisable pattern Vs. a seemingly random number.

    This is as opposed to the true probability which you keep referring to - In a lottery where 6 numbers are selected at random without replacement from
    1 to 49 the probability of 1,2,3,4,5,6 is exactly the same as 9, 14, 23, 33, 32, 47.


    Do you understand now?! If not, I give up ..
    I'm afraid I agree with CaptainBlack. Even if your point is that there are fewer six digit patterns than there are "random combinations" I have to disagree. With a bit of time and creativity I'll bet you can come up with a pattern for any combination of numbers. So they're all patterns.

    -Dan
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    Quote Originally Posted by topsquark View Post
    I'm afraid I agree with CaptainBlack. Even if your point is that there are fewer six digit patterns than there are "random combinations" I have to disagree. With a bit of time and creativity I'll bet you can come up with a pattern for any combination of numbers. So they're all patterns.

    -Dan
    hence, the reason why I said, and I quote:
    you will not be able to identify any patterns that a regular lottery player would notice
    note that I said a REGULAR lottery player - including people who may not even know know what algebra is, but can spot the pattern 2,4,6,8,10 and/or relative's birthdays or their bank sort code for example

    also note the use of "notice" - ie, NOT "be able to look for and find"
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    Grand Panjandrum
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    Quote Originally Posted by kwah View Post
    hence, the reason why I said, and I quote:


    note that I said a REGULAR lottery player - including people who may not even know know what algebra is, but can spot the pattern 2,4,6,8,10 and/or relative's birthdays or their bank sort code for example

    also note the use of "notice" - ie, NOT "be able to look for and find"
    And yet on 24th of June 1990 "22 27 32 37 42 47" would have won you a
    share of the lottery first prize. In case you can't see it, the numbers are
    arithmetic progression.

    RonL
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    i can see that you're not going to listen to me, but if the lotto on 24th of June 1990 was the last time a pattern like this occured (no mention of which lotto it was? but it isnt on that list i posted - that official national lotto UK document only goes back to 1994), then that is maybe an experimental probability of 1/2500 of getting a noticeable pattern (approximately, and not including the many thousands of lottos worldwide)?

    is this not evidence enough? one example from the past 17 years? undoubtedly there are MANY MANY more examples, but feel free to prove me wrong in what ive said before ...

    ie, in 3000 draws, there are >1500 that match some form of arithmetic progression with common intervals between the numbers?
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    Quote Originally Posted by kwah View Post
    i can see that you're not going to listen to me, but if the lotto on 24th of June 1990 was the last time a pattern like this occured (no mention of which lotto it was? but it isnt on that list i posted - that official national lotto UK document only goes back to 1994), then that is maybe an experimental probability of 1/2500 of getting a noticeable pattern (approximately, and not including the many thousands of lottos worldwide)?

    is this not evidence enough? one example from the past 17 years? undoubtedly there are MANY MANY more examples, but feel free to prove me wrong in what ive said before ...

    ie, in 3000 draws, there are >1500 that match some form of arithmetic progression with common intervals between the numbers?
    The probability for getting any set of six particular numbers is the same as for getting any other set, given a fair set of trials.

    Now if you have some specific pattern of numbers you are looking for, say something like
    k, k + 1, k + 2, etc.
    it may well be that all sets of numbers with this pattern has a better chance of being chosen than not. But the chances of getting a specific result like 1, 2, 3, 4, 5, 6 is the same chance of getting any other specific set.

    Is this what you are talking about?

    -Dan
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    Quote Originally Posted by topsquark View Post
    The probability for getting any set of six particular numbers is the same as for getting any other set, given a fair set of trials.

    Now if you have some specific pattern of numbers you are looking for, say something like
    k, k + 1, k + 2, etc.
    it may well be that all sets of numbers with this pattern has a better chance of being chosen than not. But the chances of getting a specific result like 1, 2, 3, 4, 5, 6 is the same chance of getting any other specific set.

    Is this what you are talking about?

    -Dan
    fair enough, my inability to explain myself very well didnt help but finally somebody understands ...

    yes that is what i was talking about when i repeatedly stated that i was speaking about the probability of a pattern occuring, though I (mistakenly?) omitted an algebraic example in fear that it would be mis-interpreted to mean that i mean that specific pattern ..

    but i guess that backfired and just resulted in my frustration and your degraded opinions of me ..
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