|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.