Editing 1827: Survivorship Bias

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*Lottery with '''positive return''':
 
*Lottery with '''positive return''':
 
**When item prizes are donated to a lottery (for charity or advertising purposes), sometimes the value of those items may actually be larger than the total price for all of the lottery tickets, if you otherwise would be willing to pay full price for all the prizes.
 
**When item prizes are donated to a lottery (for charity or advertising purposes), sometimes the value of those items may actually be larger than the total price for all of the lottery tickets, if you otherwise would be willing to pay full price for all the prizes.
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**In some lotteries, if the jackpot gets too big -- or goes for too many drawings -- without anyone winning it, the jackpot amount gets "rolled down" and distributed across the lower prize levels.  These can have a positive return on average -- but ''only'' on the drawings where the jackpot rolls down.  People have formed investment groups to buy hundreds of thousands of tickets to exploit these; several such groups repeatedly profited from Massachusetts's {{w|Massachusetts_Lottery#Cash Winfall|Cash WinFall}} game especially.  (The Massachusetts State Lottery has an official report ([http://www.mass.gov/ig/publications/reports-and-recommendations/2012/lottery-cash-winfall-letter-july-2012.pdf PDF, 144 KB]) on how such high-volume betting affected the game.)
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**In some lotteries, if the jackpot gets too big -- or goes for too many drawings -- without anyone winning it, the jackpot amount gets "rolled down" and distributed across the lower prize levels.  These can have a positive return on average -- but ''only'' on the drawings where the jackpot rolls down.  People have formed investment groups to buy hundreds of thousands of tickets to exploit these; several such groups repeatedly profited from Massachusetts's {{w|Massachusetts_Lottery#Cash Winfall|Cash WinFall}} game especially.  (The Massachusetts State Lottery has an official report ([http://www.mass.gov/ig/publications/reports-and-recommendations/2012/lottery-cash-winfall-letter-july-2012.pdf PDF, 144 KB]) on the latter.)
 
*'''Examples''' of survivorship bias:
 
*'''Examples''' of survivorship bias:
 
**Diogenes was shown paintings of people who had escaped shipwreck: "Look, you who think the gods have no care of human things, what do you say to so many persons preserved from death by their especial favour?", to which he replied: "Why, I say that their pictures are not here who were cast away, who are by much the greater number."  
 
**Diogenes was shown paintings of people who had escaped shipwreck: "Look, you who think the gods have no care of human things, what do you say to so many persons preserved from death by their especial favour?", to which he replied: "Why, I say that their pictures are not here who were cast away, who are by much the greater number."  

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