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maximuswolf · 5 years ago

Text

Math and data to maximize scratchoff wins. via /r/Lottery

Math and data to maximize scratchoff wins.

(Edited repost: the original post required a couple of small changes.)

I've been crunching a lot of numbers, sending a lot of FOIA requests, and searching for advantages.

I want to share a little bit of what I've learned so far.

Overview

These are a couple of the rules I've determined will help you win more often.

Play tickets that have sold many tickets and have many unclaimed grand prizes.

Prefer playing a few higher priced tickets over many lower priced tickets.

That's all there is to it. I'll explain the reason behind the rules in the rest of this post.

Play tickets that have been sold for a long time and have a large number of unclaimed grand prizes.

To understand this rule, you need to know a little bit of math. It's not much. It can be explained in simple terms. But it's powerful enough to beat blackjack in the casino. What you're about to read is the foundation behind card-counting. But here, we use it to beat scratch offs.

There is an important difference between scratch offs and draw games like Powerball.

In draw games, every draw is "independent". What I mean by that is the results of a previous draw have no effect on the results of the following draws.

If the draw for a pick 3 game is "3", "1", "9", then the odds that the following draw is also "3", "1", "9" are the exact same.

This is counter-intuitive to a lot of people. If you flip a coin 3 times and it comes up heads all 3 times, then it's natural to think that it's more likely to come up tails on the next flip. But it's not! It is still equally likely to be either heads or tails on the 4th flip.

The counter-intuitiveness of this is known as the "Gambler's Fallacy" and can be read about many places online, https://en.wikipedia.org/wiki/Gambler%27s_fallacy, so I won't go into any more detail. Just know that it's a mathematical fact. The previous results of a draw game have no effect on future draws.

How are scratch offs different?

But with scratch offs, previous results do affect the future. It's obvious when you look at an extreme example. Consider what happens if there is a single grand prize in 1 million unscratched tickets. Your odds of getting the grand prize is 1 in a million. But now imagine you just watched the person in line in front of you buy a ticket, scratch it, and reveal the grand prize. Now there are no more grand prizes. Your odds are exactly 0!

In that extreme example, it's clear that past results affect future odds.

This is completely different from a draw game. In a draw game, if someone hits the Powerball jackpot with 09, 36, 49, 56, 62, 08, then that doesn't mean you should or shouldn't play those exact same numbers next week. They are just as likely to appear again as any other set of numbers.

But scratch offs aren't randomized with each purchase. Scratch offs are randomized once, when the tickets are printed. Then, as the tickets are bought and scratched, the remaining tickets become less random.

This is just like counting cards at blackjack. The deck is shuffled once at the beginning of the game. Then, as cards are dealt, the deck becomes less random. Once it becomes less random in favor of the player (more big cards remaining than little cards), then the player has an advantage and can increase their bet.

How do you know which tickets have have many unclaimed grand prizes and few remaining overall tickets?

Most states publish this information on their lottery homepages.

Here is an example from the Florida Lottery for the $3 Multiplier Crossword https://www.flalottery.com/scratch-offsGameDetails?gameNumber=1429

https://preview.redd.it/9p5sp880x9p51.png?width=481&format=png&auto=webp&s=3d5dc49e773243274dca0952502b06f51f0d54c1

That table has a column showing the total number of tickets printed at each prize tier and another table showing the number of tickets claimed at each prize tier.

The lowest-value ticket is usually the most common. It often has hundreds of thousands of tickets printed. There is something in math known as "the law of large numbers" that makes the lowest price ticket a good indicator of what percentage of tickets have been sold. Even though the state doesn't publish how many tickets in total have been sold, and even though they don't say anything at all about the non-winning tickets that have been sold, we can use the lowest-priced ticket as a good estimator.

In the image above, you can see that 3,170,852 tickets were printed that were $3 winners. Of those, only 603,652 remain.

With some simple math, we can convert that to a percentage.

603,652 / 3,170,852 = 0.19

So about 19% of the tickets remain. 81% of the tickets have been sold.

