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Powerball Power Play Number Almost Always 2 ?

Topic closed. 73 replies. Last post 3 years ago by JADELottery.

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The Quantum Master
West Concord, MN
United States
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December 7, 2001
3675 Posts
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Posted: April 15, 2014, 8:09 pm - IP Logged

Chi-squared analysis. It's the same exact test used by lottery auditors, whose sole purpose, by the way, is to determine if the drawings are rigged/biased.

http://en.wikipedia.org/wiki/Chi-squared_test

http://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test

There are also other tests for smaller samples, i.e. auditing when a game has just been launched.

Χ2 ah, yes.

test, hmm, good.

within the test, what are you using as an expected frequency?

or better yet, how are you deriving the expected frequency?

observations we have, it's that pesky expectedness we like to see.

Red Eyes

Presented 'AS IS' and for Entertainment Purposes Only.
Any gain or loss is your responsibility.
Use at your own risk.

Order is a Subset of Chaos
Knowledge is Beyond Belief
Wisdom is Not Censored
Douglas Paul Smallish
Jehocifer

    LottoMetro's avatar - Lottery-024.jpg
    Happyland
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    Posted: April 15, 2014, 8:54 pm - IP Logged

    Χ2 ah, yes.

    test, hmm, good.

    within the test, what are you using as an expected frequency?

    or better yet, how are you deriving the expected frequency?

    observations we have, it's that pesky expectedness we like to see.

    Red Eyes

    Since PowerPlay is only 1 digit it's pretty simple: the expected frequency is derived from the proportion of digits that are theoretically supposed to come up. For the case of x2, the odds are 1 in 2. This means the expected frequency is 50% of drawings. For x3, the expected frequency is about 30% of drawings.

    For x2

    24 drawings = 12 expected

    26 drawings = 13 expected

    For x3

    24 drawings = 7.21 expected

    26 drawings = 7.81 expected

    etc.

    Obviously, 7.21 exact appearances is impossible, but that doesn't matter. It's just the expected theoretical frequency. When you do the chi-squared test it basically just compares the observed frequency versus the 'expected' frequency discussed above. You calculate a p-value for the x2 statistic and check it against significance values (i.e. 0.05, 0.10). Anything outside these levels indicates that there is insufficient evidence for a bias; on the other hand, if you see values within these levels, there's a pretty good chance you've got a biased drawing on your hands.

    If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
    If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

    2016: -48.28% (13 tickets) ||
    P&L % = Total Win($)/Total Wager($) - 1

      JADELottery's avatar - MeAtWork 03.PNG
      The Quantum Master
      West Concord, MN
      United States
      Member #21
      December 7, 2001
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      Posted: April 15, 2014, 9:00 pm - IP Logged

      Since PowerPlay is only 1 digit it's pretty simple: the expected frequency is derived from the proportion of digits that are theoretically supposed to come up. For the case of x2, the odds are 1 in 2. This means the expected frequency is 50% of drawings. For x3, the expected frequency is about 30% of drawings.

      For x2

      24 drawings = 12 expected

      26 drawings = 13 expected

      For x3

      24 drawings = 7.21 expected

      26 drawings = 7.81 expected

      etc.

      Obviously, 7.21 exact appearances is impossible, but that doesn't matter. It's just the expected theoretical frequency. When you do the chi-squared test it basically just compares the observed frequency versus the 'expected' frequency discussed above. You calculate a p-value for the x2 statistic and check it against significance values (i.e. 0.05, 0.10). Anything outside these levels indicates that there is insufficient evidence for a bias; on the other hand, if you see values within these levels, there's a pretty good chance you've got a biased drawing on your hands.

      You're sure you want to go with those values?

      We see a problem.

      Presented 'AS IS' and for Entertainment Purposes Only.
      Any gain or loss is your responsibility.
      Use at your own risk.

      Order is a Subset of Chaos
      Knowledge is Beyond Belief
      Wisdom is Not Censored
      Douglas Paul Smallish
      Jehocifer

        LottoMetro's avatar - Lottery-024.jpg
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        Posted: April 15, 2014, 9:04 pm - IP Logged

        You're sure you want to go with those values?

        We see a problem.

