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Another scratch ticket thread, for math geeks!

StephenCampbell said:
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.
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Let's say you want to maximise your chances of becoming a millionaire.

Take $775. Go to Las Vegas to a roulette table with high enough limits.
Bet $775 on a single number. If you win, you have $27,900.
Take the money and bet $27,900 on a single number. If you win, you have $1,004,400.

Your chances with two zeroes on the table are one in 1,444.
 
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gnasher729 said:
Let's say you want to maximise your chances of becoming a millionaire.

Take $775. Go to Las Vegas to a roulette table with high enough limits.
Bet $775 on a single number. If you win, you have $27,900.
Take the money and bet $27,900 on a single number. If you win, you have $1,004,400.

Your chances with two zeroes on the table are one in 1,444.
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True story:
the only time i have ever been in vegas, i was with my wife (then still my girlfriend) on the last day of an arizona/utah parks road trip.
we toured the strip, occasionally playing slots. Eventually i convinced her that we HAD to try a table. We agreed to invest $20. We searched until we found a place with $1 chips, and started playing (and were disappointed to realize we needed to put $5 total at a time, even though you could spread them around).
anyway, after some rounds when we mostly lost (with the occasional even/odd red/black win, don't remember exactly), we came down to the last few dollars.
We put them all "focused" on the day of our "anniversary" (of the day we got together, since we weren't married yet). So there was 1 dollar on the number straight, one on the double, one the dozen, one on the color, etc, until we used all the remaining chips.
wheels spins, ball rolls and BAM! the exact number comes out. We had won every single one of the bets.
great excitement ensues (especially people around us).
So we got our chips, put aside part of it (so that we would come out ahead no matter what) and set to go ahead and lose the rest without stress attached. We decided to put most everything else on the month of our anniversary for the next spin, with the same structure as before (so there was actually not much on the number itself).
BAM! exact number comes out again! the table EXPLODED! everyone was congratulating us like we won an olympic gold. or something truly extraordinary had just happened.
mind you, this was just a few hundred dollars, but to us it was a lot of money then, so we were really excited, and we did think it was a truly extraordinary event. anyway, we collected our wins and left the table.
we cashed everything except one chip which we still keep as our lucky charm.
it paid for most of the vacation :)

it was hilarious, because when people realized we were leaving the table, they were looking at us as if we went completely mad. some were begging us to stay. And there were at least two people -who had piggy-backed on our second bet- who actually won a lot more than we did.
 
StephenCampbell said:
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.
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I hope you are using the expected value methodology... I'm worried by this explanation that you are not.

StephenCampbell said:
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...
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You should also look at this as it cost you $550 to play on those 63 tickets. As a source of entertainment can you afford to spend $550 on a group of tickets in the same time period?
 
Well, here's my logic behind my birthday plan. The expected cost, if I'm not lucky nor unlucky, is $880. That will be the deficit after claiming all the expected prizes from the $2,000 of tickets. That's a reasonable price for a once-in-a-year gambling spree.

Any $500, $1,000, $5,000 etc winners will not affect the 56% return rate otherwise (the return rate if the large ticket was absent from the group), which is why I can logically think of the cost as only $880 before any 'lucky' winners.

So, for the price of $880, I have a 1 in 54 chance of winning $1,000, a 1 in 520 chance of winning $5,000, a 1 in 900 chance of winning $10,000, a 1 in 1,280 chance of winning $50,000 and a 1 in 4,500 chance of winning $1,000,000.

That seems like a pretty good game!
 
Interesting that, after two long threads of people telling you that you're fooling yourself, you still insist on telling us all about the convoluted 'logic' you use to justify your continued play.

Just who are you trying to convince?

Good luck playing only once a year.
 
StephenCampbell said:
That seems like a pretty good game!
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So based on your recent posts, you're spending a lot of time devising a plan for a large purchase of scratch tickets some months away. Doesn't that strike you as odd. I mean you're so obsessed with scratch tickets you're exhibiting signs of someone who's addicted to gambling.

