Risk Decision Lottery
Choose between a guaranteed $2,000,000 and a 99% chance at $200,000,000. Use simulations to see how often risk beats certainty.
"Stable $2,000,000 vs a 99% chance at $200,000,000—what would you choose?"
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$2,000,000.00
Expected value: $2,000,000.00
99% chance of $200,000,000.00
1% chance of $0
Expected value: $198,000,000.00
Select how many draws to run
Each draw has a 99% chance to award $200,000,000 and a 1% chance to award nothing.
Guaranteed amount you would receive every time.
Enter the probability of winning Plan B's top prize.
Amount awarded when Plan B hits.
What you take home when Plan B misses (usually $0).
Number of draws to forecast for total expected value.
Per draw expected value
Plan A
$2,000,000.00
Plan B
$198,000,000.00
Difference per draw
+$196,000,000.00
Total expected value (1 draws)
Plan A
$2,000,000.00
Plan B
$198,000,000.00
Total difference
+$196,000,000.00
- Winning probability
- 99%
- Draws
- 1
- Break-even insight
- Plan B overtakes Plan A when success chance exceeds 1%.
- Recommendation
- Expected value favors Plan B.
Actual results will vary—expected value is an average over many draws.
All calculations are theoretical and ignore taxes, fees, and capital constraints.
What the math says
- Plan B's expected value is 99% × $200,000,000 = $198,000,000, far above Plan A's $2,000,000.
- Variance is extreme: a 1% loss means zero payout, so bankroll management matters.
- More draws push results toward the expected value, but short runs remain highly volatile.