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Another scratch ticket thread, for math geeks!
- Thread starter StephenCampbell
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Extremely unlikely, as far as it is not precise, is certainly different than "there is NO way."
If you send me $20, I'll send you back $17. That's a much better return than your scratchies.
What number is "extremely unlikely" or "borderline impossible"?
If you know the confidence level of your estimate (in a statistical sense), then you should know how to calculate the range of expected values and the confidence interval thereof. If you know this, then why don't you do it that way, instead of resorting to imprecise unmathematical terms like "extremely unlikely"?
You're the one who asserted a "very good estimate". You didn't provide any evidence that it was "very good", nor numerically quantify what that meant. Is it 90% confidence? 95%? What does a 95% or even 99.9% confidence mean when applied to the odds of winning the remaining single million-dollar prize?
You go back and forth between using imprecise terms like "very good estimate" or "extremely unlikely", and precise terms like the calculation of initial expected value for a ticket. I have no reason to conclude that your imprecise terms are backed by calculations unless I ask if they are. If you fail to provide calculations, what should I conclude?
You have also used completely inaccurate calculations in the past for fundamental values, such as the odds of getting a prize (e.g. 106% in your first post). These fundamental inaccuracies suggest to me that at least some of your calculations are inaccurate. If you don't post your calculations, what should I conclude?
If I see errors in your posted calculations, why should I conclude that your use of imprecise terms like "very good estimate" are supported by an calculations at all, much less the correct calculations?
Be consistent, be precise, and get the basic calculations right.
What are you rambling about? I wasn't talking about the odds of winning the million dollar prize.
And the 106% odds thing was corrected to mean 106% expected chance, on average.
Oh, for goodness sake...will you please stop confusing everything with factual, mathematically and statistically accurate information. The whole discussion goes out the window when accurate information is thrown into the mix...it complete cuts off useless, uniformed, spitballed opinions on statistical realities.
Rambling, indeed!
<----Readers, please note!
I'm not going to do any further math for you... But you should understand that in a game of chance nothing ... absolutely nothing has a greater than 100% chance of occurring...ever.
When I talked about your last list of prize counts and statistics the information set was complete, what chown33 rightfully mentioned (in post 66)was a distribution problem after that point. What is dangerous to assume is that the number of prizes currently won some how makes your chances of winning a prize any greater.
If a lottery ticket has a 1 in 4 chance of winning a prize, and you know 'Y' prizes have already been claimed; your best guess is that 4 x Y tickets have been sold. That number could be less or could be more than 4 x Y estimated. This is where chown33 introduced the concept of confidence intervals in post 78. If Y represents only a few known winning prizes then your confidence interval would be quite low and you'd rationally expect to have a greater variance in your predictions.
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Just to make this very clear for everybody once and for all...
My question was: What sort of a ratio of $20 to $10 to $5 tickets would you buy if you were playing? And what would your rationale be for your choice?
In any case, I'm going to be taking a several month break from the game. The last day I bought tickets was Wednesday.
My question was: What sort of a ratio of $20 to $10 to $5 tickets would you buy if you were playing? And what would your rationale be for your choice?
In any case, I'm going to be taking a several month break from the game. The last day I bought tickets was Wednesday.
I would buy zero tickets.
My rationale is that statistically, that option has the highest expected value (in other words, the math says that's the option that maximizes my takeaway).
Even before calculating the odds and statistics, I can't see much logic in buying lots of different tickets period. Personally, every payday, I buy a $1 scratch-off just for the cheap thrill. Sometimes I even win my dollar back.
Even before calculating the odds and statistics, I can't see much logic in buying lots of different tickets period. Personally, every payday, I buy a $1 scratch-off just for the cheap thrill. Sometimes I even win my dollar back.
Instead of a $1 ticket every payday, buy a $20 ticket every twenty pay days. Or even a $5 ticket every five. At least then you have a chance of winning a decent sized prize.
Still haven't bought a ticket since Wednesday!
Hello, my name is Stephen Campbell, and it's been 5 days since I last bought a lottery ticket.
