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What are the odds of winning the lotto twice?

1…34689…16

Comments

  • #152
    keane2097
    Registered Users, Registered Users 2, Paid Member Posts: 17,905 ✭✭✭✭keane2097


    maw wrote: »
    because it illustrates the point perfectly

    But it has nothing at all to do with the lottery.

    As I said to someone earlier on the thread, if your method of arguing your point involves changing every element of the initial experiment, then using whatever result your tailored experiment yields as proof then grand.

    I certainly won't be changing my opinion based on such specious reasoning.


  • #153
    keane2097
    Registered Users, Registered Users 2, Paid Member Posts: 17,905 ✭✭✭✭keane2097


    Cool Mo D wrote: »
    Simple probability.

    There are 45 numbers, and 6 are drawn.

    Therefore there is a 39 in 45 chance that a particular number will not be drawn at any draw. For a number not be drawn once in 100 consecutive draws, that means the odds are 7 in a million. That means, with 2 weekly draws, you would need to watch every draw for over 100 thousand years to have a good chance of seeing a ball not come up 100 times in a row.

    EDIT: Apologies, mistaken identity.


  • #154
    witnessmenow
    Registered Users, Registered Users 2 Posts: 7,584 ✭✭✭witnessmenow


    Its all about the wording.

    Lets take for example the coin example

    "What are the odds of getting the same side twice in two tosses?"

    Flip first coin - we dont care about the outcome. It's either going to be heads or tails so the odds are 1/1

    Flip second coin - after the first coin toss we need this to a specific side so it matches the first one. there is a 1 in 2 chance of this happening

    Overall: 1/2

    "What are the odds of getting tails twice in two coin tosses"

    Flip first coin - it needs to be tails 1/2 of this happening

    flip second coin - it needs to be tails 1/2 of this happening

    Overall: 1/4

    Back to the lotto:

    "The odds of you going picking numbers to play the lotto with and them coming up twice"

    to come up the first time: 8145060 to 1

    to come up the second time: 8145060 to 1

    Total : 66342002403600 to 1

    "The odds of someone who has already won the lotto's numbers coming up again"

    They just have a set of numbers like everyone else, the fact that these numbers have already won the lotto is irrelevant, their odds are the same as anybody elses - 8145060 to 1


  • #155
    maw
    Registered Users, Registered Users 2 Posts: 51 ✭✭maw


    Cool Mo D wrote: »
    Simple probability.

    There are 45 numbers, and 6 are drawn.

    Therefore there is a 39 in 45 chance that a particular number will not be drawn at any draw. For a number not be drawn once in 100 consecutive draws, that means the odds are 7 in a million. That means, with 2 weekly draws, you would need to watch every draw for over 100 thousand years to have a good chance of seeing a ball not come up 100 times in a row.


    i see your point, but its not exactly correct. 39/45 only applies to the first ball, for the second its 38/44, 3rd 37/43 etc etc


  • #156
    28064212
    Registered Users, Registered Users 2 Posts: 11,155 ✭✭✭✭28064212


    keane2097 wrote: »
    Sorry, you're the Wiki liar from earlier in the week right? You're on my ignore list.
    Something else you were wrong about, I'm the supposed "wiki liar", not Cool Mo D.

    Apparently I'm on ignore, but I hope anyone else considering his system can see the reason that he can't answer this question:
    28064212 wrote: »
    For simplicity's sake, I'm reducing a draw to picking out one ball from a drum of balls numbered 1 to 7:
    • Before Week 1: What are the odds of number 1 not coming out 100 times in a row? Answer: 1 / (7^100), so incredibly small
    • After Week 99: Number 1 hasn't come out in the previous 99 weeks. This is a known fact. What are the odds of number 1 coming out in draw 100?

