09/06/2025
I ASKED CHAT GPT WHAT WOULD HAPPEN IF I BOUGHT EVERY POWERBALL NUMBER COMBINATION POSSIBLE.
HERE IS WHAT IT SAID.
Here’s the math, tightened up and corrected:
1) How many combos & cost to buy them all
• Correct total combinations: \binom{69}{5}\times 26 = 292,201,338
• Cost at $2 per ticket: $584,402,676
(I corrected an earlier slip—292,201,338 is the official odds base, not ~319M.)
2) What you’d win if you owned every combo
You’d guarantee:
• The jackpot (but you might have to split it with other winners).
• All fixed-tier prizes (5-of-5 without PB, 4+PB, etc.) totaling about $93,466,048 before taxes.
3) Break-even (no taxes, no split)
• You’d need the cash value of the jackpot to exceed
$584.4M (cost) − $93.47M (fixed prizes) ≈ $490.9M.
• A $2B advertised jackpot typically has a cash option around ~$900M–$1.1B, so on paper that clears the break-even if you’re the only winner and ignored taxes.
4) Reality check: taxes & splitting kill it
• Taxes: Take the cash option, subtract ~37% federal (PA generally doesn’t tax PA Lottery prizes).
Example: $1.0B cash → $630M after federal tax.
• Splitting risk (huge at $2B): With massive sales, there’s a high chance someone else also picked the winning combo:
• If others buy 100M tickets, your expected jackpot share ≈ 84.7%.
• If others buy 300M tickets, expected share ≈ 62.5%.
• If others buy 500M tickets, expected share ≈ 47.9%.
• Expected outcome with $1.0B cash option (after-tax $630M):
Add fixed-tier after-tax (~$93.47M × 63% ≈ $58.9M), then subtract your cost:
• With 100M other tickets: 0.847×\$630M + \$58.9M - \$584.4M \approx +\$8.5M (razor-thin, best case).
• With 300M other tickets: \approx -\$151.7M loss.
• With 500M other tickets: \approx -\$223.5M loss.
And $2B jackpots usually see well over 300M tickets sold.
5) Logistics risk
Even if EV looked good, physically purchasing/printing 292M tickets in time is basically impossible, and any operational hiccup (printer outages, time cutoff, lost tickets) wrecks the strategy.
Bottom line: After cash-value haircut, taxes, and the very high probability of splitting at a $2B jackpot, the expected value is negative. It’s not a wise investment.