How about the grand prizes? Are there a large number of grand prizes remaining in relation to how many tickets have been sold? To know that, we need to convert the number of grand prizes remaining to a percentage also, that we we can compare percentages to percentages, apples to apples.

There are 4 grand prizes remaining out of 20 total grand prizes printed.

4 / 20 = 0.20

So 20% of the grand prizes remain. That's almost exactly where we expect to be. That means there is not a lot of grand prizes remaining in relation to the total number of tickets remaining.

If there were 5 grand prizes remaining, then the percentage remaining would be 5 / 20 = 0.25, or 25%. Then there would be 5% more grand prizes than expected. If that were the case, this might be a good game to play!

Knowing this, you can check back daily or weekly and see how the numbers change. Every day, more tickets will be sold.

Let's say a few weeks pass and couple hundred thousand $3 winners are claimed. Now there's 400,000 $3 prizes remaining.

400,000 / 3,170,852 = 0.126

If no grand prizes have been claimed in that time, then now there's only about 12.6% tickets remaining but still 20% grand prizes remaining. Grand prizes are almost 8% more likely than average!

Check your state lottery website and you can perform these calculations for whatever games you like to play.

Prefer playing a few higher priced tickets over many lower priced tickets.

I wrote software to automatically analyze every scratch off game from many different states.

As part of that analysis, I calculate the total amount of prizes that will be paid out. Since the states publish on their websites the total number of tickets at each prize tier and the value of each prize. I simply multiply the number of tickets at each tier by that tier's value and then sum the results for each tier of a game.

Another number I calculate is the cost to buy every ticket. That's a lot easier. It's simply the total number of tickets printed times the price of each ticket. If a game prints 14 million tickets and each ticket costs $10, then the cost to buy every ticket is 14 million times $10, or $140 million.

Those two numbers are all we need to calculate the "expected value" of a game.

If a game has $100 million in prizes and it would cost $140 million to buy every ticket, that means the state will make $40 million in profit. That profit comes out of our pockets.

But we can minimize our losses by playing games where the state has the least profit.

Here's a simple example. Which game would you rather play?

Game A: $100 million in prizes where it would cost $140 million to buy every ticket. Game B: $120 million in prizes where it would cost $140 million to buy every ticket.

Obviously, game B is better. The state takes less profit. That means more money in our pockets.

This is one way to rank the quality of a game. The more money that is returned to players and the less money that the state keeps as profit, the better the game.

By analyzing data from every game for multiple states, I have determined the average quality for different priced tickets.

This graph below tells the whole story.

https://preview.redd.it/u6hm1t7gx9p51.png?width=1645&format=png&auto=webp&s=5cd0e3afc3ef411ec7d62c23dacd14ef74291b7b

It is clear that on average, higher priced tickets are better.

Spending $100 on $20 tickets will result in an average win of $71.95 while spending $100 on $2 tickets will result in an average win of $65.65. By buying $20 tickets rather than $2 tickets, you will win an average of $6.30 more!

Why do states pay out more for higher priced tickets?

This advantage comes from economics.

It costs roughly the same amount for the state to print a $1 ticket as a $20 ticket.

Here's a table that shows the prices that GTECH, a ticket printer, proposed to the Texas Lottery.

https://preview.redd.it/gqpn85whx9p51.png?width=1295&format=png&auto=webp&s=c21158fa868caa4da444a5ec8404f9a8a822d3be

Usually, lower priced tickets are smaller. A $1 ticket might be 2.4 inches x 4 inches while a $20 ticket has more gameplay options and might be 10 inches x 4 inches. Those dimensions correspond to the "A" and "E" columns in the table above.

The values you see in each row are the cost per 1,000 tickets.

Let's compare.

The cost of 1 million $1 tickets of 2.4 inches x 4 inches in packs of 250 would cost $33.78 per 1,000 tickets, or about $0.034 per ticket.

The cost of 1 million $20 tickets of 10 inches x 4 inches in packs of 50 would cost $59.50 per 1,000 tickets, or about $0.06 per ticket.

That's 3.4 cents per $1 ticket and 6 cents per $20 ticket.

