The mathematics of lotteries — honestly explained.
Ten long-form essays on probability, expected value, the gambler’s fallacy, game-design economics, and the quantum physics behind our random number generator. Written for readers who want the math, not the marketing.
How Much Information Is in a Lottery Ticket?
A Shannon-entropy view: a Powerball ticket carries about 28 bits of information. Compared to your phone, that's nothing.
Why Statistical Tests on Lottery Numbers Find Nothing
People claim to find patterns in lottery draws all the time. The honest math says: every well-implemented lottery passes every test you can throw at it.
When Does a Rollover Jackpot Make a Lottery Ticket a Good Bet?
A rigorous look at jackpot rollover math, including the often-forgotten shared-jackpot adjustment that wipes out most of the apparent gains.
The April 2025 Mega Millions Redesign: A Math Walkthrough
Mega Millions redesigned itself in 2025. Headline: better jackpot odds. Fine print: a $5 ticket and a 2.5× higher cost per dollar of expected return.
Birthday Clustering and the Shared Jackpot
Humans love their birthdays. Birthdays cluster between 1 and 31. The lottery's pool goes much higher. The consequences are quantifiable.
Quantum Randomness vs. Pseudo-Random
Quantum entropy is unforgeable. Pseudo-random is good enough for the lottery. Here's why the distinction matters more for crypto than for $2 tickets.
The Expected Value of a Lottery Ticket
Expected value is the only mathematical answer to 'is this a good bet?' For Powerball, the answer is usually -$1.50 per $2 ticket.
The Quick Pick Paradox
A textbook case of Simpson's reversal — the kind of statistic that fools smart people into wrong inferences.
The Gambler's Fallacy in Three Numbers
If a number hasn't been drawn in 80 weeks, is it 'due'? No. Independence is the most counter-intuitive truth in probability.
The 1-in-292-Million Number
The number 292,201,338 isn't a marketing figure. It's an exact count of the Powerball outcome space, derivable in two lines.