I've started creating spreadsheets and getting more elaborate with the math.
I realized that to calculate the expected value of a ticket, you can't just look at the prize payout vs. cost of all the tickets, because you're probably not going to get any of the big prizes.
In the games that I play, if you have 100 $20 tickets, the odds of getting a $200 prize or greater is something like 1 in 2.32. So there's a good chance that even in 100 tickets, you won't have a single ticket with a prize larger than $100.
So weighing the value of all tickets with prizes of $100 and below, against all the tickets that are out there, gives us an expected ticket value of 58%, even though the 'total prize payout' for the game is 75%.
I went back through my records and found 63 $20 tickets purchased in the last couple months, and added up how much they won. $1,260 of tickets won $710, a 56% payback... and these 63 tickets contained a portion of the ones with the 58% expected value, as well as a bunch with a 53% expected value according to the same calculation, so the 56% payout that I got for those 63 tickets was exactly what you would expect statistically, and there were no $200 prizes or greater in the lot, as expected.
I realized that to calculate the expected value of a ticket, you can't just look at the prize payout vs. cost of all the tickets, because you're probably not going to get any of the big prizes.
In the games that I play, if you have 100 $20 tickets, the odds of getting a $200 prize or greater is something like 1 in 2.32. So there's a good chance that even in 100 tickets, you won't have a single ticket with a prize larger than $100.
So weighing the value of all tickets with prizes of $100 and below, against all the tickets that are out there, gives us an expected ticket value of 58%, even though the 'total prize payout' for the game is 75%.
I went back through my records and found 63 $20 tickets purchased in the last couple months, and added up how much they won. $1,260 of tickets won $710, a 56% payback... and these 63 tickets contained a portion of the ones with the 58% expected value, as well as a bunch with a 53% expected value according to the same calculation, so the 56% payout that I got for those 63 tickets was exactly what you would expect statistically, and there were no $200 prizes or greater in the lot, as expected.
Since March 12th I've bought $31 of tickets, but $20 of it was a ticket in another state that I only bought because I was in another state.
SO glad I stayed subscribed to this thread.
OP, I've been thinking, and I've derived a simpler mathematical analysis of the payback of scratch tickets.
In the end, it really doesn't matter WHAT your odds are of winning a big prize, because no matter what you win or when you win it, you will just use it to buy more scratch tickets. And any winnings you get from THOSE tickets will also be spent on more tickets. And so on until you're out of money. And then, next payday, the cycle repeats.
You appear to have an addiction. I believe, for what it's worth, that you should seek help.
OP, I've been thinking, and I've derived a simpler mathematical analysis of the payback of scratch tickets.
In the end, it really doesn't matter WHAT your odds are of winning a big prize, because no matter what you win or when you win it, you will just use it to buy more scratch tickets. And any winnings you get from THOSE tickets will also be spent on more tickets. And so on until you're out of money. And then, next payday, the cycle repeats.
You appear to have an addiction. I believe, for what it's worth, that you should seek help.
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SO glad I stayed subscribed to this thread.
OP, I've been thinking, and I've derived a simpler mathematical analysis of the payback of scratch tickets.
In the end, it really doesn't matter WHAT your odds are of winning a big prize, because no matter what you win or when you win it, you will just use it to buy more scratch tickets. And any winnings you get from THISE tickets will also be spent on more tickets. And so on until you're out of money. And then, next payday, the cycle repeats.
You appear to have an addiction. I believe, for what it's worth, that you should seek help.
Well that's simply untrue. If I won a large enough prize, I wouldn't just spend it on more tickets. In fact, any prize of $5,000 or greater would probably see me never playing scratch again, because that would reimburse me more than my lifetime gambling expenditures.
Sorry, but I'm calling Bravo Sierra on this. If you won a large prize, it would only confirm your "theories" and drive you to continue playing.
My fiancé has agreed that I can buy 100 $20 tickets on my birthday, as long as I don't buy any more tickets between now and then, and as long as I keep all the winnings from the 100 tickets.
My birthday isn't for another several months.
My birthday isn't for another several months.