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  • #157
    maw
    Registered Users, Registered Users 2 Posts: 51 ✭✭maw


    keane2097 wrote: »
    No, I'm saying that the longer a number hasn't landed on in roulette, the more likely it is to come out in subsequent spins.

    this is specious reasoning. There is no MEMORY in probability.

    each turn of the roulette wheel is NOT influenced by any previous turns (my coin example) it's the same odds every time. The fact it never happens (100 of turns without #8 coming up) is simply the fact that the number has a much better probability of actually coming up than not for 100 times:

    eg 30 numbers on a roulette wheel:

    not coming up 100 times = 29/30 x 29/30 x 29/30 ....times 100 = 0.017 or 1/59

    coming up once = 1/30



    My problem with your arguement is that your are purporting to say that the reason it comes up is because of what happened in the past, this is utter nonsense


  • #158
    Jesus Wept
    Registered Users, Registered Users 2 Posts: 25,243 ✭✭✭✭Jesus Wept


    It's easier if you focus on the main draw and ignore the bonus balls.


  • #159
    keane2097
    Registered Users, Registered Users 2, Paid Member Posts: 17,905 ✭✭✭✭keane2097


    28064212 wrote: »
    Something else you were wrong about, I'm the supposed "wiki liar", not Cool Mo D.

    Apparently I'm on ignore, but I hope anyone else considering his system can see the reason that he can't answer this question:

    You're problem is you're reducing the question down to the probability of a single-event, when we're talking about the probabilty of a string of events.

    Do try to keep up.


  • #160
    28064212
    Registered Users, Registered Users 2 Posts: 11,155 ✭✭✭✭28064212


    keane2097 wrote: »
    You're problem is you're reducing the question down to the probability of a single-event, when we're talking about the probabilty of a string of events.

    Do try to keep up.
    You still haven't answered the question

    Take a row of 100 draws. At no point are any of the draws influenced by what went before. If the number 4 doesn't come up for the first 20 draws, at draw 20, it has the same probablility as coming out as any other number

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  • #161
    Iwannahurl
    Closed Accounts Posts: 8,156 ✭✭✭Iwannahurl


    robbie7730 wrote: »
    Well it is the odds squared for 2 single plays, but they go down the more you play.

    Someone that has already won it will have the same chance of now winning it a second time as anyone else has of winning it the first time for each play, so once you win once, your odds of winning it 2 times are now better than the odds of someone who never won it having 2 wins.



    That was not the question posed by the OP, IMO.

    There must be a correlation between the imprecision of an OP, the number of people misinterpreting the OP's question (and each other), and the length of a thread!


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  • #162
    maw
    Registered Users, Registered Users 2 Posts: 51 ✭✭maw


    Originally Posted by 28064212 viewpost.gif
    For simplicity's sake, I'm reducing a draw to picking out one ball from a drum of balls numbered 1 to 7:

    • Before Week 1: What are the odds of number 1 not coming out 100 times in a row? Answer: 1 / (7^100), so incredibly small
    • After Week 99: Number 1 hasn't come out in the previous 99 weeks. This is a known fact. What are the odds of number 1 coming out in draw 100?

    Question 1:
    WRONG - odds of 1 not coming out is 6/7 not 1/7

    so its 6/7 x 6/7....100 times = 0.0000002

    answer 1 in 5 million (probability of 99 events happening in sequence)


    Question 2:

    1/7 (previous 99 have nothing to do with it!)


  • #163
    keane2097
    Registered Users, Registered Users 2, Paid Member Posts: 17,905 ✭✭✭✭keane2097


    28064212 wrote: »
    You still haven't answered the question

    Take a row of 100 draws. At no point are any of the draws influenced by what went before. If the number 4 doesn't come up for the first 20 draws, at draw 20, it has the same probablility as coming out as any other number

    Yes, but the likelihood of a four being drawn is increasing draw by draw.


  • #164
    28064212
    Registered Users, Registered Users 2 Posts: 11,155 ✭✭✭✭28064212


    maw wrote: »
    WRONG - odds of 1 not coming out is 6/7 not 1/7

    so its 6/7 x 6/7....100 times = 0.0000002

    answer 1 in 5 million (probability of 99 events happening in sequence)
    Oops, yeah, 6/7, not 1/7. Doesn't change the point I made though

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  • #165
    28064212
    Registered Users, Registered Users 2 Posts: 11,155 ✭✭✭✭28064212


    keane2097 wrote: »
    Yes, but the likelihood of a four being drawn is increasing draw by draw.
    No, it's not. That's a perfect example of Gambler's Fallacy (apt title).

