Powerball Odds?

I saw this on the news the other day and something didn't add up...



It appears to me they are giving a person's lifetime odds of being bit by a shark or stuck by lightning, etc..., against winning a single game of Powerball.

So I attempted to figure out lifetime odds.

If any singly ticket for a game has a 1 in 292 Million chance of winning then if someone played every week (twice a week) for 50 years they would play 2 * 52 * 50 or 5,200 games.

Instead of having a 1 in 292 Million chance they now have a 5,200 in 292 Million chance of winning a Powerball jackpot in their lifetime (50 years of playing every game twice a week.)

Well 5,200 / 292,000,000 = 1 / 56,153....

That means if you play every game for your entire life, starting at 18 to 68 , you have a 1 in 56,000 chance of winning a Powerball jackpot!

Those odds aren't nearly as bad as I thought.

Further if you played 5 games instead 1 game ($10 instead of $2) your odds of winning a jackpot go up to a mere 1 in 11,00.

Sure it's not likely, not by a long shot- but in a country of millions of people, 1 in 11,000 isn't that bad.

And that's just winning the jackpot. Adds are far better to win the $1 million second prize in your lifetime.

As for the cost? Ignoring interest, assuming current prices, the cost of playing 1 game twice a week for 50 years is $10,400. And playing 5 games at a time, of course $52,000. About a thousand a year.

My coworkers get agitated when I thank them for funding Colorado State Parks through the lottery.

GreenGeep said:

My coworkers get agitated when I thank them for funding Colorado State Parks through the lottery.

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We typically call it the "****** tax" down here. There are two gas stations just this side of the AL line by the interstate and their parking lots are gridlocked, cars lined up on both sides of the road as far as can be seen in each direction.

Your math is wrong. What you calculated is the odds of winning if purchasing X number of individual and unique sets of numbers for a single draw.

skeptic said:

Your math is wrong. What you calculated is the odds of winning if purchasing X number of individual and unique sets of numbers for a single draw.

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He multiplied when he should have exponent-ed.

skeptic said:

Your math is wrong. What you calculated is the odds of winning if purchasing X number of individual and unique sets of numbers for a single draw.

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Precisely, your chance of winning each drawing doesn't increase just because you play in more drawings. The only way to increase your chance is to increase your play in a single drawing.

It's like flipping a coin . . . just because it's turned up heads 3 times in a row doesn't change the odds of the next flip, it's still 50/50

BobKid said:

Precisely, your chance of winning each drawing doesn't increase just because you play in more drawings. The only way to increase your chance is to increase your play in a single drawing.

It's like flipping a coin . . . just because it's turned up heads 3 times in a row doesn't change the odds of the next flip, it's still 50/50

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Well, that's different.. A more accurate analogy would be if you flip a coin 3 times in a row what are the chances or ANY of those 3 being heads. Using Joe's math, the odds would be 150%. The correct way to determine it is:

1/2 + (1/2 * 1/2) + (1/2 * 1/2 * 1/2) =
1/2 + 1/4 + 1/8 =
4/8 + 2/8 + 1/8 =
7/8

Calculating the odds of winning the lottery at least once if you bought a ticket every draw for the rest of your life is much harder to calculate. Assuming 50 years at 2 draws per week:

1/292M + (1/292 * 1/292M) + (1/292M * 1/292M * 1/292M) + .... (1/292M^100)

skeptic said:

Well, that's different.. A more accurate analogy would be if you flip a coin 3 times in a row what are the chances or ANY of those 3 being heads. Using Joe's math, the odds would be 150%. The correct way to determine it is:



1/2 + (1/2 * 1/2) + (1/2 * 1/2 * 1/2) =

1/2 + 1/4 + 1/8 =

4/8 + 2/8 + 1/8 =

7/8



Calculating the odds of winning the lottery at least once if you bought a ticket every draw for the rest of your life is much harder to calculate. Assuming 50 years at 2 draws per week:



1/292M + (1/292 * 1/292M) + (1/292M * 1/292M * 1/292M) + .... (1/292M^100)

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Your coin math is wrong. You can't add them, each flip is independent and still will always equal 50/50 odds no matter what

abqtj said:

Your coin math is wrong. You can't add them, each flip is independent and still will always equal 50/50 odds no matter what

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Your understanding of the described situation is wrong. You are correct in that it makes zero difference what the previous 1, 2 or 10,000 flips are the next flip is 50/50 heads or tails. But that's NOT what we are talking about. What we are talking about is what are the chances of ANY of those flips being heads (any of the lottery draws being your numbers). If you flip a coin 3 times the odds of the 4th being heads is still 1/2 (50%), but the odds of at least one of those 3 previous flips being heads is 7/8.

Although I you are correct, my math is wrong. It works for the coin flip, but it's more like: 1 - (n-1/n)^m

Where n = possible combinations (2 for coin, 292M for lottery), and m = number of tries. It's been a loooooong time since I've had a class or even thought about this stuff. I did it in my head with the coin and that worked, but only because 2-1 = 1 and of course 1 to any power is still 1.

I may still have it wrong, but this looks better and makes more sense.

edit: So I believe the chances of BOP winning the lottery if he buys a ticket every draw for the next 50 years is:

1 - (291,999,999/292,000,000)^100

I don't believe my calculator goes that high, we can leave the task of computing 291,999,999 to the 100th power to Joe... After that, calculating 292M to the 100th power and a bit of division should be easy enough...

