Expected Value of 540MM MegaMillions

[MRoss]

So for just winning the jackpot it is 540MM*(1/176,000,000) approx. This gives a super cool expected value of $3.06 for each $1 ticket. This is purely on the jackpot, so of course with the other prizes the EV goes up.

However, since there are other players and we have no idea of knowing how many; we cannot really calculated this correctly.

Anybody bored enough to add the other probabilities into this equation? My guess is it would drive the EV up to around $4 per ticket.

Also, this is pre-tax and pre-cash option.

 

[Drew Norton]

You might want to take taxes into account on this.

 

[MRoss]

You might want to take taxes into account on this.

Also, this is pre-tax and pre-cash option.

 

[APalley]

However, since there are other players and we have no idea of knowing how many; we cannot really calculated this correctly.

Anybody bored enough to add the other probabilities into this equation? My guess is it would drive the EV up to around $4 per ticket.

• One can estimate the # of tickets sold by the jackpot size. I believe about .50 of each ticket sold goes into the jackpot. But you would need to calculate it based on the differential between last and current jackpot.
• I think the fact that the prize can be split (numerous) ways will drive E[payout] way below $3, even with the other prizes.
• No need to do this analytically, anyone bored enough to run an MC?

 

[Drew Norton]

Yes, I read that, but if you consider that taxes will be close to 50%, stating that the value is over $3 is erroneous.

Also I would use an expected return, in effect making each ticket worth $2.06 without taking taxes into account, or $0.53 after tax.

 

[MRoss]

Ive heard people in my office saying that we should spread our ticket purchases around to different locations. Does anybody understand the reasoning behind this?

 

[alain]

Ive heard people in my office saying that we should spread our ticket sales around to different locations. Does anybody understand the reasoning behind this?

Ticket sales? are you arb-ing this thing?

 

[SYau]

He will ebay it.

 

[MRoss]

Lol. I meant ticket-purchases.

But Steven...........................not a bad idea!

 

[APalley]

Ive heard people in my office saying that we should spread our ticket purchases around to different locations. Does anybody understand the reasoning behind this?

Doesn't sound like a rational statement to me Superstition?

 

[APalley]

Ticket sales? are you arb-ing this thing?

Would be interesting to see the result if they hypothetically stopped selling tickets. How much you think a single ticket would go for?

 

[MRoss]

Not sure. I heard it from multiple sources. I agree it sounds suspicious.

Would be interesting to see the result if they hypothetically stopped selling tickets. How much you think a single ticket would go for?

$1.50

...one of those "pull the number out of the hat" things.

In any event, that would not be called arbitrage...

 

[alain]

Not sure. I heard it from multiple sources.

Let me know which sources, I have a bunch of stuff to sell...

 

[kamikade]

off topic: is it possible to buy tickets online if I am from Canada? :P

 

[AZPalta]

Something else to consider if you bought all possible combinations:
You would also win the smaller pots getting 5 out 6 correct, 4 out 6 correct, etc...
So, the total value is somewhat greater than the 6 out of 6 jackpot of 540MM

As gambling winnings are taxable income, there is a provision that allows gambling losses to be deducted.
If you bought all possible combinations, you could consider the "loser" tickets as a gambling loss to reduce your tax liability.

 

[JPAlonso]

Too bad you will probably have to share your winnings with about 4 people. The jackpot increased from 440 million to 640 million based on a percentage of the increase in sales, which means there must be about 600 million dollars of tickets sold so far (very rough estimate). There are 176 million combinations at $1 a ticket, it means that every possible combination has been, on average, chosen about 4 times already.

I would still play for fun even if the odds are all against me, but I am also in Canada

 

[APalley]

What are the odds of there being no winner? That would make next week very interesting...

 

[APalley]

Assuming 500M tickets sold:

Odds of you being the only winner:

1/3,024,244,715

 

[aaronhotchner]

Doesn't the fact that no one has won yet kind of indicate that the picks are not uniformly distributed? Maybe approximately, but it makes me very skeptical of guessing at a small probability with any real precision.

 

[APalley]

Doesn't the fact that no one has won yet kind of indicate that the picks are not uniformly distributed? Maybe approximately, but it makes me very skeptical of guessing at a small probability with any real precision.

Not really, bc the last progression was from 290-363, which is ~150M tix sold. P(no winner) is about .42. The one before that, about .56, before that .64 and so on. It's not that far out. But it would be interesting to see what sort of RNG they are using.