        There are 10 total "virtual" PowerPlay balls:

        • 1 for 5X
        • 1 for 4X
        • 3 for 3X
        • 5 for 2X

        5X = 1/10 = 10%

        4X = 1/10 = 10%

        3X = 3/10 = 30%

        2X = 5/10 = 50%

        Total 100%

        Aside from the simple method, using percentages above, you can use the Ei = N/n like so: E(2X) = 24 (drawings) * 5 (x2 balls) / 10 (total balls) =  12

        Calculating chi for 2X where observed = 16 and expected = 12:

        x2 = (16-12)2/12 = 1.3333

        p-value is essentially 1, Excel says 0.9982

        Other chi results:

        • x2 = 0.0667 for 5X
        • x2 = 0.0667 for 4X
        • x2 = 1.4222 for 3X

        Naturally, none of which are significant.

        If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
        If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

        2016: -48.28% (13 tickets) ||
        P&L % = Total Win($)/Total Wager($) - 1

          JADELottery's avatar - MeAtWork 03.PNG
          The Quantum Master
          West Concord, MN
          United States
          Member #21
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          Posted: April 15, 2014, 10:15 pm - IP Logged

          There are 10 total "virtual" PowerPlay balls:

          • 1 for 5X
          • 1 for 4X
          • 3 for 3X
          • 5 for 2X

          5X = 1/10 = 10%

          4X = 1/10 = 10%

          3X = 3/10 = 30%

          2X = 5/10 = 50%

          Total 100%

          Aside from the simple method, using percentages above, you can use the Ei = N/n like so: E(2X) = 24 (drawings) * 5 (x2 balls) / 10 (total balls) =  12

          Calculating chi for 2X where observed = 16 and expected = 12:

          x2 = (16-12)2/12 = 1.3333

          p-value is essentially 1, Excel says 0.9982

          Other chi results:

          • x2 = 0.0667 for 5X
          • x2 = 0.0667 for 4X
          • x2 = 1.4222 for 3X

          Naturally, none of which are significant.

          Hmm.

          Hmm, hmm.

          Hmm, hmm, hmm.

          Yes.

          Presented 'AS IS' and for Entertainment Purposes Only.
          Any gain or loss is your responsibility.
          Use at your own risk.

          Order is a Subset of Chaos
          Knowledge is Beyond Belief
          Wisdom is Not Censored
          Douglas Paul Smallish
          Jehocifer

            JADELottery's avatar - MeAtWork 03.PNG
            The Quantum Master
            West Concord, MN
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            Posted: April 16, 2014, 6:07 am - IP Logged

            However, we see a problem.

            We'll get back in a bit.

            Presented 'AS IS' and for Entertainment Purposes Only.
            Any gain or loss is your responsibility.
            Use at your own risk.

            Order is a Subset of Chaos
            Knowledge is Beyond Belief
            Wisdom is Not Censored
            Douglas Paul Smallish
            Jehocifer

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              Posted: April 16, 2014, 11:21 am - IP Logged

              Winning the lottery is a numbers game. Buy more lottery tickets per drawing to increase your chances of winning instead of playing Powerplay.

              US Flag

              PLAY THE LOTTERY SOMEDAY-IT IS OKAY TO DREAM!

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                Posted: April 16, 2014, 12:10 pm - IP Logged

                Been all pi$$ed off about the PB not having a multiplier for 2nd prize, and the stupid 2x multiplier which makes absolutely no sense. When I think about it, I get all-pi$$ed-off again, so I quit thinking about it. Now I'm all pi$$ed off again.

                Time to take a break from playing the lottery? You can still buy 1 Powerplay ticket monthly or yearly.

                US Flag

                PLAY THE LOTTERY SOMEDAY-IT IS OKAY TO DREAM!

                  JADELottery's avatar - MeAtWork 03.PNG
                  The Quantum Master
                  West Concord, MN
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                  Posted: April 19, 2014, 1:32 pm - IP Logged

                  However, we see a problem.

                  We'll get back in a bit.

                  we're working on it.

                  we just had a very intense work week.

                  just another $X,000.00 take home pay check.

                  the X you'll have to guess.

                  Red Eyes

                  Presented 'AS IS' and for Entertainment Purposes Only.
                  Any gain or loss is your responsibility.
                  Use at your own risk.

