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Lottery Fever!
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<blockquote data-quote="Brownslave688" data-source="post: 2000551" data-attributes="member: 34439"><p>Playing the lottery is about expected value, not probability. It's not just the odds of winning, it also has to do with the expected rate of return.</p><p></p><p>Think of it this way, suppose that we played a game where we shuffled a deck and picked the card from the top. If the card is the ace of spades I give you $0.01, any other card and you give me $0.01. Would you play?</p><p></p><p>How about if we changed the rules and I gave you $5 each time the ace of spades comes up, would you play then?</p><p></p><p>The expected value for the lottery is the probability of winning times the amount you win minus the probability of losing times the cost of the ticket. If the expected value is positive then you should play, if it is negative you shouldn't. If it's zero, it's up to you.</p><p></p><p>For example what if your odds of winning are 1/1000, the payoff is $1, and each ticket costs $1, would you play? I wouldn't, and here are the numbers to back it up: your expected value is</p><p>E = odds of winning * amount you win - odds of losing*amount you lose </p><p>= 1/1000*$1 - 999/1000*$1 </p><p>= -.998</p><p>That game is a loser, you should expect to lose $0.998 every time you play.</p><p></p><p>If the payoff is $400 and the cost of the ticket is $.50 then it might not be as obvious if you should play or not. But, your expected value is </p><p>1/1000*$10 - 999/1000*$0.5 = -0.0995</p><p>Better, but still a loser of about a dime each time you play.</p><p></p><p>If the payoff is $1,0000,000 and the cost of the ticket is $0.01 then your expected value is </p><p>1/1000*$1,000,000 - 999/1000*$0.01 = 999.99001</p><p></p><p>The expected value is positive, so you should play. In that case you should buy all 1,000 tickets for $10 and pocket the $1,000,000 for a profit of $999,990.</p><p></p><p>Forgive any math errors ahead of time, hopefully this gives you the idea.</p></blockquote><p></p>
[QUOTE="Brownslave688, post: 2000551, member: 34439"] Playing the lottery is about expected value, not probability. It's not just the odds of winning, it also has to do with the expected rate of return. Think of it this way, suppose that we played a game where we shuffled a deck and picked the card from the top. If the card is the ace of spades I give you $0.01, any other card and you give me $0.01. Would you play? How about if we changed the rules and I gave you $5 each time the ace of spades comes up, would you play then? The expected value for the lottery is the probability of winning times the amount you win minus the probability of losing times the cost of the ticket. If the expected value is positive then you should play, if it is negative you shouldn't. If it's zero, it's up to you. For example what if your odds of winning are 1/1000, the payoff is $1, and each ticket costs $1, would you play? I wouldn't, and here are the numbers to back it up: your expected value is E = odds of winning * amount you win - odds of losing*amount you lose = 1/1000*$1 - 999/1000*$1 = -.998 That game is a loser, you should expect to lose $0.998 every time you play. If the payoff is $400 and the cost of the ticket is $.50 then it might not be as obvious if you should play or not. But, your expected value is 1/1000*$10 - 999/1000*$0.5 = -0.0995 Better, but still a loser of about a dime each time you play. If the payoff is $1,0000,000 and the cost of the ticket is $0.01 then your expected value is 1/1000*$1,000,000 - 999/1000*$0.01 = 999.99001 The expected value is positive, so you should play. In that case you should buy all 1,000 tickets for $10 and pocket the $1,000,000 for a profit of $999,990. Forgive any math errors ahead of time, hopefully this gives you the idea. [/QUOTE]
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