Lottery
Expected Value
Buying more tickets raises your probability of winning — but does it ever make financial sense? Drag the sliders to see how jackpot size, lump-sum discounting, and tax rate combine to determine whether any purchase strategy produces positive expected profit.
The setup
This lottery has N = 197 = 893,871,739 possible distinct tickets. Buying k distinct tickets at $1 each gives win probability k / N. Expected profit is:
The break-even condition
Setting E[profit] = 0 and solving for k reveals that k cancels entirely:
Expected value is independent of how many tickets you buy. If Jnet < N, the lottery is always negative EV regardless of purchase size.
The default numbers
- Advertised jackpot: $1,000,000,000
- Lump-sum factor: 60% → $600,000,000
- Federal tax rate: 37% → $378,000,000 net
- Ticket space N: 893,871,739
- Net jackpot < N: always negative EV
The net jackpot ($378M) is 42.3% of the ticket space. EV per dollar spent is −$0.577 — you expect to lose 57.7 cents on every dollar invested.
What would make it profitable?
Try dragging the jackpot slider above $2,366M with default lump-sum and tax settings — watch the verdict box turn green and the curve cross above zero.
Expected Value Calculator
Adjust the sliders to see how each parameter affects expected profit.