Calculating the Value of a Scratchoff Game

• What is the average payout on a $10 ticket?
• Are you better off buying 10 $1 tickets or 1 $10 ticket?
• Can scratchoffs ever be profitable?

The answers to all of these questions can be figured out with just a little bit of simple math.

Imagine a simple game with 10 tickets that cost $1 each. There are two $2 winners and one $5 "grand prize" winner. When all tickets are sold, the state will have made $10 (10 tickets * $1). The total amount the state will have paid out will be $4 (2 tickets * $2) + $5 (1 ticket * $5) = $9. This game is profitable for the state by $1. Players will spend $10 and get back $9 for a 9/10 or 90% "expected value", a 10% loss.

Imagine the tickets aren't sold all in one day. They are sold slowly over time.

Precisely, let's imagine exactly 1 ticket sells each day. And, each day, the state publishes how many winners have been claimed.

After 5 days and 5 tickets sold, the state website shows that only a single $2 ticket has been claimed.

That means there are 5 tickets remaining and $7 in total prizes remaining. The game has suddenly become profitable. Someone could buy every remaining ticket and be guaranteed to spend $5 and win $7.

The actual numbers are much larger for state lotteries. Most games have several millions of tickets printed, with grand prizes that are often in the millions of dollars. But the math is basically the same. And even if the game never becomes profitable, if you're going to play the lottery regardless, you might as well play the game that offers you the best odds.

What is the average payout on a $10 ticket?

The answer to this varies from state to state. You can calculate the value yourself by visiting your state lotteries website if they publish information about the number of tickets printed and the number of prizes remaining. All you need to do is multiply the number of tickets printed by the price of each ticket. That will give you the total cost of all the tickets. You might get a number like $65,305,450. Next, sum the products of each remaining prize multiplied by the number of tickets remaining at the prize level. For example, there might be 2 grand prizes for $10,000,000; 10 second tier prizes for $100,000; 45 third tier prizes for $20,000; etc... Summing those would be (2 * $10,000,000) + (10 * $100,000) + (45 * $20,000) + (etc...). That number might be something like $58,702,920.

Once you have those two numbers, divide the value of the remaining prizes by the cost of the remaining tickets. $58,702,920 / $65,305,450 = 0.9128

That number is the "expected value". It represents a percentage. It's the percentage you can expect to get back for every ticket you buy. In this case, you'll get back 91% of every dollar you spend. Spend $10 on tickets, you'll get back $9.10 for a loss of $0.90.

At Scratchoff-Odds.com, we gather data from several states and run this calculation automatically. You can check to see what most $10 tickets are worth in your state. It is probably around $7, or 70% "expected value".

Are you better off buying 10 $1 tickets or 1 $10 ticket?

On average, you're better off buying a single $10 ticket rather than ten $1 tickets.

The reason for this has to do with how much money it costs states to print and distribute tickets.

We can take a guess at how much it costs the state to print and distribute a ticket. Let's assume it's $0.20 per ticket. This cost might go up for larger tickets where they use more paper and ink. It might go down for tickets which are smaller and they can ship more tickets per roll. But it probably won't vary by more than a few cents either way.

If it costs the state $0.20 to print and distribute a ticket, then they need to make that back plus more in order to turn a profit. For a $1 ticket, that means they would break even if they paid back $0.80 per ticket. To make a profit, they need to pay back less than that. If they want to make $0.20 profit per ticket, then they are only paying back $0.60 on every $1 ticket sold. If you were to buy ten $1 tickets, you would pay $10 and on average you will only get back $6. That's just 60% expected value.

Now let's imagine the costs for a $10 ticket. These tickets are usually bigger and more complex, so let's assume they cost twice as much, or $0.40. Because these are more expensive, the state probably wants to make more per ticket, so let's assume the state makes $0.60 profit per ticket. With these numbers, the state sells a ticket for $10. It cost them $0.40 to produce and they are keeping $0.60 as profit (on average), so the player will get $9 on average. That comes to 90% expected value!. $10 spent on a single $10 ticket means you'll be making $9 on average instead of $6 when you buy ten $1 tickets.

Can scratchoffs ever be profitable?

Yes.

It's rare, and it comes with some caveats, but it's possible.

See our learning center article on exploiting scratchoffs for more details.