Why are higher priced tickets better?

The state needs to make a profit on the lottery. That's the whole point of the lottery: to make money to pay for services like education and roads.

Money that goes towards ticket printing is wasted. It's money that is taken from the players and is not kept by the state.

The less money that goes towards ticket printing, the more money is available to pay out in prizes (and to go towards public goods).

While the $20 ticket may cost more to print than the $1 ticket (6 cents vs 3.4 cents), the percentage of the ticket price that goes towards printing costs is lower.

6 cents is only 0.3% of $20. That's zero-point-three percent. Less than half of a percent of the ticket price goes towards the printing costs.

3.4 cents out of $1 is 3.4%, or over 3% of the ticket price going towards printing costs.

If you were to buy $100 worth of $1 tickets, the state would have paid $3.4 to ticket printers, leaving only $96.60 in funds to split between paying players through the prize pool and funding things like public roads and education. But if you were to buy $100 worth of $20 tickets, then the state would have paid only $0.18 to ticket printers! That leaves $99.82 to split between the prizes and state funding.

Note: The above is a simplified calculation that doesn't take the full cost of each ticket from printing to disposal. There's obviously costs associated with shipping and other services. But I wouldn't expect the percentages to change much. The economics of high-price vs low-price tickets is still the same.

Good luck!

I want to close by wishing you good luck. But now you know there's more to it than just luck. Use these tips and tricks to your advantage and make your own luck.

A final word of caution: even if you follow all of my tips, it's still practically impossible to consistently make profit from scratch offs. The best that almost anyone can do is to increase their "expected value". That's a good thing. It's huge. It's great if you're playing for fun and would be buying tickets regardless of the circumstances. But that's not good enought to play more often than you otherwise would. So, please, if you or anyone you know needs support around gambling, please reach out to places like https://www.gamblingtherapy.org/en

Remember:

If you can't afford to lose, you can't afford to play.

Submitted September 25, 2020 at 04:58AM by Dr-Lotto via reddit https://ift.tt/341rPPk

0 notes

maximuswolf · 5 years ago

Text

Math behind maximizing Scratch Off wins via /r/Lottery

Math behind maximizing Scratch Off wins

I've been crunching a lot of numbers, sending a lot of FOIA requests, and searching for advantages.

I'm trying to organize everything I've learned into a single source of truth, but in the meantime I want to share a little bit.

Overview

Follow these simple rules and you will win more often.

Play tickets that have sold many tickets and have many unclaimed grand prizes.

Prefer playing a few higher priced tickets over many lower priced tickets.

That's all there is to it. I'll explain the reason behind the rules on the pages that follow. You'll also learn how to use these rules to maximum advantage.

Play tickets that have been sold for a long time and have a large number of unclaimed grand prizes.

There is an important difference between scratch offs and draw games like Powerball.

In draw games, every draw is "independent". What I mean by that is the results of a previous draw have no effect on the results of the following draws.

If the draw for a pick 3 game is "3", "1", "9", then the odds that the following draw is also "3", "1", "9" are the exact same.

How are scratch offs different?

In that extreme example, it's clear that past results affect future odds.

How do you know which tickets have have many unclaimed grand prizes and few remaining overall tickets?

Most states publish this information on their lottery homepages.

Here is an example from the Florida Lottery for the $3 Multiplier Crossword https://www.flalottery.com/scratch-offsGameDetails?gameNumber=1429

https://preview.redd.it/g3be9y2tuwo51.png?width=481&format=png&auto=webp&s=44d01216eb93c2923154e26569163027cff89da6

That table has a column showing the total number of tickets printed at each prize tier and another table showing the number of tickets claimed at each prize tier.

In the image above, you can see that 3,170,852 tickets were printed that were $3 winners. Of those, only 603,652 remain.

With some simple math, we can convert that to a percentage.

603,652 / 3,170,852 = 0.19

So about 19% of the tickets remain. 81% of the tickets have been sold.

There are 4 grand prizes remaining out of 20 total grand prizes printed.

