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Lottery Math Toolkit

Combinatorial wheels · unpopularity-weighted picks · EV analysis for US multi-state lotteries

Math is honest here. Lottery draws are independently random — nothing on this page predicts future numbers. What we do is help you pick numbers other players don't (less shared jackpot), detect when a jackpot is mathematically +EV, and construct wheel systems with proven coverage guarantees. Play responsibly; you will almost certainly lose your ticket price.
Strategy
All strategies have identical win probability. They differ only in the numbers chosen, which affects expected payout via jackpot-split risk.
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Total cost for 0 tickets: $0.00
Expected Value
Net EV = E[payout] − ticket price, adjusted for cash option, federal tax, and jackpot-split probability.
Historical Frequencies
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Why unpopular numbers help

Your probability of winning any prize tier is fixed by the game's matrix and is identical for every ticket. But if you do hit the jackpot, it's split equally among all jackpot winners. Actual ticket purchases heavily over-weight dates (1-31), cultural lucky numbers, and patterns like diagonals on the play slip. Picking numbers players avoid raises E[payout | win] — real EV improvement, no probability handwaving.

Cook & Clotfelter (1993); Chernoff (1999); Simon (1998)

What wheeling actually does

A covering design C(v, k, t, g) is a set of k-sized tickets drawn from v candidates such that if at least t of the v candidates are in the drawn set, at least one ticket matches g of them. Example: our 6-candidate 4-ticket Powerball wheel guarantees a 3-match if any 3 of your 6 picks are drawn. Wheels cost more tickets but give certainty over a conditional outcome.

Bluskov, La Jolla Covering Repository

When is a ticket +EV?

Let J be the advertised jackpot, c the cash ratio, τ tax rate, and π(J) the probability no one else wins. Expected payout per ticket ≈ (J·c·(1−τ)·π(J))/odds + Σ fixed-tier contributions. When this exceeds the ticket price, it's mathematically +EV. This does happen, briefly, for Powerball and Mega Millions at very high rollover jackpots — but variance is still extreme. The Kelly bet size for any realistic bankroll is effectively zero.

Thorp (1984); also any intro martingale text