kubikulann
Joined: Jun 28, 2011
• Posts: 798
June 18th, 2014 at 4:12:06 PM permalink
Quote: MangoJ

Again, the purpose of insurance is reducing variance (yes, it is a high-variance negative EV bet, but it is anti-correlated to other loss events, which reduces overall variance). On the contrary, playing the lottery (still a high-variance negative EV bet) is not correlated to anything, so it increases your overall variance. With taxes on winnings it is even much worse.

I'm not sure I agree that "the" purpose is reducing variance, though I admit it plays a role.

Yet most players here will agree that in -EV games, the player should prefer large variance.
Why is that?
The difference lies not in variance but in skewness. Insurance reduces the variance of a negative EV game with (large) negative skewness. Lottery increases variance of a negative EV game with (large) positive skewness.
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MangoJ
Joined: Mar 12, 2011
• Posts: 905
June 19th, 2014 at 1:38:34 PM permalink
I think the discussion goes to the right direction. One can argue whether or not a utility function should be convex or concave, or something else.

Probably it is "something else" - but we can at least imagine a concave utility function and see what decisions it would produce, and then decide if these are somewhat rational. For a everywhere concave utility function, for any independent fair bet the win per probability is larger than the utility of the loss per probabiltiy.
Which means you would play any fair game offered for any amount of time or stakes. You would basically want to bet your whole fortune on any fair game. Is that economical ? Obviously it isn't - once you lose you cannot gain utility anymore as you have nothing to stake. Even if you bet a constant fraction of your wealth, you are eventually hitting ruin. A everywhere-concave utility function is simply not sustainable, even if EV is zero. Obviously economics is worse if EV is negative.

So any rational agent with a fear of ruin has at least a convex region of utility at the lower end.

What about the upper end ? Do you risk a million for a 1:1000 chance for a billion ?
andysif
Joined: Aug 8, 2011
• Posts: 431
June 19th, 2014 at 6:16:46 PM permalink
I think the math gets a little bit complicated when the amount involved is "big", but if we restrict the amount to only your disposal income then we are still safe to assume it's concave.
kubikulann
Joined: Jun 28, 2011
• Posts: 798
June 20th, 2014 at 7:01:28 PM permalink
Quote: andysif

I think the math gets a little bit complicated when the amount involved is "big", but if we restrict the amount to only your disposal income then we are still safe to assume it's concave.

Are you sure you do not mean "convex"?

My opinion (no facts, alas) is that we humans treat differently what is perceived as a loss and what is perceived as a gain. This theory is compatible with several paradoxes raised by Allais, Ellsberg, Tversky & Kahnemann, etc.

So I can imagine our utility function as one convex function in the negative range, and another in the positive range, but the connection between both at zero makes for a (angular) concave zone. Then it may be perfectly rational to play the lottery.

Please note that what I personnally think is that we humans do not function as computers. There is, I think, no utility function. We are still waiting for philosophers, psychologists and economists to build a satisfactory model of decision under uncertainty.
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MangoJ
Joined: Mar 12, 2011
• Posts: 905
June 21st, 2014 at 3:37:40 AM permalink
Quote: kubikulann

So I can imagine our utility function as one convex function in the negative range, and another in the positive range, but the connection between both at zero makes for a (angular) concave zone. Then it may be perfectly rational to play the lottery.

This. Convex local favor insurance, concave favor lottery. Of course utility functions are highly subjective. One could indeed define a gambler's mind for relying on a concave utility - as he is willing (as he actually does) to pay for variance. The degenerate gambler then stretches his concave zone to the very lower end.

And it is likely for lottery players, to stretch their concave utility up in the higher ranges. Maybe this is the problem why some (or most) heavy-million winners fail: they have no clear concept of utility, and any unrational action gets amplified by huge amounts. Plus, there is social pressure "to do" something.
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 3693
June 21st, 2014 at 9:00:25 AM permalink
Quote: andysif

Yes I know the probability of drawing each combination is the same, BUT the payout is not.
More people to split the Jackpot, less you will receive.

So while "1,2,3,4,5,6" is "fun" to play, it would be nothing compare to the look on your face when you realize you hit the jackpot and so did 30 other people.