4 / 20 = 0.20

So 20% of the grand prizes remain. That's almost exactly where we expect to be. That means there is not a lot of grand prizes remaining in relation to the total number of tickets remaining.

Knowing this, you can check back daily or weekly and see how the numbers change. Every day, more tickets will be sold.

Let's say a few weeks pass and couple hundred thousand $3 winners are claimed. Now there's 400,000 $3 prizes remaining.

400,000 / 3,170,852 = 0.126

If no grand prizes have been claimed in that time, then now there's only about 12.6% tickets remaining but still 20% grand prizes remaining. Grand prizes are almost 8% more likely than average!

Rather than check the state lottery website every day and perform these calculations by hand, there are websites that do the hard work for you.

This is just one of the calculations used to determine the "score" of a scratchoff at scratchoff-odds.com.

Prefer playing a few higher priced tickets over many lower priced tickets.

While creating scratchoff-odds.com, I wrote software to automatically analyze every scratch off game from many different states.

As part of that analysis, I calculate the total amount of prizes that will be paid out. The states publish on their websites the total number of tickets at each prize tier and the value of each prize. I simply multiply the number of tickets at each tier by that tier's value and then sum the results for each tier of a game.

Those two numbers are all we need to calculate the "expected value" of a game.

If a game has $100 million in prizes and it would cost $140 million to buy every ticket, that means the state will make $40 million in profit. That profit comes out of our pockets.

But we can minimize our losses by playing games where the state has the least profit.

Here's a simple example. Which game would you rather play?

Game A: $100 million in prizes where it would cost $140 million to buy every ticket. Game B: $120 million in prizes where it would cost $140 million to buy every ticket.

Obviously, game B is better. The state takes less profit. That means more money in our pockets.

This is one way to rank the quality of a game. The more money that is returned to players and the less money that the state keeps as profit, the better the game.

By analyzing data from every game for multiple states, I have determined the average quality for different priced tickets.

This graph below tells the whole story.

https://preview.redd.it/pfw4b4puuwo51.png?width=1645&format=png&auto=webp&s=97d7fe0d738177d68c3b8237774e72a877e676a8

It is clear that on average, higher priced tickets are better.

Why do states pay out more for higher priced tickets?

This advantage comes from economics.

It costs roughly the same amount for the state to print a $1 ticket as a $20 ticket.

Here's a table that shows the prices that GTECH, a ticket printer, proposed to the Texas Lottery.

https://preview.redd.it/fulms2vvuwo51.png?width=1295&format=png&auto=webp&s=c96f4c2db6af08cddb242013951bd35badd9a5b4

The values you see in each row are the cost per 1,000 tickets.

Let's compare.

The cost of 1 million $1 tickets of 2.4 inches x 4 inches in packs of 250 would cost $33.78 per 1,000 tickets, or about $0.034 per ticket.

The cost of 1 million $20 tickets of 10 inches x 4 inches in packs of 50 would cost $59.50 per 1,000 tickets, or about $0.06 per ticket.

That's 3.4 cents per $1 ticket and 6 cents per $20 ticket.

Why are higher priced tickets better?

The state needs to make a profit on the lottery. That's the whole point of the lottery: to make money to pay for services like education and roads.

Money that goes towards ticket printing is wasted. It's money that is taken from the players and is not kept by the state.

The less money that goes towards ticket printing, the more money is available to pay out in prizes (and to go towards public goods).

While the $20 ticket may cost more to print than the $1 ticket (6 cents vs 3.4 cents), the percentage of the ticket price that goes towards printing costs is lower.

6 cents is only 0.3% of $20. That's zero-point-three percent. Less than half of a percent of the ticket price goes towards the printing costs.

3.4 cents out of $1 is 3.4%, or over 3% of the ticket price going towards printing costs.

Good luck!

I want to close by wishing you good luck. But now you know there's more to it than just luck. Use these tips and tricks to your advantage and make your own luck.

Remember:

If you can't afford to lose, you can't afford to play.

Submitted September 23, 2020 at 08:52AM by Dr-Lotto via reddit https://ift.tt/35ZtcAK

0 notes