Does your Lottery chances double by playing double the tickets?

Question

Cetamega,

Yes I'm sorry, I did mean to say 1:1, not 2:1.

Of course I was just talking the Gross Winnings, not the net. I do raelize that a large chunk would be taken out for taxes, and a penalty for taking it all at once in a "Lump Sum"

Answer 1

NO!

Answer 2

well here in canada lf l play pick 3 or pick 4 l can play double and win double.

Answer 3

Uhhhhh...Maryn, and original poster.....

2 in 100 IS double, or twice, 1 in 100. The reason "many people think" that is.......it's true.

2 in 100 can indeed be expressed as 1 in 50, which, if you realize that "x in y" is the same as the fraction, "x/y", you will see is obvious.

To answer the original question.. if the odds against winning with a single bet are "x", then the odds against winning with two bets (assuming the bets are independent) are "x/2". In other words, those odds are halved.

HOWEVER--and this is where you are getting confused--buying a THIRD ticket does NOT halve the odds AGAIN. The odds for three bets are "x/3", which is 1/3 the odds against, or three times the likelihood of winning (3 in 80,000,000). So if your original odds were 80,000,000 to 1, then buying two tickets decreases your odds to 40,000,000 to one, three tickets gives you 26,666,666 to one, four gives you 20,000,000 to one, 1000 gives you 80,000 to one, etc. etc.

In order to keep successively halving the odds against you, you need to buy 1, then 2, then 4, then 8, then 16, etc. tickets.

Answer 4

Assuming you are buying tickets where the computer picks your numbers, buying a second ticket will almost double the chances of winning, but not quite.  You have to look at it in reverse in order for the math to work out.  

Assume there are 100 possible numbers, and you buy one ticket.  With that one ticket, you have a 0.01 chance of winning and a 0.99 chance of losing.  If you buy a second ticket, you now have a 0.99*0.99 chance of losing or a 0.9801 chance of losing.  You chance at winning has therefore increased to 0.0199.

Let's say you bought 50 tickets. Your chance of losing would be 0.99^50, which works out to a 0.605 percent chance of losing.  Your odds of winning have increased to 0.395.  This means that your chances of winning increase 40 times, but you have to spend 50 times the money to get there.

Let's say you buy 100 tickets.  Your chance of losing would be 0.99^100, which works out to a 0.366 percent chance of losing.  Your odds of winning have increased to 0.734.  This means that your chances of winning increase 73 times, but you have to spend 100 times the money to get there.

Re Cetamega's comments.  This wasn't about buying every one of the 100 numbers, it was about buying 100 tickets, which, if the computer selects them at random, will include some duplicates.  Buying 100 tickets will indeed result in only a 73.4% chance of winning.  

This is how a lottery with a 1 in 80 million chance of winning can sell a 100 million tickets and still have no one hit the jackpot.

Buying 40 million tickets where the odds of a single ticket winning are 1 in 80 million gets you a 39.3% chance of winning.

Buying 80 million tickets where the odds of a single ticket winning are 1 in 80 million gets you a 63.2% chance of winning.

Buying 100 million tickets where the odds of a single ticket winning are 1 in 80 million gets you a 71.3% chance of winning.

To get to exactly 50% odds, where the odds of a single ticket winning are 1 in 80 million would require the purchase of almost 55.5 million tickets.

Answer 5

"Assuming you are buying tickets where the computer picks your numbers, buying a second ticket will almost double the chances of winning, but not quite. You have to look at it in reverse in order for the math to work out.

Assume there are 100 possible numbers, and you buy one ticket. With that one ticket, you have a 0.01 chance of winning and a 0.99 chance of losing. If you buy a second ticket, you now have a 0.99*0.99 chance of losing or a 0.9801 chance of losing. You chance at winning has therefore increased to 0.0199.

Let's say you bought 50 tickets. Your chance of losing would be 0.99^50, which works out to a 0.605 percent chance of losing. Your odds of winning have increased to 0.395. This means that your chances of winning increase 40 times, but you have to spend 50 times the money to get there.

Let's say you buy 100 tickets. Your chance of losing would be 0.99^100, which works out to a 0.366 percent chance of losing. Your odds of winning have increased to 0.734. This means that your chances of winning increase 73 times, but you have to spend 100 times the money to get there"

So buying every ticket gets you a 73% chance of winning?  Your math is not correct somewhere.

As for the original question, your odds do double.  

"I say this: With a $1 bet your odds are 79,999,999 to 1, and after a $2 bet your odds are 79,999,998 to 1."

A $2 makes it 79,999,998 to 2, not 79,999,998 to 1.

"If it actually brought it in half every time I doubled my bet, Mathematically you'd need to bet about $8 Million Dollars to bring the odds down to 2-to-1, which would give you a 50% chance of winning."

Your math is horrible as well.  To bring the odds down to 1 to 1, (which comes out to 50%, not 2 to 1.  2 to 1 is 33%) you would have to buy 40 million tickets.  

"So why wouldn't someone who had , lets says $50-$100 Million dollars do that? Afetr all, they'd have a 50/50 chance of winning $80 Million dollars, with a $8 Million dollar bet."

First:  They have to buy 40 million, not 8 million

Second: A lottery with 80 million to 1 odds, will not pay out $80 million.  They take huge amounts of money off of the top.    So they are spending $40 million to have a 50% chance at winning maybe $60 million.

Answer 6

Of course not. Your math is solid.

Simplified, say there are 100 lottery tickets sold. You buy one, your odds of winning are 1 in 100. You double the number you buy, and your odds are now 2 in 100--hardly double.