Adding on to Probability and MegaMillions, considering magnitude of this operation . . .

The probability of winning the MegaMillions lotto is 1 in 176Million. Buy one of each combination, you will win. You will also spend $175,711,536 in after tax dollars for the privilege of winning.So let’s make it worth our time.

## Starting jackpot, One Billion Dollars.

Very few people consider the actual opportunity to make such a large purchase. In order to rig the lotto you would have to have humans actually purchase physical tickets. There are all sorts of constraints. Lotto dispensing machine are typically inside convenience stores and bodegas. Some are open all hours, most are not. Best case you can get a dedicated employee to run the lotto machine for the full 18 hours – not realistic, but we’re going with it for now. Max number of tickets that can actually pump out of the machine depends on type/quality of the machine and operator. I tested this at a local bodega and found that my guy’s cap was 10 or fewer tickets per minute with automatic (machine generated codes). 3 per minute when hand keyed.

If you’re going to do this right, you have to have the hand keyed tickets – otherwise you will get duplicates and may miss some combinations. This also means whoever brings the tickets in to be keyed must hand bubble the tickets. So you actually have 1 staff member dedicated to each bodega operator….

18 hours of operation x 3 tickets per minute gives a total of 3240 tickets per bodega operator per day.

Cost of staff per bodega operator = $3240 ($1 MegaMillions tickets) + 18 hours of wage for our staff member ($10/hr) = $3420 per bodega operator

$175,711,536 / $3240 = 54,232 dedicated bodega operator days

Additional labor cost = 54,232 x $180 = $9,761,760

Cost to purchase all necessary tickets = $185,473,296.

Can it be done? Is it possible to have that many staff members descend upon that many bodegas within the limited time frame? Typically a lotto pulls multiple times per week so you have to make the purchases in between pulls. If our lotto pulls on Tuesdays and Fridays, we can make purchases Sat-Tue to reduce our headcount.

Total people needed: 13,558, minimum

Total bodega lotto machines needed: 13,558 minimum

Mega Millions is offered in 44 states (45 as of April 2013), so you could spread the purchases to 301 confederates in each state, approximately all the retail employees at 3 apple stores per state. Not such a big number after all. [[Be warned, anything that looks like coordination is investigated.]]

So what is our return?

$1,000,000,000 in prize money

– $350,000,000 avg taxes ($400M in New York City…)

– $182,700,000 penalty to take lump sum

$467,220,000 total for a single winning ticket

– $185,473,296 cost to acquire tickets

$281,746,704 Total

Return on Investment: 152%

I looked at the MegaMillions jackpots over $200M to identify patterns of multiple winning tickets on big jackpots. Of the 18 large jackpots, 6 had multiple winning tickets. Most of the remaining jackpots had multiple winners, but only one winning ticket. So for large jackpots, the incidence of multiple winning tickets getting created is 1/3. The average number of tickets per large jackpot is 1.6. Buying 60% of a ticket is not feasible so we will round to two winning tickets, 6 of the 18 had two or more winning tickets with one jackpot producing 4 winning tickets.

$1,000,000,000 in prize money

– $350,000,000 avg taxes ($400M in New York City…)

– $182,700,000 penalty to take lump sum

$467,220,000 total to distribute

– $233,610,000 amount to share with second ticket holder

– $185,473,296 cost to acquire tickets

$48,136,704 Total

Return on Investment: 26%