Re: Lotteries
Bret Taylor (bret@IAG.NET)
Sun, 19 Jan 1997 17:49:12 -0500
At 12:05 PM 1/19/97 -0500, you wrote:
>At 10:39 PM 1/18/97 EST, you wrote:
>
>>
>>Certainly this whole issue is a ripe one for some of that critical
>>thinking stuff we talk about for our students.
>>
>>By the way, I am proud to say that, using all of my mathematical skills, I
>>have NEVER lost in the lottery.
>>
>>Phil Mahler
>>Middlesex CC
>>Bedford, MA
>>
>
>Phil and others in the Great Lottery Debate:
>
>If the lottery is of the 6/49 vriety such as the one here in Canada, then
>there are 49_C_6 = 13,983,816 combinations of which only one will be the
>winner on any one play of the game. Thus if the prize is $1,000,000 and the
>ticket costs $1, the mathematical expectation of the game is approximately
>-$0.93; if the prize is $10,000,000 the expectation is about -$0.28. This
>ignores all subsidiary prizes such as for any 5,4, or 3 numbers, so in fact
>the expected loss will be considerably less than $0.93 and $0.28
>respectively. Assignment question: determine the expected loss if the first
>prize is $1,000,000, the prize for having any 5 numbers is $100,000, the
>prize for any 4 numbers is $1,000, the prize for any 3 numbers is $10. Do
>the relatively small expected losses per game "justify" playing the
lottery? :)
>
>Brian
>
>
Just a little more to make it even more complicated (and an even worse
"investment." In Florida, if you win, say 10 million bucks, you don't get
the check, you get a twenty year annuity which pays 1/2 mill per year. So
the real question should be how much would the annuity cost if you wnet out
and purchased it from your corner insurance store? That is your actual
winnings.
When I teach prob and stat I usually make a statement like, "If you are
crazy enough to gamble, go to Las Vegas. You'll eventually lose all your
money, but it will take a lot longer than buying lottery tickets. (We also
point out that if any casino, dog track or horse track tried to return the
same portion of money to the bettors as the lottery does they would be shut
down immediately for being groosly unfair. In FL, dog tracks are required to
return 86% of the money wagered; the state returnsd less than 50%)
Bret Taylor Lake-Sumter Community College Leesburg FL
"It matters not the subject taught, nor all the books on all the shelves.
What matters more, yes most of all, is what the teachers are themselves."
John Wooden
John 3: 33 + 3