You continue to say you don't have a problem, you've posted a number of times that you've quit only to reply shortly afterwards of buying more tickets.

Its your life, and your decision but what you post seems to indicate a problem with gambling.
 
So I have a few more math questions related to scratch, for anyone who's interested!

Let's say I bought 100 each of $20, $10 and $5 tickets.

I'm trying to calculate what my odds will be of various kinds of winnings happening, and here's what I've done so far.

Let's take $5 tickets as an example. I'm assuming that I'm going to get about 20 tickets each of five different games at the $5 level. So I looked at the odds of various prize levels being hit for five different games, assuming that each game alone had 100 tickets... i.e...

Game 1. 1,000,000 tickets. 1,000 $75 prizes in the game. Odds of winning $75 on a $5 ticket when purchasing 100 tickets = 1,000,000 divided by 1,000 = 1,000. 1,000 divided by 100 (the number of tickets) = 10. So with 100 tickets you would on average have a 1 in 10 chance of getting a $75 prize.

Then I did the same calculation for the four other games, and let's say I got a variation of odds, such as 1 in 9, 1 in 12, 1 in 11, etc. I then added all those together and divided them by five.

Is that the correct way to get the overall odds of hitting $75 when taking into account equal proportions of those five different games?

In this particular case actually, there was one of the five games that didn't have a $75 prize. So I instead did the same calculation with just the four games that had $75 prizes, and divided the odds-per-ticket in each game by 80 instead of 100, because only 80 of my hundred tickets will be tickets that even have a $75 prize as a possibility. Again, was this the correct way to do this?

If this is all good so far, I then end up with something like this:

With 100 $5 tickets, odds of hitting...

$75 is 1 in 9.86
$100 is 1 in 9.97
$500 is 1 in 1,571
$1,000 is 1 in 1,923
$50,000 is 1 in 3,107

Again, this is contingent on my above methods yielding accurate results.

Now, if these numbers are correct, how would I calculate the odds of hitting any one of those five prizes? Or the odds of hitting a $500, $1,000 or $50,000 prize? Etc.
 
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I can't believe I'm doing this again, but your math is appallingly bad.
StephenCampbell said:
Game 1. 1,000,000 tickets. 1,000 $75 prizes in the game. Odds of winning $75 on a $5 ticket when purchasing 100 tickets = 1,000,000 divided by 1,000 = 1,000. 1,000 divided by 100 (the number of tickets) = 10. So with 100 tickets you would on average have a 1 in 10 chance of getting a $75 prize.
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NO! Odds are (given your data) of 1,000 $75 prizes in a lot of 1 million tickets is 1,000/1,000,000 = 0.1% (or 1 in 1,000 chance).
EXPECTED VALUE on purchasing 100 tickets for winning the $75 prize is 100 x 0.1% x $75 or $7.5

StephenCampbell said:
Is that the correct way to get the overall odds of hitting $75 when taking into account equal proportions of those five different games?
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No absolutely not. You have the information in this thread to calculate your odds and expected values correctly but you have repeatedly shown an inability to either comprehend or apply the principles discussed previously in this thread. A grade 12 stats text would be a great introduction into this area of mathematics. Again I would highly stress that you use percentages rather than ratios. I think one of the obstacles you face is that ratios are obfuscating your determination of odds and expected value.
 
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Raid said:
I can't believe I'm doing this again, but your math is appallingly bad.
NO! Odds are (given your data) of 1,000 $75 prizes in a lot of 1 million tickets is 1,000/1,000,000 = 0.1% (or 1 in 1,000 chance).
EXPECTED VALUE on purchasing 100 tickets for winning the $75 prize is 100 x 0.1% x $75 or $7.5
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I'm sorry. But correct me again if I'm wrong.

The odds of one ticket being a $75 winner is 1 in 1,000, of course, since there are 999 non-$75 winners for every $75 winner in the game.

If you bought all the 1,000,000 tickets, you would get 1,000 $75 prizes, correct?

