Probability problem: The odds of winning the lottery is 1:1million, but a lotto ticket costs $2 each

[JEDI]

if a ticket costs $1, then it's easy. the jackpot will have to be $1million to match the odds.

but if each tix cost $2, then how much more will the jackpot have to be?

$2million???

Can someone explain it?

THX

 

[91TTZ]

Keep in mind that even if you buy a million tickets, you still aren't guaranteed to win. Also, just because you're buying all those tickets doesn't mean that other people aren't buying some also.

 

[Random Variable]

I'd help you if I understood your question.

 

[cjgallen]

There are several hundred million combinations of numbers . . .

 

[glenn1]

if a ticket costs $1, then it's easy. the jackpot will have to be $1million to match the odds.

Even thinking in terms of the "payout matching the odds" is somewhat misguided when the probabilities are that small. Whether the ticket costs a buck, two bucks, five or ten makes no difference when you have a one-in-a-million shot at winning, it's basically throwing your money away no matter what the face value of the ticket is.

 

[KLin]

42 million dollars

 

[Gibsons]

Originally posted by: JEDI
if a ticket costs $1, then it's easy. the jackpot will have to be $1million to match the odds.

but if each tix cost $2, then how much more will the jackpot have to be?

$2million???

Can someone explain it?

THX

Divide total winnings by cost of single chance to win. If the cost/winnings ratio matches the chance/odds ratio, then it's even. ie, 1 in a million chance to win matches 1 dollar for 1 million dollars.

 

[mugs]

Originally posted by: cjgallen
There are several hundred million combinations of numbers . . .

If the odds are 1:1 million, then there are 1 million combinations of numbers...

 

[Ronin]

It is not a 1:1 ratio. Because of the number variables (even though you will only see each number once per draw), 1 million combinations is abysmally small to the actual number.

 

[mugs]

ASSUMING there is only one payout level in your HYPOTHETICAL situation, the jackpot would need to be $2 million or more for your expected outcome to be $2 or more (for one ticket).

However, if the only prize was the jackpot, nobody would ever play the lottery because they'd never win. If there are multiple payout levels, you need to multiply the probability of winning at each payout level by its respective payout, and add the results. That is your expected outcome.

Example:
Payout * Odds
$1 million * 1/1 million = $1
$100k * 1/200k = $.50
$50k * 1/150k = $.33
$5 * 1/20 = $.25

$1 + $.50 + $.33 + $.25 = $2.08, so if the tickets are $2 your expected payout is greater than the cost to play. That doesn't mean you're likely to come out ahead though, the guy that wins the jackpot throws off the average for everyone else.

 

[GagHalfrunt]

A coin flip needs to pay out the same as the bet since it's 50/50. If the odds are a million to one $1 a dumb bet for a payout less than a million and a good bet if the payout is more than a million. Up the ticket price to $2 and retain the same million to one odds and the break even point is $2 million payout. Less than that is a bad bet at $2, more than that is a good bet. That of course assumes the drawing is taking place in a vacuum. In the real world you're going to lose at least 40% in taxes. On a $1 bet the break even point is close to $1.7 million and on a $2 bet 3.4 million.

 

[mrrman]

14 million to 1 odds...buying more tickets doesnt improve your odds..you just get more tickets...the question is if you buy x number of tickets, what are the odds if that ticket will win.....answer 14 million to 1

 

[DrEldarion]

Originally posted by: mrrman
14 million to 1 odds...buying more tickets doesnt improve your odds..you just get more tickets...the question is if you buy x number of tickets, what are the odds if that ticket will win.....answer 14 million to 1

If the numbers aren't repeats, then you don't increase the odds of the ticket, but you do increase YOUR odds. If you have one of every combination, your chances of winning are 1:1.

The problem is that there is a HUGE number of combinations. For instance, if there are 65 balls and 6 are picked to determine the winning number, the amount of combinations is 65*64*63*62*61*60, or 59,471,193,600. If each ticket is $2, you'll need $118,942,387,200. That means the jackpot has to be nearly $119 BILLION dollars. Not very practical.

Oh, that's also assuming that nobody else wins as well. If you both win, you both get half, and then you're screwed

Oh, that's also assuming that you don't have to pay taxes on the winnings as well, which you do, so that's even more of a jackpot you'd need...

So, basically, this method should never be considered.

(I think my math is right...)

Edit: No, my math is NOT right. I forgot that the numbers can be arranged in different ways and that those ways don't count as separate instances. Therefore, the total would be 65*64*63*62*61&60/ 6! to get $165,197,760 which is slightly more reasonable, but still quite a lot.

 

[JEDI]

so if the odds are 1:1million and each lotto ticket is $2, then i need a $2million prize to break even (assuming no taxes)

thx

 

[DaveSimmons]

Originally posted by: JEDI
so if the odds are 1:1million and each lotto ticket is $2, then i need a $2million prize to break even (assuming no taxes)

thx

Except the payout is often only half the amount if you take it immediately instead of over 20+ years, and you do have 30-50% taken out of that half for taxes.

So for 1:1 million odds you need a $3-4 million prize.

 

[aplefka]

You have to also account that even if you bought one ticket for every single combination there is, you're still only going to make some money from it as you spent a good $750,000 on tickets alone. I remember hearing the math, some actuaries or stock brokers in New York tried to do this. It's basically not worth it unless it gets up to something in the $200+ million range.

 

[mugs]

Originally posted by: aplefka
You have to also account that even if you bought one ticket for every single combination there is, you're still only going to make some money from it as you spent a good $750,000 on tickets alone. I remember hearing the math, some actuaries or stock brokers in New York tried to do this. It's basically not worth it unless it gets up to something in the $200+ million range.

The math is not difficult at all... the amount of money necessary to make it worthwhile depends entirely on the odds of winning. Unfortunately it's impossible to know if someone else will win (cutting the jackpot in half), and it would take an army of people to buy the millions of tickets necessary to guarantee winning most lotteries, and then another army of people to find the winning ticket when you do win.