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Actually, the probability of $300 M jackpots in MM is slightly higher with new states.

Topic closed. 2 replies. Last post 7 years ago by Prob988.

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New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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Posted: January 12, 2010, 9:54 pm - IP Logged

I did an analysis of the probability of $300M jackpots in MM with 1.7 as large a population as is currently obtained, using average sales for each drawing compiled over several years.

The number, 1.7, is all (PB states population + MM population)/(MM population).

I then used a poisson distribution for 0 winners (a rollover) showing with these sales figures for each drawing.

I then multiplied each previous rollover probability for all drawings (product) to find the overall probability of a $300M + annuity jackpot occuring.

Note that the larger sales mean larger contributions to the jackpot, roughly 31%.

Thus the jackpot grows faster.

To reach a $300M jackpot now takes roughly 15 or 16 drawings.   In the new scenario it would take roughly 13 drawings.   The probability of lasting to a 13th drawing is about 6% on a first draw, using average numbers times 1.7.

The probability under the existing population, again based on average performance is about 5%.

To see that this sort of thing is actually obtained, look at the rump state lotteries, pick 6 games, etc.   Except in very large states like California, they can rollover lots of times without generating very large jackpots.   New Jersey for instance, has been rolling over since September and still has only a $16.5 M annuity jackpot.

It's subtle, but true.   We might actually see as many  very large jackpots than we saw previously, but more quickly generated.

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    Urbandale, IA
    United States
    Member #8624
    November 11, 2004
    115 Posts
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    Posted: January 13, 2010, 4:02 pm - IP Logged

    Using pure numbers, the average jackpot will be the same.  Just more more hits more often.  As this writer points out, as coverage goes up, so do sales, so does coverage, and so on.  More sales means more coverage and more hits, but is also means higher jackpots.  One of those magical reciprocity things. 

    But there is an unknown.  Where humans are involved, you can't use pure numbers.  No one can predict exactly what will happen with four jackpot draws per week.  You have to start over with sales experience when you try to predict future play.

    But, more sales do NOT increase the percentage to the jackpot.  The percentage of sales given to the jackpot pool is set by the game's design and does not change with more sales.

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      New Jersey
      United States
      Member #21206
      September 4, 2005
      949 Posts
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      Posted: January 13, 2010, 4:48 pm - IP Logged

      Using pure numbers, the average jackpot will be the same.  Just more more hits more often.  As this writer points out, as coverage goes up, so do sales, so does coverage, and so on.  More sales means more coverage and more hits, but is also means higher jackpots.  One of those magical reciprocity things. 

      But there is an unknown.  Where humans are involved, you can't use pure numbers.  No one can predict exactly what will happen with four jackpot draws per week.  You have to start over with sales experience when you try to predict future play.

      But, more sales do NOT increase the percentage to the jackpot.  The percentage of sales given to the jackpot pool is set by the game's design and does not change with more sales.

      I agree with most of what you say.

      The media however is claiming that they do know.

      I just hope that MM and PB will be kept intact and not replaced by a $2 lottery with ridiculously higher odds, although the odds are already ridiculously high.

      I choose to play, myself, based on expectation values, and such a move might effectively mean I will hardly ever play either lottery.

      I like when the expectation value approaches 1, which it sometimes does with existing MM and, less often, with PB.