    Also, likelihood and probablility are synonyms. They mean exactly the same thing. How can the likelihood be increasing if it has an exactly 1 in 7 chance of being drawn?

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  • #166
    maw
    Registered Users, Registered Users 2 Posts: 51 ✭✭maw


    keane2097 wrote: »
    Yes, but the likelihood of a four being drawn is increasing draw by draw.

    you are phrasing your question incorrectly

    the probability of getting a 4 is the same for every draw (1/7)

    the probability of getting 100 in a row with no 4s reduces from 1/5Mil after every non-4 draw is made - eventually reducing to 6/7 at the 100th draw

    these are two seperate things folks (but you are suggesting the 1/7 probability is affected by what is happening in the 100 draws)


  • #167
    Pherekydes
    Registered Users, Registered Users 2, Paid Member Posts: 16,339 ✭✭✭✭Pherekydes


    maw wrote: »
    i see your point, but its not exactly correct. 39/45 only applies to the first ball, for the second its 38/44, 3rd 37/43 etc etc

    Surely it's 44/45 for the first ball, 43/44 for the second and so on?

    Getting the product, we are left with 39/45 (all the other numbers cancel).


  • #168
    keane2097
    Registered Users, Registered Users 2, Paid Member Posts: 17,905 ✭✭✭✭keane2097


    28064212 wrote: »
    No, it's not. That's a perfect example of Gambler's Fallacy (apt title).

    Also, likelihood and probablility are synonyms. They mean exactly the same thing. How can the likelihood be increasing if it has an exactly 1 in 7 chance of being drawn?

    I know what Gambler's Fallacy is, I'm in this game a long time.

    Mathematical odds don't change but the 'chance' does.

    This is not the same as Michael Owen being first goalscorer three matches in a row and then giving 30/1 on him doing it a 4th time, as that would not be a random event, where the law of large numbers play a role.

    You take any random event that has 22 random possibilities and one of those possibilities comes out 3 times running and allthough the mathematical odds of that possibility remain the same, the chance of it does not.

    It doesn't mean that it won't happen, but the chances are very very slim and no where near a 21/1 shot, which is all that it will be based on mathematics.


  • #169
    Pherekydes
    Registered Users, Registered Users 2, Paid Member Posts: 16,339 ✭✭✭✭Pherekydes


    keane2097 wrote: »
    Mathematical odds don't change but the 'chance' does.

    The "odds" of an event is [latex]\frac{p}{1-p}[/latex] , where p is the probability. That's the mathematical definition.

    Chance and probability are the same.


  • #170
    28064212
    Registered Users, Registered Users 2 Posts: 11,155 ✭✭✭✭28064212


    keane2097 wrote: »
    I know what Gambler's Fallacy is, I'm in this game a long time.
    And yet you're arguing for something which is a direct contradiction of it
    keane2097 wrote: »
    Mathematical odds don't change but the 'chance' does.
    Back to a coin flip. 10 heads happen in a row. What are the mathematical odds that tails is next. What is the 'chance' that tails is next?

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  • #171
    keane2097
    Registered Users, Registered Users 2, Paid Member Posts: 17,905 ✭✭✭✭keane2097


    28064212 wrote: »
    And yet you're arguing for something which is a direct contradiction of it


    Back to a coin flip. 10 heads happen in a row. What are the mathematical odds that tails is next. What is the 'chance' that tails is next?

    I've told you, changing the experiment to a different experiment is no way to prove anything about the initial experiment.


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  • #172
    keane2097
    Registered Users, Registered Users 2, Paid Member Posts: 17,905 ✭✭✭✭keane2097


    Pherekydes wrote: »
    The "odds" of an event is [latex]\frac{p}{1-p}[/latex] , where p is the probability. That's the mathematical definition.

