A card is decided before it is scratched
A scratch card looks as if something happens when you scratch it. In fact, the outcome was fixed when the card was printed. The coating only hides what is already there. That makes scratch cards different from a lottery draw, where the result is created after tickets are sold, and it explains why the maths works the way it does.
This article describes the general structure, using invented figures and no particular product. Real games publish their own prize tables and rules, which should be read for the facts of any specific card.
Fixed prize pools
Cards in a game are typically printed in large runs, and the game’s design says how many cards in the run carry each prize. Some cards win a small prize, a few win a large one, and the great majority win nothing. The collection of prizes planned for a run is the prize pool.
Because the pool is set in advance, the odds are not created by chance at the moment of scratching. Instead, the cards are shuffled or distributed so that winners are scattered unpredictably, and a buyer receives whichever card they are given.
An illustrative print run
Imagine a game with a print run of 1,000,000 cards sold at 2 each, with this simplified prize pool:
| Prize | Number of cards | Total paid out |
|---|---|---|
| 2 | 250,000 | 500,000 |
| 5 | 50,000 | 250,000 |
| 50 | 4,000 | 200,000 |
| 10,000 | 20 | 200,000 |
Adding the payouts: 500,000 + 250,000 + 200,000 + 200,000 = 1,150,000. Total sales are 1,000,000 × 2 = 2,000,000. So the prizes return 1,150,000 ÷ 2,000,000 = 57.5 per cent of sales in this example, an average of about 1.15 per card against a price of 2.
The number of winning cards is 250,000 + 50,000 + 4,000 + 20 = 304,020, so about 1 in 3.29 cards wins something, since 1,000,000 ÷ 304,020 is about 3.29. The top prize appears on 20 cards out of 1,000,000, which is 1 in 50,000. Note that the 2 prize only returns the price paid, so it is a prize in name but not a gain.
The figures illustrate the structure. They do not describe any real game, and real return rates differ.
What printed odds mean
Many scratch card games print overall odds, such as “the chance of winning any prize is about 1 in 4”. That statement generally refers to the whole print run. It does not mean that every fourth card wins, and it does not mean that a buyer who has just had three losing cards is closer to a winner. Cards are distributed unpredictably, and the sequence of winners and losers in the cards you see is just what randomness looks like.
It also matters what the odds cover. “Any prize” includes small prizes that merely refund the price, so a figure such as 1 in 3.29 does not mean you are likely to profit. The odds of the top prize are much longer than the odds of any prize, and good presentation of both is a sign of clear information.
Prizes are used up as cards are sold
Because the pool is fixed, a prize that has already been won is no longer available to later buyers of the same game. If a top prize has been claimed, the remaining cards from the run cannot win it. Some lotteries publish which prizes remain unclaimed, but unless you know how many cards in the run have been sold, which is rare, this information does not tell you much about your own chance. The idea that a card is “due” to win has the same flaw as the gambler’s fallacy. Remaining prizes also tell you nothing about where in a shop the remaining winning cards are.
Why the design feels exciting
Scratch cards are built to create anticipation. Layouts often show two matching symbols and one that is missing, so many losing cards feel like near misses. Near misses are a result of how the card is laid out, not a sign of a close call, and they can encourage people to buy again. The ideas behind variable rewards and near misses are discussed in more detail in the safety articles on this site.
What the average return tells you
The average return per card is the key statistic, and the example’s 57.5 per cent illustrates the usual pattern: a card is priced above the average prize. Over many cards a player should expect to receive back less than they spend. The expected value of a scratch card is therefore negative, just as it is for a lottery ticket, and no choice of card, shop or timing changes that.
Scratch cards are a form of gambling, and they can be bought quickly and repeatedly, which adds to the risk. Set a limit you can afford, treat the money as the cost of entertainment, and never buy more cards to recover earlier spending. If it becomes hard to stop, a local support service can help.