And how many batches of 1,000 tickets would you have bought?

1,000. You would have gotten precisely one $75 prize for each batch of 1,000 tickets, even though occasionally there would have been a batch with none and occasionally a batch with two or three.

And how many batches of 100 tickets would you have bought?

10,000.

For every ten batches of 100 tickets that you got, you would have gotten one $75 prize.

The odds of hitting a $75 prize with 100 tickets is 1:10. This doesn't mean a guaranteed $75 prize every ten batches of 100 tickets.. it means that on average, if you continuously bought batches of 100 tickets, on average you'd have one $75 prize every ten batches.

How on earth could this be wrong?

Edit: Isn't it like rolling a 10 sided die? On average every ten rolls you'll get one, say, 7. But you could easily go ten or twenty rolls without getting a 7. But on average over time you'll get one 7 for every ten rolls you do. Making the odds 1:10.
 
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StephenCampbell said:
Edit: Isn't it like rolling a 10 sided die? On average every ten rolls you'll get one, say, 7. But you could easily go ten or twenty rolls without getting a 7. But on average over time you'll get one 7 for every ten rolls you do. Making the odds 1:10.
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No, it's not like that at all.

There are a finite number of winning tickets, regardless of how many you buy, regardless of how many everyone else buys, and regardless of how lucky you (or others) are in picking winning tickets. There will never be more than a pre-determined number of winning tickets.

In rolling a die, there is no limit to the number of times you can roll a particular number; in your example of a 10-sided die, you could theoretically roll a 7 on every single roll, no matter how many times you roll the die. You could also theoretically never roll a 7, regardless of how many times you roll the die.
 
Tomorrow said:
No, it's not like that at all.

There are a finite number of winning tickets, regardless of how many you buy, regardless of how many everyone else buys, and regardless of how lucky you (or others) are in picking winning tickets. There will never be more than a pre-determined number of winning tickets.

In rolling a die, there is no limit to the number of times you can roll a particular number; in your example of a 10-sided die, you could theoretically roll a 7 on every single roll, no matter how many times you roll the die. You could also theoretically never roll a 7, regardless of how many times you roll the die.
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Okay, I understand the distinction here.. but what about the rest of my post? Leave the die analogy aside.
 
Maybe it is because I don't really 'get' the whole idea of a scratch card obsession, (or, for that matter, betting on horses,) and I do get the idea of higher education, (I used to be a teacher at university)……

But, I confess myself a little bewildered. Actually, I am puzzled as to why you - or anyone - would devote two threads to the topic of scratch cards, while simultaneously attempting - with commendable vigour, tenacity and persistence (but with less logic) to persuade other posters, but most of all yourself, that you will one day win, (and win big-time), while devoting yet another to the far less pressing issue of whether your financée ought to embark upon a graduate degree, given that cost may be an issue, one of several.

You know, rather than calculating how much you wish to, or expect to, or plan to, spend - or blow - on scratch cards before your birthday, why not instead put it into a piggy bank with the label 'my partner's next degree' attached; the payoff will be far more worthwhile, and the notional expenditure a hell of a lot more logical.
 
Scepticalscribe said:
Maybe it is because I don't really 'get' the whole idea of a scratch card obsession, (or, for that matter, betting on horses,) and I do get the idea of higher education, (I used to be a teacher at university)……

But, I confess myself a little bewildered. Actually, I am puzzled as to why you - or anyone - would devote two threads to the topic of scratch cards, while simultaneously attempting - with commendable vigour, tenacity and persistence (but with less logic) to persuade other posters, but most of all yourself, that you will one day win, (and win big-time), while devoting yet another to the far less pressing issue of whether your financée ought to embark upon a graduate degree, given that cost may be an issue, one of several.

You know, rather than calculating how much you wish to, or expect to, or plan to, spend - or blow - on scratch cards before your birthday, why not instead put it into a piggy bank with the label 'my partner's next degree' attached; the payoff will be far more worthwhile, and the notional expenditure a hell of a lot more logical.
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Thank you for your input. I did not ask for your opinion on the personal matters in my life. The other thread you refer to was about that topic, and this one is about this topic.

