We had an issue like this with a small office lottery at work. So our "setup" was simple. Our national lottery has a 'bonus ball' mechanism. Each participant

We had an issue like this with a small office lottery at work. So our "setup" was simple. Our national lottery has a 'bonus ball' mechanism. Each participant in the office lottery bought a number. If this week's bonus ball is your number, you win the pot. If no-one wins, the pot rolls over. The issue we hit was people joining mid-roll. Say we have 10 players, rolled over 9 weeks putting $90 in the pot. On week 10, a new player joins, $11 joins the pot, and the new player wins $101 for their $1 in. This is legally fair, but everyone with $10 in the pot feels robbed by the $1 newbie. We took the easy out and only accepted new members during a 'fresh' pot - which isn't practical for a state lottery. But it shows the difference between legal fairness and perceived fairness. Someone being able to buy every combination is game-breaking - who would play a lottery where millionaires are guaranteed to win? But roll-overs twist the math until it pays off, and now everyone who's entered in the previous weeks is unwillingly playing a lottery where millionaires are guaranteed to win. It's not impossible to fix either - if you want to fix it. Cap wins at $x and return the remainder to the pot; keep the maximum prize far under the point where buying combinations pays off, and you can keep offering that maximum prize until the roll-over is exhausted. But if you're the one making a profit from the lottery, you don't want to fix it. Massive jackpots are a feature - they encourage more participants, more spending, more profit. And it does seem unfair to protect a mechanism that's so easily exploited, just because it attracts more people to be exploited. And it really can't be good for the long-term health of the game, if people know that roll-overs will be exploited.