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Another scratch ticket thread, for math geeks!
- Thread starter StephenCampbell
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Well these tickets also have other prizes. The $20 tickets also have $20 and $25 prizes, as well as $500, $1000, $5000, etc.
The $10 tickets also have $10, $20, $25, etc.
Yup they do and you may win some.
Consider this though. This thread is 3 pages long and you are the only one justifying your actions as a good plan. Everyone else is calling this at best, foolish and naive and at worst an indication you have a gambling problem.
Why not step back away, and take an honest review of why you're trying so hard at creating a methodology to beat the lottery system.
in fairness, hasn't he indicated he doesn't expect to beat the inevitable odds of the lottery system, but rather is just looking to stretch his entertainment dollars as far as possible before they're "spent"?
Not EVERYBODY who enjoys a little gambling as part of their fun is a compulsive gambler.....mostly not anyway
in fairness, hasn't he indicated he doesn't expect to beat the inevitable odds of the lottery system, but rather is just looking to stretch his entertainment dollars as far as possible before they're "spent"?
Not EVERYBODY who enjoys a little gambling as part of their fun is a compulsive gambler.....mostly not anyway
One person realizes this. One. Thank you. Thank you very much sir.
I was just about to post this very thing myself. I never said I expect to win a big prize, I never said I believe there's a way to get all my money back when I play. I never said any of that.
I asked those who are math-savvy to share with me what kind of ratio of $20 tickets, $10 tickets and $5 tickets they would buy if they were playing scratch and wanting to stretch their money as far as possible, while at the same time getting a handful of tickets that have really big prizes out there.
First, there are two goals here. I have hilited them in blue and red.
These two goals may well be contradictory. If you have to choose between them, which one is more important? In short, prioritize your goals.
Second, the first goal can be simply stated as maximizing the expected value. This number can be calculated, given specific input details.
The second goal is not clearly stated, so I have no idea how one would go about calculating that. "A handful" is how many exactly? "Really big" is how much exactly? What rate of "getting" these tickets is acceptable (stated as a percentage of tickets purchased)?
Raid has already described how to calculate expected value. He/she even gave an example. To calculate a more accurate expected value, you need to supply more accurate details. Either provide a complete list of odds and payouts for every ticket price, or provide the URL of the scratch lottery you're buying tickets from, so someone else can find the numbers.
If you're not willing to provide those, then at least describe what tools you have for doing calculations. Do you have a spreadsheet program? Which one? Do you understand right now how to take Raid's post #48 and make a spreadsheet from its example? If not, then you need to tell us what level of skill you have at making spreadsheets, so we can tell you what steps to take.
You should realize that a specific and accurate answer for expected return requires specific and accurate details of odds, prices, etc. If you can't provide that information, you won't get an accurate expected return.
You know, in light of how poorly tickets have paid back over the past couple months, I think back with wonder on this incident that I had on January 12th. I had only been playing for two weeks at that point, so I didn't realize how unusual it was.
I walked into Safeway with a $50 scratch budget, walked to the scratch vending machine, and bought two $5 tickets.
One of them was a loser, the other won $50.
I bought more tickets with the winnings, which in turn won more money. Within a few more tickets I got a $25 winner and then another $50 winner.
Not long after that I got a $100 winner, which put my total budget (including the original $50 I had) at $165. I should have quit then.
Nevertheless, I kept going. Prizes kept coming... my money just wouldn't all get lost. A couple times I got down to my last $5, and then I'd win another $50.
Three hours later, I finally thought it was going to wind down, and at this point I was hoping it would because I was running out of time.... but then I won $100 on a $10 ticket. Now I had about $130 total.
I bought a few losing tickets, bringing my total down to $90, and then left, because I had to get to a dinner.
Over the course of those three hours I put $560 into the machine and claimed $600 in prizes. I wonder if I hadn't been short on time, whether the $90 I was left with would have finally gotten lost if I had stuck around and spent it. But in any case, I now realize how extremely unusual and lucky that incident was. I've never had anything like it happen since.
I walked into Safeway with a $50 scratch budget, walked to the scratch vending machine, and bought two $5 tickets.
One of them was a loser, the other won $50.
I bought more tickets with the winnings, which in turn won more money. Within a few more tickets I got a $25 winner and then another $50 winner.
Not long after that I got a $100 winner, which put my total budget (including the original $50 I had) at $165. I should have quit then.
Nevertheless, I kept going. Prizes kept coming... my money just wouldn't all get lost. A couple times I got down to my last $5, and then I'd win another $50.
Three hours later, I finally thought it was going to wind down, and at this point I was hoping it would because I was running out of time.... but then I won $100 on a $10 ticket. Now I had about $130 total.
I bought a few losing tickets, bringing my total down to $90, and then left, because I had to get to a dinner.
Over the course of those three hours I put $560 into the machine and claimed $600 in prizes. I wonder if I hadn't been short on time, whether the $90 I was left with would have finally gotten lost if I had stuck around and spent it. But in any case, I now realize how extremely unusual and lucky that incident was. I've never had anything like it happen since.
