Need an Odds Maker

[marko]

Any math wizards out there?

"Numbers is hard" for me so--for fun--trying to figure my odds of winning:

Massachusetts is holding FIVE, one million dollar lotteries for those who've been vaccinated against Covid; it's an effort to get more people injected.

DW, myself, mom and my brother are all eligible and have signed up for the lottery.

Now we've learned that out of the ~4 million eligible (vaccinated) only about half have signed up for the lottery.

So. With 4 players in my family, 5 separate lotteries and only about 2 million eligible to win (you cannot win twice), what are the odds of one of us in the family winning?

 

[38Chevy454]

The odds are pretty easy to figure. Take each condition separately to help follow the math. Assume that 2 million eligible for each drawing, therefore each drawing has 1 in 2,000,000 odds. Your chance of a family member winning in one of the drawings is 4 times 1 in 2 million, or 4 in 2 million. With 5 separate drawings, there is now 5 times more chances, so odds of someone in your family is 5 x 4 in 2 million, or 20 in 2 million. Doing some math reduction, 20 / 2,000,000 = 1 in 100,00. So the chances of one of your family members winning one of the million dollar prize over the five total drawings is 1 in 100,000.


Just as a side note. I think my state Ohio was the one that originated the vaccine lotteries. OH did it and then many states have followed. It did get a few more in the beginning to get vaccinated, before the drawings started, but then faded after that so it was a quick one time blip. OH did also give out full 4 year college scholarships in addition to anyone under 18, so each drawing had a $1M cash winner and 1 full scholarship winner.

 

[The Cosmic Avenger]

OK, so let's look at each lottery:

Each person has 1 chance in 2 million, but if it's any of you, it's 4 in 2 million, or 1 in 500,000.

I believe the odds of any event happening once during repeated chances would be summed, so your chances for all 5 lotteries would be 5 in 500,000, or 1 in 100,000. (That's not counting that previous winners might be disqualified from subsequent drawings, the effect of that would be trivial.)

I like the way Maryland did it; $40K per day for a couple of months, with $400K given away on the last day.

 

[The Cosmic Avenger]

Oh, and for anyone interested in odds and chance: one of my all-time favorite books is "The Drunkard's Walk: How Randomness Rules Our Lives" by Leonard Mlodinow, who interestingly also wrote for Star Trek:TNG. It's a real eye-opener.

 

[marko]

OK, so let's look at each lottery:

Each person has 1 chance in 2 million, but if it's any of you, it's 4 in 2 million, or 1 in 500,000.

I believe the odds of any event happening once during repeated chances would be summed, so your chances for all 5 lotteries would be 5 in 500,000, or 1 in 100,000. (That's not counting that previous winners might be disqualified from subsequent drawings, the effect of that would be trivial.)

I like the way Maryland did it; $40K per day for a couple of months, with $400K given away on the last day.

Thanks! We never buy lottery tickets but these look like really good odds. I'll keep you posted!!

 

[finnski1]

The odds are pretty easy to figure. Take each condition separately to help follow the math. Assume that 2 million eligible for each drawing, therefore each drawing has 1 in 2,000,000 odds. Your chance of a family member winning in one of the drawings is 4 times 1 in 2 million, or 4 in 2 million. With 5 separate drawings, there is now 5 times more chances, so odds of someone in your family is 5 x 4 in 2 million, or 20 in 2 million. Doing some math reduction, 20 / 2,000,000 = 1 in 100,00. So the chances of one of your family members winning one of the million dollar prize over the five total drawings is 1 in 100,000.


Just as a side note. I think my state Ohio was the one that originated the vaccine lotteries. OH did it and then many states have followed. It did get a few more in the beginning to get vaccinated, before the drawings started, but then faded after that so it was a quick one time blip. OH did also give out full 4 year college scholarships in addition to anyone under 18, so each drawing had a $1M cash winner and 1 full scholarship winner.

Wouldn't the odds stay at 1 in 500,000?
Each time there is a new drawing there are another 2,000,000 people so the odds are 1 in 5000,000(4/2,000,000) at each drawing. If you are going to multiply the 4 people times 5 drawings then you have to multiply the total people as well.

 

[ERD50]

Thanks! We never buy lottery tickets but these look like really good odds. I'll keep you posted!!

I guess it all depends on your view. But let's put some perspective on that.

Let's imagine you had a 1 in 100,000 chance of hitting a small target with a dart.

Let's say you threw a dart every ten seconds, eight hours a day, no breaks. On average, assume you'd hit the target by the 50,000th throw.

That's 500,000 seconds, divided by 60 = 8333.33 minutes, divided by 60 = 138.89 hours, divided by 8 hours a day, 17.36 days of throwing darts continuously, for 8 hours a day.

-ERD50

 

[ERD50]

The odds are pretty easy to figure. Take each condition separately to help follow the math. Assume that 2 million eligible for each drawing, therefore each drawing has 1 in 2,000,000 odds. ....

Wait - is there a winner for each drawing? Most lotteries generate a number, and if no one picked it, no one wins. If multiples pick it, they split the win.

So the number of people entered would have nothing to do with the chance of winning. The number entered only affect your odds of having to split the prize.

edit/add:

https://www.mass.gov/news/commonwealth-launches-mass-vaxmillions-vaccine-lottery-program

OK, they pick a person each time, no numbers to choose. So yes, in 5 drawings, each person has a 5/(total people in each pick) chance to win.

-ERD50

 

[ERD50]

Wouldn't the odds stay at 1 in 500,000?
Each time there is a new drawing there are another 2,000,000 people so the odds are 1 in 5000,000(4/2,000,000) at each drawing. If you are going to multiply the 4 people times 5 drawings then you have to multiply the total people as well.

No.

