Five Years of Scratch Cards vs Five Years of a Savings Account

Scratch cards get compared to draw games and lose, which is unfair: they pay back substantially more. The comparison worth running is against the boring alternative, over a period long enough for the arithmetic to be visible.

Five years, $20 a week, $5,200 in total. Two routes.

The scratch-card return rate, sourced

We need a return-to-player figure that comes from audited accounts rather than a manufacturer's claim. The Michigan Lottery's FY2025 Annual Comprehensive Financial Report is the best available, because Michigan is the rare operator that publishes sales and prizes by game type:

Retail instant (scratch) tickets, FY2025: sales $2,265,049,278, prizes $1,722,936,453.

$1,722,936,453 ÷ $2,265,049,278 = 0.7607, or 76.07%

That is a realised, year-long, audited figure across a whole state's scratch programme — not a single game's printed structure. For context, from the same report, Michigan's Powerball returned 51.39% and Mega Millions 48.75%. Scratch cards return roughly half as much again as draw games, which is the honest starting point and the reason this comparison is worth doing carefully rather than dismissively. The full breakdown across operators is in return to player by game.

We use 76.07% below. If your state's rate differs, substitute it; the structure of the arithmetic does not change.

Route A: $20 a week on scratch cards

Model it the way people actually play: buy $20 of cards each week from income, and bank whatever comes back.

Expected return per week:

$20 × 0.7607 = $15.21

Expected net cost per week: $20 − $15.21 = $4.79

Over 260 weeks the gross outlay is $5,200 and the expected winnings are:

$5,200 × 0.7607 = $3,955.64

If the winnings are banked at the FDIC national savings rate of 0.38% (August 2026), we apply the ordinary-annuity formula to a weekly deposit of $15.21:

FV = 15.21 × ((1 + 0.0038/52)^260 − 1) ÷ (0.0038/52) = $3,993.11

Route B: $20 a week straight into savings

Same formula, weekly deposit of $20:

• r = 0.0038 ÷ 52 = 0.0000730769
• n = 52 × 5 = 260
• (1 + r)^260 = 1.019173
• FV = 20 × (0.019173 ÷ 0.0000730769) = 20 × 262.38 = $5,249.52

Difference after five years: $5,249.52 − $3,993.11 = $1,256.41.

At a competitive rate rather than the national average — say 4.0%, which is available from online savings accounts — the same arithmetic gives $5,754.03 for the savings route and $4,376.87 for the banked-winnings route, a gap of $1,377.16.

The three things this model gets wrong, all in the cards' favour

Honesty requires stating where the simple model flatters the scratch route.

1. It uses the expected value, not your value. Prize distributions are heavily right-skewed. The 76.07% includes the top prizes, which a handful of tickets win. The median player does worse than 76%, in the same way the median Premium Bonds holder does worse than 4.35%. A typical five-year outcome is somewhat below $3,955.

2. It assumes the printed odds apply to your box. They do not, exactly. Overall odds describe the full print run at the moment of printing. As big prizes are claimed the remaining tickets get worse while the printed figure stays the same — the subject of why the printed odds are not your odds. The correction is usually adverse.

3. It assumes you bank the winnings. In practice small wins are frequently restaked, and restaking compounds the house edge geometrically. A single $20 restaked in full each time is worth $20 × 0.7607^k after k rounds:

Ten cycles of a 76% return leaves 6.5% of the stake. That is not a moral point; it is what repeated multiplication by 0.76 does, and it is the single largest divergence between the model above and how the product is used. A 76% return-to-player is only a 76% return if the money leaves the game.

The one thing the model gets wrong in savings' favour

Inflation. Both columns are nominal. In real terms the 0.38% savings account loses purchasing power in most years, so route B is not "safe", it is merely a smaller loss with a positive nominal sign. That is why invest instead of tickets runs the same money at equity-like rates, and why the invest-instead calculator lets you set your own assumption.

What the comparison actually establishes

Not that scratch cards are irrational. At 76.07% they are the best-value lottery product on sale, and a $2 card genuinely buys thirty seconds of anticipation that some people value at $2.

What it establishes is the size of the gap, which is the thing people cannot estimate by feel: $1,256 over five years at $20 a week, before the three adjustments above, all of which widen it. Multiply out to a forty-year habit and it is a five-figure sum, computable in advance by the lifetime spend calculator.

If you want to evaluate a specific card rather than a state average, the scratch EV calculator works from published prizes-remaining data, and scratch card expected value explains what to feed it. And if the conclusion is "keep playing but cap it", that is a perfectly defensible conclusion and the mechanics are in setting a lottery budget.