                  Order is a Subset of Chaos
                  Knowledge is Beyond Belief
                  Wisdom is Not Censored
                  Douglas Paul Smallish
                  Jehocifer

                    CARBOB's avatar - FL LOTTERY_LOGO.png
                    ORLANDO, FLORIDA
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                    Posted: April 19, 2014, 1:36 pm - IP Logged

                    we're working on it.

                    we just had a very intense work week.

                    just another $X,000.00 take home pay check.

                    the X you'll have to guess.

                    Red Eyes

                    x=10

                      JADELottery's avatar - MeAtWork 03.PNG
                      The Quantum Master
                      West Concord, MN
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                      Posted: April 19, 2014, 1:44 pm - IP Logged

                      x=10

                      No, but good guess.

                      We're not quite that greedy.

                      Just enough to keep us happy and pay the bills; with a little leftover for fun.

                      Presented 'AS IS' and for Entertainment Purposes Only.
                      Any gain or loss is your responsibility.
                      Use at your own risk.

                      Order is a Subset of Chaos
                      Knowledge is Beyond Belief
                      Wisdom is Not Censored
                      Douglas Paul Smallish
                      Jehocifer

                        JADELottery's avatar - MeAtWork 03.PNG
                        The Quantum Master
                        West Concord, MN
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                        Posted: April 19, 2014, 1:45 pm - IP Logged

                        Now the problem.

                        We'll start with a simple view of odds.

                        When odds are stated, they generally refer to the likely chance the event or selection will happen, not it won't happen.

                        Examples are:

                        You don't hear it phrased as "Your odds of Not being struck by lightening are ...", it's "Your odds of being struck by lightening are ..."

                        You don't hear it talked about as "Your odds of Not dieing in a plane crash is .."

                        You don't read about "Your odds of Not being in a car accident is ..."

                        When you hear or read about odds of something, it's expressed as what is chance it will happen.

                        Anyone that tells us otherwise, we tend to think of them as having behavior consistent with a scam or con artist.

                        So, as we move forward, keep in mind we are talking about the odds of a multiplier being selected, not the odds it won't be selected.

                        Presented 'AS IS' and for Entertainment Purposes Only.
                        Any gain or loss is your responsibility.
                        Use at your own risk.

                        Order is a Subset of Chaos
                        Knowledge is Beyond Belief
                        Wisdom is Not Censored
                        Douglas Paul Smallish
                        Jehocifer

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                          The Quantum Master
                          West Concord, MN
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                          Posted: April 20, 2014, 11:17 am - IP Logged

                          Alright, here we go.

                          Throughout this topic odds have made an appearance and have been used to explain the occurrences of the various multiplier selections.

                          The Megaplier does have problems, but it seems to benefit the player more than the Power Play multiplier does.

                          For now we'll focus on the Power Play multiplier.

                          There are 3 different odds to work with: Stated, Calculated and Estimated.

                          The Stated and Calculated should always be in exact agreement with each other.

                          The Estimated odds should be very close to the Stated and Calculated odds.

                          If we state the odds of something is 1 in 50 and a 100 selections later we estimate the odds to be 1 in 3, something is wrong.

                          Overall, all 3 of these odds need to be in general agreement of each other.

                          The Stated odds for the Power Play are fixed by the lottery and they are:

                          Power PlayOdds
                          21 in 2
                          31 in 3.33
                          41 in 10
                          51 in 10



                          LottoMetro has given us some virtual bias values for a possible explanation of the high number of x2 selections, with the Power Play in ascending order:

                          Power PlayNumber of Virtual "Power Play" Balls
                          25
                          33
                          41
                          51



                          From these values we can Calculate the odds of each Power Play.

                          A = 5, B = 3, C = 1, D = 1

                          Power PlayCalculated OddsStated Odds
                          21 in (B + C + D) / A1 in 2
                          31 in (A + C + D) / B1 in 3.33
                          41 in (A + B + D) / C1 in 10
                          51 in (A + B + C) / D1 in 10



                          Substitute the values it becomes:

                          Power PlayCalculated OddsStated Odds
                          21 in (3 + 1 + 1) / 51 in 2
                          31 in (5 + 1 + 1) / 31 in 3.33
                          41 in (5 + 3 + 1) / 11 in 10
                          51 in (5 + 3 + 1) / 11 in 10



                          This becomes:

                          Power PlayCalculated OddsStated Odds
                          21 in 5 / 51 in 2
                          31 in 7 / 31 in 3.33
                          41 in 9 / 11 in 10
                          51 in 9 / 11 in 10



                          Finally, make the fractions decimal values.

