Scratch cards and instants

The Expected Value of a Scratch Card, Calculated Properly

Scratch EV is genuinely computable — unlike a draw game's, it depends on how much of the deck is left. Here is the full method.

Expected value is more meaningful for scratch cards than for any other lottery product, because the deck is finite, the prize structure is published, and — unusually — the answer changes over the life of the game.

Two different numbers

Launch EV — the expected value of a ticket drawn from the complete print run. Fixed by design, and equal to the game's stated return to player.

Current EV — the expected value of a ticket drawn from what is left in the racks today. This moves as prizes are claimed, and it is the number that applies to you.

Most articles compute the first and call it the second.

Launch EV

EV = (total prize money in the run) ÷ (number of tickets in the run)

Using the worked game from how scratch card odds work — a $5 game, 4,000,000 tickets, $13,600,000 in prizes:

EV = $13,600,000 ÷ 4,000,000 = $3.40 per $5 ticket → 68% return

Equivalently, summing prize × probability:

Prize Count Probability Contribution
$500,000 2 1 in 2,000,000 $0.25
$10,000 20 1 in 200,000 $0.05
$1,000 1,000 1 in 4,000 $0.25
$100 40,000 1 in 100 $1.00
$20 140,000 1 in 28.6 $0.70
$5 920,000 1 in 4.35 $1.15
Total $3.40

Both routes agree, as they must. Note where the value actually sits: the two headline $500,000 prizes contribute 25 cents of the $3.40, while the $5 and $20 tiers contribute $1.85 between them. The top prize sells the game; the small prizes are the game — the same pattern as lower-division prizes in draw games.

Current EV

EV = Σ (prize × prizes remaining) ÷ tickets remaining

Suppose the published table now shows both $500,000 prizes claimed, half of everything else claimed, and roughly half the run sold:

Remaining prize money = ($13,600,000 ÷ 2) − $1,000,000 = $5,800,000 Tickets remaining ≈ 2,000,000 EV = $5,800,000 ÷ 2,000,000 = $2.90 per $5 ticket → 58% return

A ten-point drop, with nothing on the card changed. The scratch card EV calculator runs this from the operator's published numbers.

The assumption that does the damage

Tickets remaining is the weak input, and it dominates the result.

Operators publish prizes remaining, not tickets remaining. The standard workaround assumes tickets sold is proportional to prizes claimed, which introduces two errors:

  • Claim lag. A ticket can be sold weeks before it is scratched, and claimed later still. Prizes claimed therefore understates tickets sold, biasing your denominator down and your EV up.
  • Unclaimed prizes. Some winning tickets are never presented — lost, discarded, forgotten (what happens to unclaimed prizes). These stay in the "remaining" column forever, again flattering the estimate.

Both errors push the same way: naive prizes-remaining calculations overstate current EV. Any tool quoting a scratch EV to the cent is ignoring this. Treat the output as an estimate with a meaningful error bar.

What EV does not tell you

Variance. A $5 ticket with EV $3.40 does not return $3.40. It returns $0 about 72% of the time. Expected value describes an average over a deck you will sample a handful of times.

Play rate. This matters more than the percentage and is the subject of do scratch cards have better odds than the jackpot draw?. A 68% return is better than a draw game's ~50% — but you can buy and scratch twenty cards in an hour, and you cannot play twenty draws in an hour. Loss per hour is far higher on the better-returning product.

Reinvestment. Winnings on instant games are overwhelmingly small and immediately available at the same counter. A $5 win re-spent is $5 that returns 68% again — and again. Applying the 68% repeatedly is what makes the real, realised return so much worse than the headline. Model your own history with the lifetime spend calculator.

The bottom line

Scratch cards return more per dollar than draw games and are the only lottery product whose current expected value you can genuinely compute. They remain a product with a negative expected value, sold at a speed that amplifies the loss — and the honest version of that sentence needs both halves.

Try it yourself

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Sources

Last verified: 2026-08-29