Scratch cards and instants
Draw games generate a result when you play. Instant games printed theirs months ago — which means the odds genuinely change as the game sells through.
Scratch cards and draw games look like the same product sold two ways. Mathematically they are opposites, and almost every confusion about instant games comes from applying draw-game intuition to them.
When you buy a Powerball ticket, the winning numbers do not exist yet. They are created at the draw, independently of your ticket. That is why draw odds are fixed forever and why no analysis of past draws can help you (the gambler's fallacy).
A scratch game is the reverse. The operator decides in advance how many tickets to print and exactly how many of each prize to include, then prints them. Your ticket was a winner or a loser before you walked into the shop. Buying is a sampling problem, not a probability event.
That means scratch games are drawn without replacement from a finite deck — and a deck that is being depleted by everyone else buying from it.
Take a hypothetical $5 game with 4,000,000 tickets:
| Prize | Number printed | Total prize money |
|---|---|---|
| $500,000 | 2 | $1,000,000 |
| $10,000 | 20 | $200,000 |
| $1,000 | 1,000 | $1,000,000 |
| $100 | 40,000 | $4,000,000 |
| $20 | 140,000 | $2,800,000 |
| $5 | 920,000 | $4,600,000 |
| Total winners | 1,101,022 | $13,600,000 |
From this we can derive everything the back of the card would tell you:
That 68% is deliberately realistic. The Minnesota Lottery publishes its actual payout percentages by price point, and $5 games return 68% — see which price point has the best return.
Suppose half the run has sold — 2,000,000 tickets remain — and, by chance, both $500,000 top prizes have already been claimed, with the smaller prizes claimed roughly in proportion.
The prize money left in the remaining tickets is:
($13,600,000 ÷ 2) − $1,000,000 = $6,800,000 − $1,000,000 = $5,800,000
Spread across 2,000,000 remaining tickets:
$5,800,000 ÷ 2,000,000 = $2.90 expected value per $5 ticket
The return to player on the tickets still in shops has fallen from 68% to 58%. Nothing was announced. Nothing changed on the card. The overall odds printed on the back still say 1 in 3.63 — and that figure is still true, because roughly the same proportion of remaining tickets are still winners. They are simply worth less.
This is the single most important fact about instant games, and it has its own article: why the odds printed on the back are not the odds you face.
Because the deck is finite and public, two things follow that have no equivalent in draw games:
1. You can compute the real EV of a specific game right now. Most US state lotteries publish a prizes remaining table for each active game. With that table you can calculate the expected value of the tickets still out there rather than the value the game had at launch — see how to check prizes remaining and the scratch card EV calculator.
2. Instant games can, in principle, leak information. Because the result is printed, the visible face and the hidden face have to be generated together — and if the generation is flawed, the visible face can betray the hidden one. This is exactly what a Toronto statistician found in an Ontario game in 2003 (the Srivastava scratch flaw). No draw game can have this failure mode, because there is nothing to leak.
Instant games return more of your money than draw games do — 63% to 74% depending on price point, against roughly half for most draw games (return to player by game). They are also played far faster, which matters more than the percentage. That trade-off is worked through in do scratch cards have better odds than the jackpot draw?.
Last verified: 2026-08-29