                          Power PlayCalculated OddsStated Odds
                          21 in 11 in 2
                          31 in 2.331 in 3.33
                          41 in 91 in 10
                          51 in 91 in 10



                          Based on LottoMetro's biased virtual ball counts, there's a problem with the calculated odds matching up with the stated odds.

                          Both of these Must be exactly equal for each of the Power Play odds.

                          So, which is correct in values.

                          Simple, test them using the formula we gave earlier: w·x·y·z - w·x - w·y - w·z - x·y - x·z - y·z - 2·w - 2·x - 2·y - 2·z - 3 .

                          This formula will always be 0 if the odds have been stated or calculated correct.

                          We have already done Power Play's stated odds using the formula and it does not become 0.

                          Let's run LottoMetro's virtual odds.

                          If w = 1, x = 7 / 3, y = 9, z = 9, then the formula works out to the following:

                          1 · (7 / 3) · 9 · 9 - 1 · (7 / 3) - 1 · 9 - 1 · 9 - (7 / 3) · 9 - (7 / 3) · 9 - 9 · 9 - 2 · 1 - 2 · (7 / 3) - 2 · 9 - 2 · 9 - 3

                          189 - (7 / 3) - 9 - 9 - 21 - 21 - 81 - 2 - (14 / 3) - 18 - 18 - 3

                          (560 / 3) - 9 - 9 - 21 - 21 - 81 - 2 - (14 / 3) - 18 - 18 - 3

                          (533 / 3) - 9 - 21 - 21 - 81 - 2 - (14 / 3) - 18 - 18 - 3

                          (506 / 3) - 21 - 21 - 81 - 2 - (14 / 3) - 18 - 18 - 3

                          (443 / 3) - 21 - 81 - 2 - (14 / 3) - 18 - 18 - 3

                          (380 / 3) - 81 - 2 - (14 / 3) - 18 - 18 - 3

                          (137 / 3) - 2 - (14 / 3) - 18 - 18 - 3

                          (131 / 3) - (14 / 3) - 18 - 18 - 3

                          39 - 18 - 18 - 3

                          21 - 18 - 3

                          3 - 3

                          0

                          Looks like LottoMetro's assertion the virtual biased ball counts are correct, however, the odds do not match the stated odds.

                          Therein lay the problem, the stated and calculated odds do not match Exactly.

                          It's our assertion, you will never find any combination of virtual ball counts that can produce the exact same odds as the ones stated by the lottery.

                          Since we have shown the test for odds correctness works when odds are calculated and stated correctly, it becomes fairly obvious, the stated Power Play odds appear to be bogus.

                          This is also demonstrated by the Estimated odds.

                          As of 2014-04-20, the frequency of the Power Play for this run of the game's version is:

                          Power PlayFrequency
                          216
                          35
                          42
                          53



                          The estimated odds based on this frequency and compared to the stated odds is:

                          Power PlayFrequencyEstimated OddsStated Odds
                          2161 in 0.631 in 2.00
                          351 in 4.201 in 3.33
                          421 in 12.001 in 10.00
                          531 in 7.671 in 10.00



                          The odds are fairly close except Power Play 2 appears stick out as being bogus.

                          When we look and compare LottoMetro's virtual odds to the sampled estimated odds we can see they are a much better fit:

                          Power PlayFrequencyEstimated OddsLottoMetro's Odds
                          2161 in 0.631 in 1
                          351 in 4.201 in 2.33
                          421 in 12.001 in 9
                          531 in 7.671 in 9

                           

                          The x2 value is much closer to 1 in 1 than 1 in 2.

                          So, this boils down to a simple assertion.

                          The stated odds are most likely Not Correct.

                          With more drawings, we can see how the Estimated odds fair against both the Stated and LottoMetro's odds.

                          We'll monitor this for a bit and may post a reply or two as there are more drawings to estimate odds.

                          For now, you can debate this among yourselves.

                          We've said all we have to up to this point.

                          Presented 'AS IS' and for Entertainment Purposes Only.
                          Any gain or loss is your responsibility.
                          Use at your own risk.

