
Do Not Play the Lottery Unless You Are a Millionaire - soundsop
http://r6.ca/blog/20090522T015739Z.html
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asmithmd1
The chances of winning are close enough to zero to safely consider them zero.
If it is entertaining to you to buy a ticket and dream about winning then go
ahead and buy _one_ ticket. But never buy more than one thinking you are
increasing your odds of winning. 5 tickets * 0 is 0. 100 * 0 is still 0 - any
practicle number of tickets * 0 is still 0 zero

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ssanders82
But if you have a large enough bankroll to do so, you should buy as many
tickets as you can get your hands on - assuming #1.) the expected value is
positive and #2.) your total investment falls below your Kelly criterion. I
believe a city in Texas did this once when the lotto odds were in their favor
but my google-fu escapes me.

So, according to your theory, you should buy ONE ticket or ALL the tickets,
but nothing in between?

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JacobAldridge
And don't forget to factor split winnings into the calculations. Here in Qld
(Australia) the media coverage of lottery prizes starts well before the Kelly
criterion tips in your favour, which means prizes are almost always split -
there was one case where $20-odd million was split so many ways that the first
division prize was less than $750K.

In that situation, even buying ALL the tickets wouldn't help ... you'd need to
buy MULTIPLE copies of ALL the tickets, so you would have several shares in
the split. I'd like to see the math for that!

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joshu
This just lowers your odds, and can be factored into the likelyhood (although
I assume that this actually tops the expected return below zero.)

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djehuty
I think there's a reasonable argument for using the Kelly criteria, but
leaving that question aside, the author misses a most important factor: the
marginal utility of the money. If I am a millionaire, the upside of extra
money is low, and the downside of losing all my money is high. If I am
choosing between a cup of coffee and a lottery ticket, the upside (even
divided by my chance of winning) is high and the downside low.

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dejb
A agree with the importance of marginal utility but disagree with your
'marginal' maths. The pay off with these mega jackpots needs to be in the 10s
of millions to make it positive net value. I'd argue that the marginal value
of money starts to taper of considerably at around between $2m and $5M. So the
extra say $35M of jackpot money won't really have as much value to you on top
of the $5M you might normally win. So in marginal terms you are back to
negative expectation.

Of course I think the marginal entertainment value is what gets most people
playing.

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ecuzzillo
That is, unless you're like everybody who actually plays the lottery, and you
derive utility from the hope it gives you.

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zimbabwe
It's sad to think that some people derive their hope entirely from the
lottery. I wish there was more of a fervent drive to discover how to _make_
money rather than just win it.

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dxjones
Although the discussion of the Kelly criterion is an interesting academic
exercise, the analysis does not apply to an actual lottery like 6/49, because
it is based on a false assumption:

... "assuming that I can avoid picking the same numbers as someone else".

Unfortunately, as the number of tickets purchased increases, the probability
that another person chooses the same numbers as you also increases. Thus, when
there is a large prize, it becomes very likely that it will be shared.

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swombat
Hey, if buying one ticket makes sense, then surely buying more than one ticket
makes more sense. So you should spend all your $65m buying lottery tickets for
the $49m jackpot lottery. If each $2 has an expected $3.50 return, then $65m's
worth of tickets will have an expected $113m return! Bingo. Safe as houses.

Or perhaps this is an absurd argument, as proven by the above _reductio ad
absurdum_ , and you should keep your money to spend it on things that make
sense.

But don't let me stop you. After all, the people who run the lottery need to
eat too.

~~~
bmelton
Your comment reminds me of a group which, I apologize for being vague on the
details of, planned to buy as many lottery tickets as needed to have a 1/1
chance of winning. I can't remember if that meant just getting enough
individual numbers that their odds "went up" or if they were actually planning
to purchase all the possible number combinations. Irrelevant I suppose.

Probability math aside, they were able to raise the funds required to purchase
the necessary tickets, but were eventually undone in a rather unexpected
way... turns out, it's harder to procure 2 million lottery tickets than they
had anticipated. The day of, they simply weren't able to get enough tickets to
make it happen.

I honestly don't remember if they won or lost, but I remember expecting them
to fail through having to split the winnings, throwing their math off... as if
it weren't already off anyway.

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sireat
If I am not mistaken, it happened in Australia, and while they were not able
to cover all the numbers, they did win (they had covered 90%+ of
combinations).

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CalmQuiet
Hey, don't they realize that us little people (at least in U.S.) don't play
because we want to win. Having such big hearts, most of us just like having an
additional way to funnel money into state government (since they allow us to
pay so little in taxes). [/tongue-cheek]

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andylei
the reliance on the Kelly criterion doesn't make any sense. the Kelly
criterion is based on a game you can play over and over. it calculates an
exponential expected growth rate based on how much you're favored.

favorable lotteries don't show up very often. if a favorable lottery that you
could play existed every day, then the Kelly criterion makes sense (it sort of
makes sense in its original context, the stock market).