    Chance and probability are the same.

    Not exactly.


  • #173
    28064212
    Registered Users, Registered Users 2 Posts: 11,155 ✭✭✭✭28064212


    keane2097 wrote: »
    I've told you, changing the experiment to a different experiment is no way to prove anything about the initial experiment.
    It's to find out whether you understand the principles involved. And once again, you haven't answered the question.

    But if you insist on using coloured balls in a drum: 10 draws in a row, number 4 hasn't come out. What are the mathematical odds that 4 comes out in the next draw? What is the 'chance' that 4 comes out in the next draw?

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  • #174
    keane2097
    Registered Users, Registered Users 2, Paid Member Posts: 17,905 ✭✭✭✭keane2097


    28064212 wrote: »
    It's to find out whether you understand the principles involved. And once again, you haven't answered the question.

    But if you insist on using coloured balls in a drum: 10 draws in a row, number 4 hasn't come out. What are the mathematical odds that 4 comes out in the next draw? What is the 'chance' that 4 comes out in the next draw?

    On any individual draw the mathematical odds are the same.

    Over a series of draws the non-mathematical possibility/likelihood changes.


  • #175
    28064212
    Registered Users, Registered Users 2 Posts: 11,155 ✭✭✭✭28064212


    keane2097 wrote: »
    On any individual draw the mathematical odds are the same.
    And the 'chance'?
    keane2097 wrote: »
    Over a series of draws the non-mathematical possibility/likelihood changes.
    Very well, even though once again, you didn't answer the question: 10 draws in a row, number 4 hasn't come out. What are the mathematical odds that 4 comes out in the next 10 draws? What is the 'chance' that 4 comes out in the next 10 draws?

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  • #176
    kc66
    Registered Users, Registered Users 2 Posts: 2,272 ✭✭✭kc66


    A guy that lives just outside Dundalk won the lotto, he won again as part of a syndicate, and a few weeks ago he won the Monday millions.


  • #177
    Pherekydes
    Registered Users, Registered Users 2, Paid Member Posts: 16,339 ✭✭✭✭Pherekydes


    keane2097 wrote: »
    Not exactly.

    Ah come on, I'm dying to know what the difference is.

    It's ok, you needn't answer, as I've concluded you've never formally studied probability. Except maybe for the LC.


  • #178
    keane2097
    Registered Users, Registered Users 2, Paid Member Posts: 17,905 ✭✭✭✭keane2097


    28064212 wrote: »
    And the 'chance'?


    Very well, even though once again, you didn't answer the question: 10 draws in a row, number 4 hasn't come out. What are the mathematical odds that 4 comes out in the next 10 draws? What is the 'chance' that 4 comes out in the next 10 draws?

    How do you expect me to quantify something I've already defined as "non-mathematical"?


  • #179
    keane2097
    Registered Users, Registered Users 2, Paid Member Posts: 17,905 ✭✭✭✭keane2097


    Pherekydes wrote: »
    Ah come on, I'm dying to know what the difference is.

    It's ok, you needn't answer, as I've concluded you've never formally studied probability. Except maybe for the LC.

    Tell me, if statistics and probabilty are solved areas of mathematics, why do have people still employed in research in those areas?


  • #180
    Jesus Wept
    Registered Users, Registered Users 2 Posts: 25,243 ✭✭✭✭Jesus Wept


    kc66 wrote: »
    A guy that lives just outside Dundalk won the lotto, he won again as part of a syndicate, and a few weeks ago he won the Monday millions.

    Exactly.


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  • #181
    28064212
    Registered Users, Registered Users 2 Posts: 11,155 ✭✭✭✭28064212


    keane2097 wrote: »
    How do you expect me to quantify something I've already defined as "non-mathematical"?
    This should be good. What realm those it fall into so?

    And just so we're clear (since you didn't answer the question again), you agree with this statement: The mathematical odds that 4 comes out in the next 10 draws are exactly equal to any other number, regardless of how long its been since 4 last came out

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