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#1




Does buying 10 lottery tickets increase my odds by a power of ten?
If the odds of winning a lottery jackpot are 1 in 175,711,536, if I buy 10 tickets, do my odds change to 1 in 17,571,153.6? And 100 tickets increases it to 1 in 1,757,115.36?
That is, is "10 in 175,711,536" the same as "1 in 17,571,153.6"? 
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#2




If you buy multiple tickets each with a different number, your chances increase by a factor of how many tickets you buy.
The "power of 10" phrase is a little misleading. If you buy 5 tickets, your chances increase by a factor of 5. If you buy 127 tickets, your chances increase by a factor of 127. Powers of 10 have nothing to do with it, except that your examples use powers of 10 for the number of tickets. And yes, "10 in 175,711,536" is the same as "1 in 17,571,153.6". 
#3




Alternatively, if you buy one lottery ticket with 1 chance in 175,711,536 of winning you have 175,711,535 chances of not winning.
If you buy 10 tickets you have 175,711,526 chances of not winning. So you have improved your chances of not winning from 99.999999430885402993688473590032% to 99.999994308854029936884735900322% This represents an improvement of .00000512203166455910240060177% 
#4




Whoa! Buzzkill.



#5




There's the old joke about the poor guy that used to pray every night for God to let him win the lottery. After several years of this, he's praying one night when there's a thunderbolt, a cloud appears, a giant hand comes out the cloud, points a finger at him and says "You cheap bastard! The least you could do is help me out by buying a ticket once in a while!"
So  your odds of winning go up tremendously with the first ticket. With the second, you spend $1 (or whatever) and double your chances. By the fift, an extra dollar only adds 20% to your chjnce of winning. By 10, it's only 10% for a buck. You have to spend $10 to double your chances of winning. So the more tickets you have, the less useful your marginal extra dollar spent is. That's another way of looking at it. But yes, the theory is every (different) ticket has an equal chance of winning so every dollar is equally well spent. The only unpredictable factor is whether there are duplicate winners. One group of people where I worked won the lottery  about $2million  but had to share it 6 ways. That's a very large split compared to usual, then among the group it was split 11 ways. Each person got $30,000 or so. Better than nothing, but still... 
#6




Also, you forget that once you buy more tickets, the total amount of tickets sold will be larger. It comes down to whether this is a lotery where they draw a number from all possible numbers or a lottery where they guarantee someone is going to win. If you include the possibility of having the same number as somebody else it becomes different alltogether.
poss. 1 As explained above, your chances increase whith the factor of the amount of tickets you buy (buying 10 has a chance of winning of 10 times the probability when buying 1). poss 2 Almost the same as poss 1, but a tiny bit less because the total amount of tickets sold also grows when you buy more tickets. poss 3 Depends on how many people have the same number and whether there has to be a winner or not. 
#7




But let's consider the case where you buy one of every available ticket number. Then for sure when they pull the lucky number out of the bowl (or whatever), you're a winner.
On the other hand, I believe the finances work out that your prize is only 50%, maybe less, of what you spent buying tickets. That's assuming you don't have to share the prize. And further that's before they take out taxes (I doubt you can deduct the cost of the tickets) So, what may really count is not the odds of winning, but the expected return. Granted for very low numbers of tickets as could realistically happen, that does track the number of tickets bought. And its still depressingly low. 
#8




I did the math and decided that my chances of winning the lottery were pretty much the same whether I played or not.

#9




I did the math and played the numbers instead of the state sanctioned version.



#10




[QUOTE=md2000;12182134]
So  your odds of winning go up tremendously with the first ticket.QUOTE] The difference between 0.0000005% and 0.00000000% is only tremendous for certain values of tremendous. 
#11




Is that better than getting a 300% raise at your volunteer nopay job?

#12




Quote:
1  (175,711,535/175,711,536)^{n} where n = the number of tickets you buy. There's a slight diminishment of returns on the second and subsequent tickets with regards to probability, because of the small chance that two (or more) of your tickets will win. 
#13




Quote:
If you buy a $1 ticket, your expected return is $0.50 (depending on the game) whereas if you put the $1 in your pocket the expected return is $1. 
#14




With some progessive jackpots,sometimes it happenes that the payout is over the number of combinations (say, 200,000,000 combinations but the payout is 300,000,000). But even if you buy every combo, you are not guaranteed a profit because someone else may have the same combo. (say only one, the payout diminishes to 150,000,000). (though you might also win some lesser prizes for matching X numbers)
Not to mention the logistics of buying millions of tickets. Brian 


#15




Actually, if you put the dollar in your pocket your return (or expected return) is zero.

