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# Poisson Rollover/Winner Probabilities on the \$635M Jackpot

Topic closed. 4 replies. Last post 3 years ago by Prob988.

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New Jersey
United States
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September 4, 2005
949 Posts
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 Posted: December 17, 2013, 5:00 pm - IP Logged

The lottery is estimating that they will sell around 342.5 M tickets, based on the cash value size.

If this proves accurate, the randomized poisson distribution suggests the following probabilities for numbers of winners:

 k, number of winners p(m,k) 0 26.64% 1 35.24% 2 23.30% 3 10.27% 4 3.40% 5 0.90% 6 0.20% 7 0.04% 8 0.01%

In reality, anything can happen, but the most probable outcome is a single winner, and there is about a 1 in 4 chance of another rollover.

Because the sales on this unprecedented number of draws is not nearly as high as the previous record jackpot (which took place on a 19th draw) the expectation value is surprisingly high, something I thought I'd not see with the new matrix and the reduced lower level prizes, an expectation value over 1.00.   It is 1.04.

Happyland
United States
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September 1, 2013
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 Posted: December 17, 2013, 5:12 pm - IP Logged

Did you factor in the excess from last draw? MUSL is projecting sales of 319,490,000.

 Any Winner 0.7089 0 0.2911 1 0.35924 2 0.22167 3 0.09118 4 0.02813 5 0.00694 More than 5 0.00172

If it rolls til Friday, MUSL is projecting sales of 536,700,000.

 Any Winner 0.8742 0 0.1258 1 0.26079 2 0.27032 3 0.1868 4 0.09681 5 0.04014 More than 5 0.01935

I agree about the expectation, I did not think it would be very good.

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

New Jersey
United States
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September 4, 2005
949 Posts
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 Posted: December 17, 2013, 7:12 pm - IP Logged

I used the last announced cash prize and the current cash prize to calculate the approximate sales.  I fully concede that the sales numbers may prove to be different.

It's just an approximation.

Happyland
United States
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September 1, 2013
1129 Posts
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 Posted: December 17, 2013, 7:20 pm - IP Logged

I used the last announced cash prize and the current cash prize to calculate the approximate sales.  I fully concede that the sales numbers may prove to be different.

It's just an approximation.

Yeah, my numbers are just projections.....they are usually pretty close but during mega mania they can be understated. Anyway, during the last drawing they didn't adjust the cash jackpot upwards from the additional 35 million+ in sales, so this is probably what caused the difference.

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

New Jersey
United States
Member #21206
September 4, 2005
949 Posts
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 Posted: December 18, 2013, 10:12 am - IP Logged

Yeah, my numbers are just projections.....they are usually pretty close but during mega mania they can be understated. Anyway, during the last drawing they didn't adjust the cash jackpot upwards from the additional 35 million+ in sales, so this is probably what caused the difference.

The actual sales were 342.2M, and the actual outcome, two winners was slightly less probable than another rollover.    Note that these sales figres were a little more than half of what they were in the last \$600+ (annuity) drawing, albeit with a reduced cash fraction on the new matrix.   It also took 22 draws to get there, as opposed to 19 the last time this happened.

It will be interesting to watch the behavior of the lottery under the new matrix for a full run starting from \$15M annuity.     Compared draw to draw, they've been lower than before the matrix change, and much, much lower than MM sales before the \$2 Powerball, showing that lottery players may be smarter than they assumed when they made the change with the somewhat absurd "better odds" claim.

The final probability distribution for numbers of winners came out as follows:

 k, number of winners p(m,k) 0 26.64% 1 35.24% 2 23.30% 3 10.27% 4 3.40% 5 0.90% 6 0.20% 7 0.04% 8 0.01%

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