These can be quantified and evaluated if you'd spend the time to actually work out the math. As I've demonstrated it's not that complicated.
What has me really concerned is this:
Dude, you spent 3 hours hanging around a Safeway. If there's any indication you have a problem; it's that!
You seem to like ratios ... here's the last bit of math that I'll give you because at this point I'm pretty sure your basis for playing is beyond rational choice.
From the expected values I've given you:
Expected Value of $20 ticket = $9.35 means you win $1 for every $2.14 spent or 1:2.14
Expected Value of $10 ticket = $4.67 means you win $1 for every $2.14 spent or (again) 1:2.14
Expected Value of $5 ticket = $1.32 means you win $1 for every $3.79 you spend. or 1:3.79
Again the same assumptions and missing information applies... we have no complete information on the odds and prize value nor much in the way of quantifiable information on your risk preference.
All this would be needed to calculate your utility of just playing the game. The only data we have on that was that at one point you decided $165 won was worth putting back into scratch tickets above all other possible utility at the time... Just imagine the dinner you could of had for that money!
Okay, how do I calculate the expected ticket value of this $20 game? Here are all the numbers:
$19,725,000 of tickets (total cost if you purchased all the tickets)
$1,578,000 in $20 prizes
$2,958,750 in $25 prizes
$2,054,600 in $50 prizes
$3,948,400 in $100 prizes
$525,400 in $200 prizes
$368,500 in $500 prizes
$159,000 in $1,000 prizes
$50,000 in $5,000 prizes
$250,000 in $50,000 prizes
$3,000,000 in $1,000,000 prizes
Total prizes: $14,892,650
It seems they're giving back 75% of the ticket cost in prizes.. does that make the expected ticket value $15?
Edit:
I just added up the numbers for a new $5 game as well:
$6,175,750 of tickets
$1,049,975 in $5 prizes
$308,690 in $10 prizes
$370,545 in $15 prizes
$494,060 in $20 prizes
$36,100 in $25 prizes
$215,430 in $30 prizes
$1,344,600 in $50 prizes
$102,000 in $75 prizes
$124,200 in $100 prizes
$10,000 in $1,000 prizes
$200,000 in $50,000 prizes
Total prizes: $4,255,600
Here the total prizes is only 69% of the total ticket cost... so that would be a $3.45 expected ticket value?
$19,725,000 of tickets (total cost if you purchased all the tickets)
$1,578,000 in $20 prizes
$2,958,750 in $25 prizes
$2,054,600 in $50 prizes
$3,948,400 in $100 prizes
$525,400 in $200 prizes
$368,500 in $500 prizes
$159,000 in $1,000 prizes
$50,000 in $5,000 prizes
$250,000 in $50,000 prizes
$3,000,000 in $1,000,000 prizes
Total prizes: $14,892,650
It seems they're giving back 75% of the ticket cost in prizes.. does that make the expected ticket value $15?
Edit:
I just added up the numbers for a new $5 game as well:
$6,175,750 of tickets
$1,049,975 in $5 prizes
$308,690 in $10 prizes
$370,545 in $15 prizes
$494,060 in $20 prizes
$36,100 in $25 prizes
$215,430 in $30 prizes
$1,344,600 in $50 prizes
$102,000 in $75 prizes
$124,200 in $100 prizes
$10,000 in $1,000 prizes
$200,000 in $50,000 prizes
Total prizes: $4,255,600
Here the total prizes is only 69% of the total ticket cost... so that would be a $3.45 expected ticket value?
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Seems about right, looks like you're getting a handle on the math, though your method is from the aggregate, if this represents the total prize payout and the total tickets sold then yes it still works.
Well, the lottery that I play has all the games listed on the website with "total tickets printed" and then the numbers of each prize amount that were printed.
If you add up all the ticket amounts for each prize, and multiply it by the overall odds of the game (i.e. 300,000 prizes multiplied by 3.76) you get a number very close to their "total tickets printed" number.
So that's how I got all the numbers.
Edit: So after calculating a $10 ticket as well, it seems that on average $5 tickets pay $0.69 on the dollar, $10 tickets pay $0.72 on the dollar and $20 tickets pay $0.75 on the dollar.
I'm sure $3, $2 and $1 tickets are miserable compared to any of those three. So I've been doing the right thing sticking to the upper three prices.
Logically I should only buy $20 tickets, but if I'm just going to be buying one or two, it really feels like I'd have much better odds of getting more of my money back with four $10 tickets or eight $5s. But I guess the math says otherwise, on average.
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Note that the odds will change over the life of the game, as prizes are won. This means that the expected value of a purchased ticket also changes.
I glanced at some scratch lottery sites, and some of them publish updated counts of how many prizes remain in each amount category. However, I never saw a published number of how many tickets remain, so it's not possible to recalculate an accurate expected value of a ticket.