There was an ad campaign for California's Lotto where they asked celebrities what numbers they played. Either Steve Jobs or Steve Wozniak said "1 2 3 4 5 6, since that's just as likely a combination as any other."

In a 6-number game, I expect the most popular combinations to be the ages and birthdays of a couple and their only child, so I would also try to keep away from any set where four of the numbers are in 1-31. In MegaMillions, I would expect the child's age to be the "red" number, so 3 of the 5 "white" numbers would be in 1-31.
AcesAndEights
Joined: Jan 5, 2012
• Posts: 4264
June 22nd, 2014 at 5:31:58 PM permalink
Quote: kubikulann

I have won the Belgian lottery once.

I had written a program to analyze the results for some twenty years of draws. As such I was able to (unprecisely) gather what kinds of bulletins the people were playing. The intuition I read above about prime numbers is wrong: people do play them, they probably look more random to them. There is an excessively great amount of people playing "1,2,3,4,5,6" or "2,12,22,32,42,52" or the like. Also birth dates and such.

But mostly, before the generalisation of QuickPicks, people were influenced by the visual pattern of their bulletin. Consequently, thay play more in the centre than on the borders and, conspicuously, the corners. On the other hand, there are those who reason like the OP did, try to play "differently" and they overreact, playing for example the six numbers that are less played, or geometric figures.

In the end, I was using broken patterns : one part was "too geometric" to be played by the common, but one or two numbers were at odds with the pattern (which was not going to be played by the strategic players). I used some but not all the less-played numbers, often adding one of the often-played numbers, agin to break the pattern.

Alas ! My technique was not optimal. The day I won, where the jackpot was € 2,000,000 , we still were five winners, so the €400,000 were not enough to stop working. It allowed me to buy a house.

Whoa, seriously? When did you win? How much taxes did you pay on the 400K? Do you still live in Belgium?
"So drink gamble eat f***, because one day you will be dust." -ontariodealer
kubikulann
Joined: Jun 28, 2011
• Posts: 798
June 23rd, 2014 at 5:10:54 AM permalink
Quote: AcesAndEights

Whoa, seriously? When did you win? Back in 2008
How much taxes did you pay on the 400K? None. Lottery gains (and casino) are not taxable. Belgium is sort of a fiscal paradise for capital and a fiscal hell for work.
Do you still live in Belgium? Yes. It was not enough to quit working for a living, and as a teacher it is difficult to be hired in another country (EU free circulation, my ass!)

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AcesAndEights
Joined: Jan 5, 2012
• Posts: 4264
June 23rd, 2014 at 7:20:30 AM permalink
Quote: kubikulann

Quote: AcesAndEights

Whoa, seriously? When did you win? Back in 2008
How much taxes did you pay on the 400K? None. Lottery gains (and casino) are not taxable. Belgium is sort of a fiscal paradise for capital and a fiscal hell for work.
Do you still live in Belgium? Yes. It was not enough to quit working for a living, and as a teacher it is difficult to be hired in another country (EU free circulation, my ass!)

Wow, I'm just surprised I've never heard this story before. If you've told it on the forum, I missed it!

I agree that it wouldn't be enough to retire on, but I certainly hope it moved your schedule up quite a bit! If I won the equivalent in USD (about \$544K based on current exchange rates, not sure what it was like back in 2008) I would still need to work, but probably only for another 4 or 5 years. Hmmm. Would have to run the numbers on that.

I hope you didn't go on a shopping spree and change your lifestyle too much after that windfall...would be tough for most people...
"So drink gamble eat f***, because one day you will be dust." -ontariodealer
kubikulann
Joined: Jun 28, 2011
• Posts: 798
June 23rd, 2014 at 8:02:14 AM permalink
Quote: AcesAndEights

I hope you didn't go on a shopping spree and change your lifestyle too much after that windfall...would be tough for most people...

Oh ! no. I put it on an account and waited for a good opportunity of finding a new house. Real estate is not cheap in Brussels (siege of the EU, NATO, etc.)

Return rates are quite low (or too risky) to generate a decent revenue from €400,000 , I don't know how you would manage to retire after 5 years :-)

The good thing, as lond as that money was on an account, was that I felt sooo free in my relationship with the hierarchy. "If they don't like it, bugger them!"
Now that all is in my house, I'm back in the sad inferior position where I need the job.
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