Each drawing is a separate event. Makes no difference if the other people are the same people or not, and one has no effect on the other. As long as you are one of the 2M in each pick, your odds in each are 1 in 2M. So in 5 picks, your odds are 5 in 2M. Odds for 4 people and 5 picks are 20 in 2M, which is 1 in 100,000 if you did all 5 picks.

-ERD50

 

[finnski1]

No.

Each drawing is a separate event. Makes no difference if the other people are the same people or not, and one has no effect on the other. As long as you are one of the 2M in each pick, your odds in each are 1 in 2M. So in 5 picks, your odds are 5 in 2M. Odds for 4 people and 5 picks are 20 in 2M, which is 1 in 100,000 if you did all 5 picks.

-ERD50

But.. After the first drawing( at which your odds were 1 in 2 million x 4 people or 1 in 500,000) there are now 1,999,999 people eligible for the 2nd drawing. So your odds on the 2nd drawing are now 4/1,999,999 and by the final drawing your odds improve greatly to 4 in 1,999,996 or effectively 1 in 500,000.

What am I missing? I didn't think is was additive. There are 5 separate events(drawings) with 1 less person each time. Don't you have to look at it this way?

 

[finnski1]

But.. After the first drawing( at which your odds were 1 in 2 million x 4 people or 1 in 500,000) there are now 1,999,999 people eligible for the 2nd drawing. So your odds on the 2nd drawing are now 4/1,999,999 and by the final drawing your odds improve greatly to 4 in 1,999,996 or effectively 1 in 500,000.

What am I missing? I didn't think is was additive. There are 5 separate events(drawings) with 1 less person each time. Don't you have to look at it this way?

Never mind. I see my mistake.

 

[easysurfer]

Odds are I'm not going to dwell on this as won't get the time back in my life .

 

[The Cosmic Avenger]

Actually, I knew it was much more complicated than that to do it right, but that was a rough guess without looking it up, and I was right, the difference is negligible. The formula for something happening once for a repeated draw/chance with identical odds each time is actually pn = (1 - pn-1) * p1 + pn-1, where pn is the probability of something occurring in n iterations, and the only way I know how to do this manually is start where you know p1 and solve for p2, then use p2 to solve for p3, etc. So here are my results, feel free to double check:

p1 = 0.000002 (1/500,000)

p2 = 0.000003999992 (1/250,000.5)

p3 = 0.000005999984(1/166,667.1)

p4 = 0.000007999972000032 (1/125,000.43)

p5 = 0.000009999956000088 (1/100,00.44)

 

[OldShooter]

Thanks! We never buy lottery tickets but these look like really good odds. I'll keep you posted!!

The way I (math/science/engineering geek) look at odds like that is that your chances of winning are about the same whether you enter or not. Better than PowerBall, though.

According to the National Weather Service, a person has a 1-in-15,300 chance of getting struck by lightning in their lifetime, defined as an 80-year span. Are you worried?

 

[marko]

I guess it all depends on your view. But let's put some perspective on that.

Let's imagine you had a 1 in 100,000 chance of hitting a small target with a dart.


-ERD50

I meant "good odds" versus a regular lottery. I'm not sure of the odds in a regular state type lottery but I'd guess that they're considerably worse than 1 in 100,000.

 

[marko]

The way I (math/science/engineering geek) look at odds like that is that your chances of winning are about the same whether you enter or not. Better than PowerBall, though.

According to the National Weather Service, a person has a 1-in-15,300 chance of getting struck by lightning in their lifetime, defined as an 80-year span. Are you worried?

I was already hit by lightning as a kid. What are my odds of it happening twice?

 

[OldShooter]

[/B]

I was already hit by lightning as a kid. What are my odds of it happening twice?

Odds on getting a second hit are the same as the odds getting the first one. Low.

 

[Chuckanut]

The odds are pretty easy to figure. Take each condition separately to help follow the math. Assume that 2 million eligible for each drawing, therefore each drawing has 1 in 2,000,000 odds. Your chance of a family member winning in one of the drawings is 4 times 1 in 2 million, or 4 in 2 million. With 5 separate drawings, there is now 5 times more chances, so odds of someone in your family is 5 x 4 in 2 million, or 20 in 2 million. Doing some math reduction, 20 / 2,000,000 = 1 in 100,00. So the chances of one of your family members winning one of the million dollar prize over the five total drawings is 1 in 100,000.

I wonder if those odds are just too great to overcome vaccine hesitancy. Maybe if they split the money into groups of $50,000 the odds might be good enough to overcome vaccine hesitancy. If, my math is right, that would bring the odds of winning down to 1 in 5,000. And 50 Grand is nothing to sneeze at for most of the working people in this world

 

[OldShooter]

I wonder if those odds are just too great to overcome vaccine hesitancy. Maybe if they split the money into groups of $50,000 the odds might be good enough to overcome vaccine hesitancy. If, my math is right, that would bring the odds of winning down to 1 in 5,000. And 50 Grand is nothing to sneeze at for most of the working people in this world

I think most people don't understand at anything like this level. Proof is the continuing existence of stunningly profitable lotteries and casinos.

 

[ERD50]

I wonder if those odds are just too great to overcome vaccine hesitancy. Maybe if they split the money into groups of $50,000 the odds might be good enough to overcome vaccine hesitancy. If, my math is right, that would bring the odds of winning down to 1 in 5,000. And 50 Grand is nothing to sneeze at for most of the working people in this world

I think most people don't understand at anything like this level. Proof is the continuing existence of stunningly profitable lotteries and casinos.

But I think Chuckanut makes a good point. I do think more people would go for it if the odds were better. After all, $50,000 is nothing to sneeze at.

edit - delete a part of message, everyone who is vaccinated is eligible, not just the late ones.

-ERD50