WHEN THE SIX New England state lotteries started the Lucky for Life game, with the grand prize of $1,000 a day for the rest of your life, good fortune didn’t exactly fill  government coffers. In the first four months, five people picked the right combination to win the jackpot, which is a minimum of $7.2 million over 20 years or a one-time cash payout of $5.75 million. The high number of winners meant the big-stakes game lost $5 million region-wide.

But after that early rough stretch the odds started working in favor of the lottery commissions and Lucky for Life became a cash cow. No one has hit the top prize in two years. Over that period, the state lottery commissions have paid out in prize money less than half of what they have taken in in sales. The typical cash prize payout percentage for other games is 70 percent or higher. And unlike MegaMillions and Powerball, which have unclaimed jackpots that roll over from week to week, the top prize in the Lucky for Life game remains the same regardless of how long there is no winner. No wonder 12 more state lottery commissions have joined the game.

The lotteries tweaked the Lucky for Life game in January, making it statistically easier to win the grand prize but doubling the odds for winning the second prize of $25,000 a year for life. Since then, there have been no grand prize winners (the odds of winning are still 31-million-to-1) while the number of second-prize winners has fallen. In 2014, there were 15 second-prize winners in Massachusetts alone. Through the first six months of this year, there have been three. The house always wins.