MegaMillions

Apr 15, 2006 17:33

The MegaMillions jackpot is now $265M, after nobody won it last night. Given that the odds of winning the JACKPOT are 1:175,711,536, this means that at first blush, you stand to make some bank. However, you need to account for a few other factors to determine how big the prize needs to for it to make sense to play MegaMillions, probabilistically speaking. Those factors are: (1) {local, state, federal} taxes; (2) the % of the jackpot that gets paid out as a lump sum instead of as the a26-year nnuity -- i.e., their figure for the time value of money; (3) the typical % of the jackpot pool paid to other prizes -- given that these are fixed-size prizes, the analysis is straightforward and the average non-jackpot output should be a roughly constant percentage of the total price pool [[note -- I need to follow up on this, and see how much I skewed the final analysis by assuming that the 4/14 payout was typical]].

For my analysis, I assume that the getting the cash up front results in 55% of the jackpot (because the website says "roughly half") instead of the 26-year annuity, which only applies to the Jackpot. All other payouts are in lump-sum form. I also assume no taxation on the small prizes {$2, $3, $7, $10, $150}, 30% total taxation on the $10K prize, and 45% taxes on the $250K and Jackpot prizes. Note that the resulting number assumes only one jackpot (which is a pretty reasonable assumption, given the odds), and is the number left in the pool once all the non-jackpot prizes have been paid out.


Prize Value
Odds (1/n)
E(X ) [in $]
E(X ) after taxes

$2.00
75
0.026666667
0.02666666666667

$3.00
141
0.021276596
0.02127659574468

$7.00
306
0.022875817
0.02287581699346

$10.00
844
0.011848341
0.01184834123223

$150.00
7253.3324
0.02068015
0.02068014971987

$10,000.00
689,065
0.014512419
0.01088431425192

$250,000.00
3,904,701
0.064025389
0.03521396388610

Jackpot after other prizes:
$494,056,781.53
175,711,536
2.811749261
1.54646209365275

E(X) of $1 spent:

1.69590794214767

After Cash Option

1.000000000003940

And remember, that's AFTER the prizes have been paid. Yesterday, the jackpot was $220M, and it paid a total of $12,937,200 in prizes. So assuming that the smaller prize proportions are roughly the same, you'd expect 6-7% of the total prize pool to be paid in those smaller prizes, so, in short, you shouldn't play unless the Jackpot is $528.4M or above. It needs to slightly less than than double from its current $265M for it to be statistically worth playing.

math, geekiness, innumeracy

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