The tickets remaining can always be calculated based on how many prizes won. It's always going to be extremely close to the average expected amount of tickets sold in order for the number of prizes claimed to be claimed. Things always regress to the average or whatever.
I could re-do the calculations on the specific games that I based my calculations on, and do it based on the actual current number of tickets still out there. You just add up all the prizes remaining and multiply it by the odds of the game.
The expected ticket value throughout the duration of the game will always hover right around the original number.
Here's a puzzler. This $20 ticket now appears to pay $0.98 on the dollar at this point in the game. Check it out:
Originally, there were 1,729,725 tickets printed. The overall odds for the game are 1 in 3.07.
The original breakdown went like this:
$34,594,500 to buy all the tickets
$2,767,560 in $20 prizes
$6,918,900 in $25 prizes
$3,604,400 in $50 prizes
$6,933,100 in $100 prizes
$1,012,000 in $200 prizes
$1,005,500 in $500 prizes
$293,000 in $1,000 prizes
$50,000 in $5,000 prizes
$100,000 in $10,000 prizes
$500,000 in $50,000 prizes
$3,000,000 in $1,000,000 prizes
Total prizes: $26,184,460
Expected return value: $0.7569 on the dollar, typical for a $20 game.
But now, check out the prizes remaining:
$224,440 in $20 prizes
$605,725 in $25 prizes
$283,750 in $50 prizes
$515,100 in $100 prizes
$77,200 in $200 prizes
$80,500 in $500 prizes
$25,000 in $1,000 prizes
$5,000 in $5,000 prizes
$20,000 in $10,000 prizes
$50,000 in $50,000 prizes
$1,000,000 in $1,000,000 prizes
Total prizes: $2,886,715
The prizes remaining consist of 47,854 winning tickets. Multiply that by 3.07 to get a very good estimate of how many tickets are still in existence, and you get 146,911, which multiplied by the $20 cost makes $2,938,220.
But there are still $2,886,715 of prizes out there!
85% of prizes have been claimed (and consequently we can surmise that about 85% of tickets have been purchased in this game), and yet because there is still a $1,000,000 prize out there, the expected ticket value is $0.9824 on the dollar.
If that $1,000,000 gets claimed, the expected ticket value drops to $0.6421 on the dollar.
Originally, there were 1,729,725 tickets printed. The overall odds for the game are 1 in 3.07.
The original breakdown went like this:
$34,594,500 to buy all the tickets
$2,767,560 in $20 prizes
$6,918,900 in $25 prizes
$3,604,400 in $50 prizes
$6,933,100 in $100 prizes
$1,012,000 in $200 prizes
$1,005,500 in $500 prizes
$293,000 in $1,000 prizes
$50,000 in $5,000 prizes
$100,000 in $10,000 prizes
$500,000 in $50,000 prizes
$3,000,000 in $1,000,000 prizes
Total prizes: $26,184,460
Expected return value: $0.7569 on the dollar, typical for a $20 game.
But now, check out the prizes remaining:
$224,440 in $20 prizes
$605,725 in $25 prizes
$283,750 in $50 prizes
$515,100 in $100 prizes
$77,200 in $200 prizes
$80,500 in $500 prizes
$25,000 in $1,000 prizes
$5,000 in $5,000 prizes
$20,000 in $10,000 prizes
$50,000 in $50,000 prizes
$1,000,000 in $1,000,000 prizes
Total prizes: $2,886,715
The prizes remaining consist of 47,854 winning tickets. Multiply that by 3.07 to get a very good estimate of how many tickets are still in existence, and you get 146,911, which multiplied by the $20 cost makes $2,938,220.
But there are still $2,886,715 of prizes out there!
85% of prizes have been claimed (and consequently we can surmise that about 85% of tickets have been purchased in this game), and yet because there is still a $1,000,000 prize out there, the expected ticket value is $0.9824 on the dollar.
If that $1,000,000 gets claimed, the expected ticket value drops to $0.6421 on the dollar.
You're estimating that it pays $0.9824 on the dollar.
You made an estimate of the number of tickets remaining. You haven't included an error term for that estimate, so no one knows how accurate that estimate is. You assert that it's "a very good estimate" based on what evidence?
There is a winning ticket every 3.07 tickets. There is NO way that the number of tickets sold is not very close to 3.07 times the number of prizes sold.
Though I don't have the official, technical mathematical terms to explain why, I would bet you $50,000 that I'm right. That's just how things works. With numbers this large, they average out and get very close to the expected value.
That's lot of strong and ambiguous statements coming from someone who doesn't know the "official, technical mathematical terms to explain why."
Do you always talk this way about things you don't know?
I said what's mathematically true. I know it the way a child knows that there's gravity.
Prove me wrong. Please.
If x number of prizes have been sold, the odds that the number of tickets sold are less than x times 2.95 or more than x times 3.20 (for a game whose overall odds are 1 in 3.07) is extremely unlikely. Borderline impossible.