#16




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#17




Sure, but you'd be hard pressed to legally deduct gambling losses from your taxes.

#18




You can deduct gambling losses, but only against gambling wins. So if you lose $1000 at the blackjack tables today, win $8000 tomorrow, and lose $3000 the next day, you only owe taxes on $4000.

#19




Oh god, the sigfigs. THEY BURN!



#20




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#21




I'll buy a $1 ticket for big lotteries, simply to buy the dream.
Sometimes, I'll even throw in $20. Not because I know that does anything to increase my winnings it just gives me 20 numbers to patiently check versus just one, allowing me to dream a little bit more. O/T, personally, I hate lotteries. It's not that they're a tax on stupid people I think most people, rich or poor, understand that the math is ridiculously against them but simply because they're a tax, period. If governments want to raise money for a useful public service, let them do that honestly and openly. Bribing us with dreams of wealth just to get (some, very few) schools funded... skeevy. 
#22




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If it makes you feel better, you can consider the lottery as a voluntary tax on people who would like to help provide more support to education, and the drawing as a little game they include to make paying the voluntary tax more fun and less painful. Just keep telling yourself that virtually nobody thinks of the lottery as an investment program, and you may eventually come to believe it.
__________________
Christian "You won't like me when I'm angry. Because I always back up my rage with facts and documented sources."  The Credible Hulk 
#23




A reallife case of a man buying a ton of lottery tickets and making a profit
Stefan Klincewicz, PolishIrish businessman, headed a team of 28 Dubliners to try to buy all winning combinations for an Irish lottery in 1992. The National Lottery tried to thwart the group once they became aware of their plan (turning off some lottery vending machines etc.) so they weren't able to buy all numbers but amongst their 1.6 million tickets they got the winning numbers. Other people won too so the jackpot had to be split, but the group won in other categories. The syndicates final profit: £310,000 before expenses. (Note: after that, the lottery system changed in Ireland to prevent another group from trying the same thing.) A word to the wise: all this seems too complicated. The easiest way is to go splurge on a dinner at your local Chinese restaurant. The fortune cookie will reveal the winning lottery numbers.
__________________
Add your photo to the SDMB Portrait Gallery! 
#24




Ditto. For one measly dollar from my entertainment budget, I get a halfweek worth of daydreaming. Much more bangforthebuck than a $10 movie ticket, in my opinion.



#25




Don't get too excited about a scheme to buy all 175 million possible number combinations. You need order blanks to buy specific numbers, and they run through the machines a bit slower than randompick tickets do. If you figure out how many lottery outlets are in your state, and multiply by how many customordered tickets you could possibly buy in all the available minutes at each outlet in the days until the next draw, you're probably going to find your flock of henchmen won't have enough time to buy all the 175 million tickets you need.
There are other interfering factors, too. Every few thousand tix, every machine will need a new roll of paper. Does the cashier need to take an hourly reading? Can all those henchmen and all those cashiers go that long without a pee break? Can your henchmen fight off the regular customers who also want to buy tix? Can you be sure your henchmen won't cheat you?
__________________
"You know what they say about sleeping dogs; you can't trust 'em." Oliver Faltz 
#26




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Why, according to my emails, I've won multiple lotteries in Nigeria and never bought a ticket. 
#27




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#28




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Si (who once did the math on the NZ Lottery for a bit of fun) 
#29




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#30




[Gump]Momma always said  you got a 50% chance of winning the lottery, either you win or you don't![/Gump]

#31




Count me in the lottery = entertainment column.

#32




Quote:
The crowning moment came later when the professor used Alchemy as a straw man and the same student complained. He claimed that he had spent four years studying Alchemy and that the professor was misrepresenting it. There really is no hope for some people. Last edited by Lestrade; 03042010 at 09:21 AM. 
#33




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#34




I daydream about winning the lottery, too. I don't buy tickets, but I still manage to daydream about it. After all, my chances of winning are only 1 chance in 175,711,536 less than someone who does buy a ticket.



#35




I save my $1 each week and daydream that one of my relatives wins the lottery. I may not get rich but the return on investment is great.

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