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PB lower odds = greater payout than MM??

Topic closed. 10 replies. Last post 10 years ago by ryanm.

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Posted: September 28, 2006, 12:47 pm - IP Logged

Not that it matters...

The last 100 PB jackpots have paid out approximately 1.8 billion more than MM.  That's an average of 18 million more per drawing!

And MM's new matrix was touted as the game that could finally reach a 500 million dollar jackpot!?!

Yeah, right!

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    Posted: September 28, 2006, 2:55 pm - IP Logged

    One can calculate an expectation value, which is the potential reward vs. the risk (i.e. the odds).

    In general, if the cash values are equal, the expectation value for PB is better than that of MM.  However this is not always the case.

    The expectation value of either game seldom rises above 1.00, at which point the game is considered a good bet.  Because of long odds, such a value is only approached when the jackpot is in the $300 million annuity range.

    It is not possible however to assert that either game is consistently a better bet than the other.  However it is possible to determine, as you suggest, that on average, PB offers a better return.


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      Posted: September 29, 2006, 12:09 am - IP Logged

      I agree with Prob988 on this one. PB has lower odds but a better reward chance than MM.

        dvdiva's avatar - 8ball

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        Posted: September 29, 2006, 1:31 am - IP Logged

        Well if you like hitting a jackpot of less than 50 million Megamillions is great. For those seeking more you can always play something else. No wonder WA state had to pass a no gambling on the internet bill.

        At least there is the 6/49 game in BC but judging from the current jackpot of 24M I'd doubt it would roll to the thirties. 

          johnph77's avatar - avatar
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          Posted: September 29, 2006, 6:12 am - IP Logged

          One can calculate an expectation value, which is the potential reward vs. the risk (i.e. the odds).

          In general, if the cash values are equal, the expectation value for PB is better than that of MM.  However this is not always the case.

          The expectation value of either game seldom rises above 1.00, at which point the game is considered a good bet.  Because of long odds, such a value is only approached when the jackpot is in the $300 million annuity range.

          It is not possible however to assert that either game is consistently a better bet than the other.  However it is possible to determine, as you suggest, that on average, PB offers a better return.

          In actuality, the expectation value reaches 1.0 at substantially lower jackpot values. I didn't take the time to do the exact math, but Powerball reaches a 1.0 value at around $118 million. MegaMillions must reach $144 million before a 1.0 expectation value is attained.

          With its higher starting jackpot of $15 million, Powerball offers a minimum payout percentage of 29.98% vs. MegaMillions $10 million minimum jackpot and a minimum payout percentage of 23.89%. This is despite the higher payouts in most of the lower-tiered prizes in MegaMillions.

          gl

          j

          Blessed Saint Leibowitz, keep 'em dreamin' down there..... 

          Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

           =^.^=

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            Posted: September 29, 2006, 7:17 am - IP Logged

            You are relying on annuity values - which in my estimation are worthless.   

            I track cash values.    I also account for the probability distribution of various winners.    On November 11, 2005, the advertised annuity for MM was $315M, cash was around $180 and ticket sales were around 105M.  The expectation value was around 1.09.

              johnph77's avatar - avatar
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              Posted: September 29, 2006, 11:38 am - IP Logged

              Agreed if cash value is your only consideration. I don't quite understand why you'd factor in probability, though, since the expected value is computed on a specific occurance rather than all possibilities.

              gl

              j

              Blessed Saint Leibowitz, keep 'em dreamin' down there..... 

              Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

               =^.^=

                Raven62's avatar - binary
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                Posted: September 29, 2006, 11:56 am - IP Logged

                In actuality, the expectation value reaches 1.0 at substantially lower jackpot values. I didn't take the time to do the exact math, but Powerball reaches a 1.0 value at around $118 million. MegaMillions must reach $144 million before a 1.0 expectation value is attained.

                With its higher starting jackpot of $15 million, Powerball offers a minimum payout percentage of 29.98% vs. MegaMillions $10 million minimum jackpot and a minimum payout percentage of 23.89%. This is despite the higher payouts in most of the lower-tiered prizes in MegaMillions.

                gl

                j

                FYI the MegaMillions Jackpot starts at: $12 Million

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                  Posted: September 29, 2006, 1:23 pm - IP Logged

                  The expectation value is, by definition, very much a function of probability, including the probability that there will be more than one winner, which obviously effects the potential size of the grand prize.

                  As a first approximation, though, because of the exceptionally long odds, the case where the probability of multiple winners exceeds the probability of one winner, is very unusual.    In the new matrices, I don't recall that such a case has ever prevailed.

                  The expectation values for lower prizes are less than 0.2 (except, possibly, in California where the MM prizes are all parimutuel) for both MM and PB.

                    johnph77's avatar - avatar
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                    Posted: September 29, 2006, 6:01 pm - IP Logged

                    Prob988 -

                    I've never worked out a probability table for MM or PB - just too much time and disk space what with all the possibilities. I have worked one out for the 6/49 lottery matrix. But it'd be an interesting workout doing one from the possibility of rollovers. Maybe when I get some time.....

                    You may be correct regarding the chances of multiple winners but then you'd have to dial in the possibility of a rollover, which would have a tendency to minimize or even negate that factor.

                    Spot on the probability factor, with PB approaching that mark much closer than MM.

                    Raven62 -

                    Thanks for the updated info. I'll make the appropriate changes.

                    gl

                    j

                    Blessed Saint Leibowitz, keep 'em dreamin' down there..... 

                    Next week's convention for Psychics and Prognosticators has been cancelled due to unforeseen circumstances.

                     =^.^=

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                      Posted: September 29, 2006, 6:39 pm - IP Logged

                      While Powerball's annuity jackpots start at $15 million and Mega Millions' annuity jackpots start at $12 million, their cash jackpots start at approximately the same value ($7 million average).