You don't know anything about how we manage our lives, and frankly we're both quite happy and doing very well. Thanks for asking though.

I guess the thread may as well be closed now, as this will derail from here. Unless people can have the civility to just stay on topic and discuss the math of scratch tickets...
 
Scepticalscribe said:
But, I confess myself a little bewildered. Actually, I am puzzled as to why you - or anyone - would devote two threads to the topic of scratch cards, while simultaneously attempting - with commendable vigour, tenacity and persistence (but with less logic) to persuade other posters, but most of all yourself, that you will one day win, (and win big-time),
Click to expand...

Because, sadly enough, we keep responding.:(
 
Scepticalscribe said:
But, I confess myself a little bewildered. Actually, I am puzzled as to why you - or anyone - would devote two threads to the topic of scratch cards, while simultaneously attempting - with commendable vigour, tenacity and persistence (but with less logic) to persuade other posters, but most of all yourself, that you will one day win, (and win big-time)
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When did I say this?

Quote me, please.
 
ucfgrad93 said:
Yep.

I often wonder if StephenCampbell and Squilly are related. They both post ridiculous threads and then try and argue or ignore the many people who tell them they are wrong, wasting their time, etc.
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How can a question be wrong?

And if I'm wasting my time, isn't that my business?
 
$2,000 in scratch off tickets could be spent on far better things. Donate that money to charity for god sake, anything but waste it on scratch offs.

If I had $000 to spend on my birthday the first thing I would do is put granite counter tops in my kitchen, or pour that concrete patio I have been wanting for the last couple years but have only this summer been able to get around to.
 
ucfgrad93 said:
Because, sadly enough, we keep responding.:(
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Tomorrow said:
That makes us enablers.
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Sigh. You are right, both of you. Completely right.

ucfgrad93 said:
Yep.

I often wonder if StephenCampbell and Squilly are related. They both post ridiculous threads and then try and argue or ignore the many people who tell them they are wrong, wasting their time, etc.
Click to expand...

Actually, the exact same thought has occurred to me; I have wondered about this.

Worse, although I tell myself to ignore these utterly bonkers threads, a little like a mosquito bite that demands a scratch, they itch. And I, more fool me, after much internal resistance ('resistance is futile') I succumb to the temptation to sink my nails into that……..thread.

ucfgrad93 said:
Sure it is your business. It is your time and money and you can spend both any way you see fit. That said, when you post how you spend them online then you open yourself up for criticism, etc.
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Exactly.

And anyone who excuses (while denying) a fatuous addiction to scratch cards - and attempts to justify this expenditure - while attempting - elsewhere - to argue against higher education partially on the grounds of cost - will get the sharp edge of my pen.
 
Scepticalscribe said:
Sigh. You are right, both of you. Completely right.



Actually, the exact same thought has occurred to me; I have wondered about this.

Worse, although I tell myself to ignore these utterly bonkers threads, a little like a mosquito bite that demands a scratch, they itch. And I, more fool me, after much internal resistance ('resistance is futile') I succumb to the temptation to sink my nails into that……..thread.



Exactly.

And anyone who excuses (while denying) a fatuous addiction to scratch cards - and attempts to justify this expenditure - while attempting - elsewhere - to argue against higher education partially on the grounds of cost - will get the sharp edge of my pen.
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We could pay off our student loans in 101 weeks instead of 104 if I didn't buy any scratch tickets on my birthday.

That's if I don't win anything big obviously.
 
StephenCampbell said:
We could pay off our student loans in 101 weeks instead of 104 if I didn't buy any scratch tickets on my birthday.

That's if I don't win anything big obviously.
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And you don't feel that paying that load off 3 weeks early is worth it?

I would buy $100 in scratch of (I would actually buy none, just spend $100 on a nice dinner) and put the remaining money towards the student loans
 
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