Calculate the expected value of scratch-off lottery tickets
EV = Σ(Prize × 1/Odds) - CostEnter ticket cost and prize structure
Expected value breakdown
Return Rate
35.5%
House Edge
64.5%
Win Any Prize
1 in 5.3
Win Probability
18.7%
Quick-start with common scenarios
Scratch-off EV = Sum of (Prize × 1/Odds) - Ticket Cost. Most scratch-offs return 60-70%, meaning for a $1 ticket, you get back $0.60-$0.70 on average. The house edge is 30-40%. Better than some games, but still negative EV. Higher-priced tickets often have slightly better return rates.
Add up each (Prize Amount × Probability of Winning) for all prize tiers, then subtract the ticket cost. For example: ($100 × 1/1000) + ($10 × 1/50) + ($2 × 1/10) - $1 = $0.10 + $0.20 + $0.20 - $1 = -$0.50 EV.
Generally, higher-priced tickets ($10-$30) have slightly better return rates (65-70% vs 60-65%). However, no scratch-off has positive expected value. Check your state lottery website for remaining prizes - games with more top prizes left are better.
Mathematical strategy is limited. You can: 1) Check remaining prizes online before buying, 2) Avoid games where top prizes are claimed, 3) Buy higher-denomination tickets for slightly better odds. But no strategy overcomes the house edge.
Most scratch-offs have overall odds of 1 in 3 to 1 in 5 for winning ANY prize (including breaking even). However, most wins are small - just getting your money back or winning $1-$2. Big prizes remain very rare.