Thank you, I consulted a self professed math expert earlier in the day but he couldn't figure out what was wrong b/c he's not a "probability" expert. He mentioned something about something but the explanation in post 7 makes more sense.

I was concerned because if I followed my "logic" I could plainly see there was some amount I could spend on lottery tickets a week that would "guarantee" a win, which of course is impossible.

Anyway the final math...
(1 - (291,999,999/292,000,000)^100) * 100 =

0.000034246569536968185596590939%

Or

1 in 2,920,000 chance of winning if playing every game for your life!

Makes much more sense now... Glad we figured this out before I put everything I had to future lottery tickets!

They've always said even with one jackpot big enough to be larger than the cost to purchase every number combo and thus guaranteeing a win, they couldn't physically print that number of tickets in time before the drawing.

abqtj said:

They've always said even with one jackpot big enough to be larger than the cost to purchase every number combo and thus guaranteeing a win, they couldn't physically print that number of tickets in time before the drawing.

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Well, no one person, or even group of people (it's been tried) have been able to buy every combination in time. But over the course of a week (or half week) they can sell more than 292 million tickets for a jackpot like this.

I suspect the biggest problem is producing enough of the correctly filled out cards with the manual numbers and scanning them as it's vastly faster to use "quick pick."

If they ever allowed online entries... then it would change the game. I know some states have online subscriptions you could buy (I actually had one for the regular NY Lottery before I got sick) but not for single games.

I'll take your word on the odds - I didn't search for a scientific calculator that could calculate to that many digits, but apparently they are out there... One in ~3 million just sounds more likely than one in 56,000.

I'm not a math expert, nor do I claim to know much about probability. I just did it in my head for 3 coin flips then 2 dice rolls then putzed around with simple formulas until one worked. This is why I say it might still be wrong, but at least it seems to work with numbers low enough to count.

Here is another way to look at it - if you don't play you have a zero chance of winning. If you spend $20/month on lottery, you have ALMOST zero chance of winning, but if $20/month doesn't make any difference to you then almost zero is better than zero.

On that note, I've been up since 5:30am and it's almost 3am. I'm going to bed.

Agreed. People laugh at those who play the lottery but for the vast majority of americans, even a 1 in 292 million chance is still the best chance they have at getting mega rich, without having to be the victim of some painful accident anyway.

Think of all the hungry kids that could have been fed if their parents didn't give the money away.

GreenGeep said:

Think of all the hungry kids that could have been fed if their parents didn't give the money away.

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That is what Food Stamps are for!

Since the math people are in this thread, I have a question. I have no education in game theory or statistics, so bear with me while I explain.

If a man offers me a bet where I put in a dollar, and the odds of me winning ten dollars are 1 in 20, that is obviously a bad bet, and I should not take it.

If a man offers me a bet where i put in a dollar, and the odds of me winning ten dollars are 1 in 10, that's even money and in the long run I come out even. Again, not a great bet, and I won't participate, but better than deal #1.

If a man offers me a bet where I put in a dollar, and the odds of me winning ten dollars are 1 in 5, I should do this, and keep on doing it as long as possible, because I'm going to be making good money over the long haul.

Am I right so far?

If that was correct, then any time the lotto big prize (ignoring the smaller ones) is larger than the odds of winning, it's a "good bet" and you should participate, right? (Also assuming the ticket is $1. If tickets are $2, the payout needs to be more than double the odds against you.)

Is that correct? Or do I have a basic bad assumption or misunderstanding in there somewhere?

I have no math skills in probabilities or statistics.....

All I know, is for the mere sum of $2, I get a couple of days of dreaming of what I MIGHT get to do should I win.

I'll bite.

Al Johnson said:

Since the math people are in this thread, I have a question. I have no education in game theory or statistics, so bear with me while I explain.

If a man offers me a bet where I put in a dollar, and the odds of me winning ten dollars are 1 in 20, that is obviously a bad bet, and I should not take it.

If a man offers me a bet where i put in a dollar, and the odds of me winning ten dollars are 1 in 10, that's even money and in the long run I come out even. Again, not a great bet, and I won't participate, but better than deal #1.

If a man offers me a bet where I put in a dollar, and the odds of me winning ten dollars are 1 in 5, I should do this, and keep on doing it as long as possible, because I'm going to be making good money over the long haul.

Am I right so far?

If that was correct, then any time the lotto big prize (ignoring the smaller ones) is larger than the odds of winning, it's a "good bet" and you should participate, right? (Also assuming the ticket is $1. If tickets are $2, the payout needs to be more than double the odds against you.)

Is that correct? Or do I have a basic bad assumption or misunderstanding in there somewhere?

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Your logic is generally correct however the problem with a lottery jackpot is that if multiple people win the prize is divided amongst all winners. So while you might win the full jackpot you might win half, or even a quarter, in which case your winnings may not have been enough to make it favorable to play.

SAD said:

I have no math skills in probabilities or statistics.....

All I know, is for the mere sum of $2, I get a couple of days of dreaming of what I MIGHT get to do should I win.

I'll bite.

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Same here. If it gets over $300m I'll go drop $20-30. Fully worth it in my opinion.