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Re: [Phys-L] lottery fundamentals



You MIGHT be the only winner. But you might not. If I ran these
lotteries, I would actually make it easy for wealthy people to purchase a
complete set of numbers any time they wanted to. I may even offer that at
a discount. The 99% might complain, but actually they would benefit! The
jackpot would rise. And the state would have more money for roads,
education, shiny new toys...

In general, calculating the expected value of a lottery ticket for this
kind of lottery is not as straight-forward as multiplying the odds of
winning by the size of the jackpot. You have to factor in the chances of
having to split the pot with one (or more!) other winners. To know that,
you have to estimate how many players there are in this round.


On Wed, Feb 26, 2014 at 10:19 PM, Anthony Lapinski <Anthony_Lapinski@pds.org
wrote:

But what if you buy all the numbers and everyone else buys a few numbers
each. So the jackpot is huge, but not every number combination was taken
by everyone else. And then you would be the only winner? No split with
anyone. Then you would win more than you put in, right?

Phys-L@Phys-L.org writes:
PowerBall and MegaMillions have (and will) reach the stage where the
'Jack Pot' is larger than the cost/ticket x odds of winning.
This is when the 'frenzy' sets in.
The last such situation with PowerBall (last week) did indeed have only
one winner.

HOWEVER - if you select the Immediate Cash payout it is but a fraction of
the advertised JackPot.
Approximately HALF the advertised JackPot.
To get the Advertised Amount you must accept the Annuity - paid out over
20 - 26 years (depending on the Game).

So, no, you can't buy every number and expect to Break Even.
Even if you are the only player to get the Winning Number.

On Feb 26, 2014, at 4:14 PM, John Denker <jsd@av8n.com> wrote:

On 02/26/2014 01:24 PM, Anthony Lapinski wrote:
In theory, could you ever pick all the combinations in a lottery, pay
for
the tickets, and win money?

No, for at least two reasons.

First of all, suppose you were the only player, or the only
really big player. If you did that the best you could hope
for is to win all the money in the pot, but that's less than
you paid, because the house takes its cut before the money
goes into the pot.

Secondly, suppose you weren't the only big player. Then
you would have to /share/ the prize.

Perhaps more importantly, use your physics intuition: Use
the /conservation/ idea. You're playing a less-than-zero-sum
game. Ticket-holders collectively cannot get out more than
they put in *and* your share of the pot is, on average,
proportional to the share of the tickets you bought.

This demonstrates an important idea: gambling is infamous
for being in a different category from ordinary commerce.
Ordinary commerce creates value. It is a positive-sum
game.

_______________________________________________
Forum for Physics Educators
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_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l



_______________________________________________
Forum for Physics Educators
Phys-l@phys-l.org
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