The one where we discuss scratch off lottey ticket odds (Questions re: Probabilities)

Miscellaneous and Personal Stuff I Must Share
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Some people ignore the math tax, others just go ahead and pay it without thinking. Then there are some people who understand the risk, understand the limited rewards and then try to work out where the greatest advantage is. That’s why I’m starting this thread.

In my spare time I have been studying probabilities. Working with expected value matrix, calculating odds of occurance and so on. I started with a video poker book (cause I loves me some video poker) but have moved on to other areas as well.

One of these areas is scratch off lottery tickets. It seems to me that, given the overall odds of the game (listed on the back of the ticket) and the number of top prizes (available on the internet) it should be possible to calculate the remaining prizes, estimate the total number of tickets ran, estimate the number of tickets remaining and work up an EV for particular games. Once the EV is determined then it is as simple as buying the optimum number of tickets for the game with the highest EV and, although the overall odds of winning remain the same for both the consumer and the Commission, increasing the edge of the consumer over the Commission.

Granted, applying the formula listed in the second link could increase the edge, but my question is: Does this provide the optimum advantage?

Other questions are: Could the volitility of a game (in probability the VI) be calculated on games this way and, if so, would they follow the intuitive direction of Higher Cost + Lower Overall Odds = Greater Volitility? Would this be dependant of the ratio of the payout or the upper limit of the payout?

Assuming I am not the only person to think along these lines, are there net sources that my Google skills are not bringing up?

There were a lot of books when I went to get the poker book, including several on lotteries both analog (bouncing balls) and digital (computerized random numbers) but none on an intelligent scheme of scratch off play. Does this and the aparent lack of internet information preclude that the odds are readjusting at the rate of being reasonably unpredictable as far as EV and VI are concerned?

Am I barking up the wrong tree here? The reason I started studying this in the first place (aside from the interest in the math) is to play video poker at casinos with a more realistic chance of leaving closer to a break-even point. I can aspire to greatness as much as I want but the truth is I don’t have enough time to devote to perfect play and sitting on a riverboat dropping quarters and sucking down Winstons to realistically and reliably make it profitable.

So here it is, the thread in which I ask questions and encourage discussion about Lottery Scratch-offs. I chose MPSIMS because of the futile nature of the games. Granted I know there are real answers to my questions and there are many debatable fine points to those answers. It’s not really a poll although it could be recipe for disaster. If a wise mod feels the need to move this then feel free.

Thanks in advance to all.

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I occasionally buy a scratch off ticket because it’s fun (and more immediately gratifying than lottery tickets), and while I’m certainly aware of the tiny odds, that doesn’t bother me. I don’t pretend it’s a real financial investment lol.

What bugs me is that I found out recently that even after the big prize is awarded, they are still selling the tickets. I had the impression that there was one big award per certain number of printed tickets, but that the ticket run would sell out soon enough that there would be a new run with a new prize. It’s annoying to have to research whether or not the prize has already been awarded, that takes away half of the fun of buying the ticket.

Although this might be to the OPs advantage - it seems that they must list what prizes have already been claimed. I don’t know if there’s any way to find out how many tickets are left though. Even knowing all these things though, I doubt there’d be a situation where the odds would be advantageous.

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In the first link for each game it gives the release date, the number of top prizes left and the overall odds. I think that the date could be used somehow as a metric for remaining tickets and this metric could be multiplied into occurance of each prize so that the expected value goes up or down at any given point in time for any particular game. The overall odds never change, this would just point out which game is mathematically better.

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jackdavinci, I used to work for the Louisiana Lottery and it was our policy not to do that. I’m not sure about other states, but as soon as all of the top prize tickets(there were usually 3-6, or sometimes a lot more) were sold we pulled the game off the market. We did it the next day, as a matter of fact. If I recall correctly, the Texas Lotto was sued a few years ago for leaving games ‘on the shelves’ after all of the top prizes were claimed. Maybe you could buy some tickets from which all top prizes were claimed and make some real bucks! :wink:

As to the OP, I just woke up and refuse to think hard enough to give you a really good answer. I will give you some information, though. I worked for the Lotto for over 4 years. When I quit I bought a few scratch-offs. Since I turned 21 while I was working for them I hadn’t been able to buy any before. The only criteria I used in my purchase was not to buy $1 tickets because the payout if you do hit a winner sucks and to get one that looked cool. I like to get the 2, 3, 5, and 10 dollar tickets because, if you do win, your winnings will generally be much better than a $1 ticket. Also, on the topic of the grand prizes, the winners are usually inserted fairly evenly throughout the game. So, if we receive 6 pallets full of tickets and there are 6 grand prizes there will usually be 1 per pallet. Getting the information as to how many large prizes are left compared to how many tickets are left could help you pick your tickets. You may have a better chance of hitting a grand prize, but the odds of you hitting a winner at all are still the same, about 1:4 for most games. So, all of your info might be able to help you pick the game with the best chance of hitting the ‘big winner’, but that is about it. Even that is moderately unlikely, as these games are set up so that if you have 1,000,000 tickets at the start and 10 grand prizes, when you get to 500,000 tickets you should have 5 grand prizes. It doesn’t always work perfectly, but the printers and lotteries try to keep the prize ratios the same throughout the entire life of the game. In conclusion, I have scratched off entire rolls of tickets( we used to have to do this whenever a new game came in), and not had a winner over $10. I’ve also seen stretches of 20 and 30 tickets without a winner followed by 10 in a row that won. What I’m getting at is that the lotteries and printers have had a long time to work on this stuff and as a general rule, you will lose money on tickets. You may, just maybe, be able to push your odds one way or another by a tiny fraction, but generally not. I hope that helped a bit, if not I apologize. I have the excuse of being sleep-addled.

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I think the reason that there isn’t much in the way of literature is that, regardless of your analytical techniques, the odds are very unlikely to ever be in your favor.

Consider counting cards in Blackjack. With precise counting, a good blackjack player can get a 1-2% edge over the casino a small amount of the time. But that’s on a game that has a house edge of only a percent or so against basic strategy. So, based on random fluctuation, counting can swing the odds by < 5%.

The house edge in the lottery is something like 50%. Now, maybe with careful counting you could get it to 45%, but the optimal number of tickets to buy is going to be 0 in all but the most unlikely cases. In fact, if you do find a particular scratch-off game where the big prizes are still out there in a small number of remaining tickets, it’s probably more likely that the winning ticket was lost, destroyed, or simply hasn’t yet been claimed than that it’s still out there in a very small pool of remaining tickets.

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So, if I understand correctly for the big ticket prizes the EV or payout remains close to the same for the feasible life of the game? That’s one of the things I was wondering about. I’ve been trying to come up with a value for aging the game verses the remaining prizes to determine and readjust the overall odds so I could put a cleaner number into the Expected Value equation but if the Overall stays fairly consistant due to the spread of the top prizes then I should be able to represent it as a constant.

iamthewalrus(:3=, that’s kind of what I was figuring as well. One of the test calculations I did last night came up with a 47% payout but as this was a multiprize ticket and there is no way of knowing how many prizes are combined on a single purchase there was a deviation that I did not get worked out.

Hopefully by tonight I will be able to post some of the calculations I have come up with for review and criticism. I don’t think I’ll ever get rich but I love to play and even a 1% - 2% edge makes it more interesting.

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A Second Thought:

Given the optimum bet as *action=(odds x 2.5) x cost * then it shouldn’t matter how many lower value prizes (including losers) remain.