                          Order is a Subset of Chaos
                          Knowledge is Beyond Belief
                          Wisdom is Not Censored
                          Douglas Paul Smallish
                          Jehocifer

                            LottoMetro's avatar - Lottery-024.jpg
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                            September 1, 2013
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                            Posted: April 20, 2014, 12:22 pm - IP Logged

                            I've never seen a lottery that had a number frequency matching its odds of appearance exactly. Randomness keeps this from happening. As such anything is game for the short run.....streaks, skips, whatever.

                            There's only been 26 draws of Power Play and you already believe it's rigged/bogus/biased....despite me providing statistical evidence to the contrary. Honestly I don't think there have been enough draws to reach this conclusion. Last night Power Play number 5 came up.

                            On an unrelated note, yesterday I heard via recording of a panelist in November that they are going to change Powerball again. Apparently an average of 14 jackpots per year is too many, so they will probably raise the bonus ball pool from 35 to 45 but keep the price $2. Don't know when this will take place though, but it came from the horse's mouth.

                            If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
                            If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

                            2016: -48.28% (13 tickets) ||
                            P&L % = Total Win($)/Total Wager($) - 1

                              Jon D's avatar - calotterylogo
                              Los Angeles, California
                              United States
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                              January 5, 2011
                              1530 Posts
                              Offline
                              Posted: April 20, 2014, 12:53 pm - IP Logged

                              Alright, here we go.

                              Throughout this topic odds have made an appearance and have been used to explain the occurrences of the various multiplier selections.

                              The Megaplier does have problems, but it seems to benefit the player more than the Power Play multiplier does.

                              For now we'll focus on the Power Play multiplier.

                              There are 3 different odds to work with: Stated, Calculated and Estimated.

                              The Stated and Calculated should always be in exact agreement with each other.

                              The Estimated odds should be very close to the Stated and Calculated odds.

                              If we state the odds of something is 1 in 50 and a 100 selections later we estimate the odds to be 1 in 3, something is wrong.

                              Overall, all 3 of these odds need to be in general agreement of each other.

                              The Stated odds for the Power Play are fixed by the lottery and they are:

                              Power PlayOdds
                              21 in 2
                              31 in 3.33
                              41 in 10
                              51 in 10



                              LottoMetro has given us some virtual bias values for a possible explanation of the high number of x2 selections, with the Power Play in ascending order:

                              Power PlayNumber of Virtual "Power Play" Balls
                              25
                              33
                              41
                              51



                              From these values we can Calculate the odds of each Power Play.

                              A = 5, B = 3, C = 1, D = 1

                              Power PlayCalculated OddsStated Odds
                              21 in (B + C + D) / A1 in 2
                              31 in (A + C + D) / B1 in 3.33
                              41 in (A + B + D) / C1 in 10
                              51 in (A + B + C) / D1 in 10



                              Substitute the values it becomes:

                              Power PlayCalculated OddsStated Odds
                              21 in (3 + 1 + 1) / 51 in 2
                              31 in (5 + 1 + 1) / 31 in 3.33
                              41 in (5 + 3 + 1) / 11 in 10
                              51 in (5 + 3 + 1) / 11 in 10



                              This becomes:

                              Power PlayCalculated OddsStated Odds
                              21 in 5 / 51 in 2
                              31 in 7 / 31 in 3.33
                              41 in 9 / 11 in 10
                              51 in 9 / 11 in 10



                              Finally, make the fractions decimal values.

                              Power PlayCalculated OddsStated Odds
                              21 in 11 in 2
                              31 in 2.331 in 3.33
                              41 in 91 in 10
                              51 in 91 in 10



                              Based on LottoMetro's biased virtual ball counts, there's a problem with the calculated odds matching up with the stated odds.

                              Both of these Must be exactly equal for each of the Power Play odds.

                              So, which is correct in values.

                              Simple, test them using the formula we gave earlier: w·x·y·z - w·x - w·y - w·z - x·y - x·z - y·z - 2·w - 2·x - 2·y - 2·z - 3 .

                              This formula will always be 0 if the odds have been stated or calculated correct.

                              We have already done Power Play's stated odds using the formula and it does not become 0.

                              Let's run LottoMetro's virtual odds.

                              If w = 1, x = 7 / 3, y = 9, z = 9, then the formula works out to the following:

                              1 · (7 / 3) · 9 · 9 - 1 · (7 / 3) - 1 · 9 - 1 · 9 - (7 / 3) · 9 - (7 / 3) · 9 - 9 · 9 - 2 · 1 - 2 · (7 / 3) - 2 · 9 - 2 · 9 - 3

                              189 - (7 / 3) - 9 - 9 - 21 - 21 - 81 - 2 - (14 / 3) - 18 - 18 - 3

                              (560 / 3) - 9 - 9 - 21 - 21 - 81 - 2 - (14 / 3) - 18 - 18 - 3

                              (533 / 3) - 9 - 21 - 21 - 81 - 2 - (14 / 3) - 18 - 18 - 3

                              (506 / 3) - 21 - 21 - 81 - 2 - (14 / 3) - 18 - 18 - 3

                              (443 / 3) - 21 - 81 - 2 - (14 / 3) - 18 - 18 - 3

                              (380 / 3) - 81 - 2 - (14 / 3) - 18 - 18 - 3

                              (137 / 3) - 2 - (14 / 3) - 18 - 18 - 3

                              (131 / 3) - (14 / 3) - 18 - 18 - 3

                              39 - 18 - 18 - 3

                              21 - 18 - 3

                              3 - 3

                              0

                              Looks like LottoMetro's assertion the virtual biased ball counts are correct, however, the odds do not match the stated odds.

                              Therein lay the problem, the stated and calculated odds do not match Exactly.

                              It's our assertion, you will never find any combination of virtual ball counts that can produce the exact same odds as the ones stated by the lottery.

                              Since we have shown the test for odds correctness works when odds are calculated and stated correctly, it becomes fairly obvious, the stated Power Play odds appear to be bogus.

                              This is also demonstrated by the Estimated odds.

                              As of 2014-04-20, the frequency of the Power Play for this run of the game's version is:

                              Power PlayFrequency
                              216
                              35
                              42
                              53



                              The estimated odds based on this frequency and compared to the stated odds is:

                              Power PlayFrequencyEstimated OddsStated Odds
                              2161 in 0.631 in 2.00
                              351 in 4.201 in 3.33
                              421 in 12.001 in 10.00
                              531 in 7.671 in 10.00



                              The odds are fairly close except Power Play 2 appears stick out as being bogus.

                              When we look and compare LottoMetro's virtual odds to the sampled estimated odds we can see they are a much better fit:

                              Power PlayFrequencyEstimated OddsLottoMetro's Odds
                              2161 in 0.631 in 1
                              351 in 4.201 in 2.33
                              421 in 12.001 in 9
                              531 in 7.671 in 9

                               

                              The x2 value is much closer to 1 in 1 than 1 in 2.

                              So, this boils down to a simple assertion.

                              The stated odds are most likely Not Correct.

                              With more drawings, we can see how the Estimated odds fair against both the Stated and LottoMetro's odds.

                              We'll monitor this for a bit and may post a reply or two as there are more drawings to estimate odds.

                              For now, you can debate this among yourselves.

                              We've said all we have to up to this point.

                              JADE,

                              I think the discrepancy you're seeing is just due to the fundamental problem with the lottery industry referring to probability as odds.

                              I posted about this many times before, eg:
                              http://www.lotterypost.com/news/267366/3307806

                              Basically:

                              probability = chances for / total chances (or x in y)
                              odds = chances for : chances against (or x to y)

                              So for Powerplay, what the lottery calls "odds" is really the probability:
                              2x - 1 in 2 (or 5 in 10)
                              3x - 1 in 3.33 (or 3 in 10)
                              4x - 1 in 10
                              5x - 1 in 10

                              The equivalent *actual* odds for Powerplay:
                              2x - 5 to 5 (or 1:1, aka "50:50")
                              3x - 3 to 7 (or 1:2.33)
                              4x - 1 to 9
                              5x - 1 to 9
                              Which you have confirmed, and your assessment is technically correct based on proper terminology.

                              Have a Happy Easter! Sun Smiley


                              P.S. Don't mind LottoMetro's arrogant condescending remark from above:
                              "There's only been 26 draws of Power Play and you already believe it's rigged/bogus/biased....despite me providing statistical evidence to the contrary."
                              LottoMetro can't help acting like a jerk if anyone dares question him. He has even admitted this himself in a previous post: I admit my social skills are lacking.
                              But since LottoMetro lacks that sensitivity chip, he's the last one to be evaluating wherther or not he's being offensive. Wink