Mathematician Skip Garibaldi has been studying lottery games and the math behind winning them.

A keen lottery player, the American mathematician does research on algebraic groups and especially exceptional groups.

Scratchers, Powerball, and Mega Millions are just a few of the games he has looked at in his research.

Through his study, Garibaldi has discovered several important tips about lottery games, and he's developed strategies for players who want to try their luck.

Scratchers can also have a high rate of return. However, Garibaldi cautions that the total value of the prizes is usually less than the amount spent on tickets.

Yet, there can be situations where the big prizes in a scratcher game are not claimed at the beginning, leaving a higher proportion of winning tickets to be bought later.

The odds of winning the Powerball or Mega Millions are roughly one in 300,000,000, according to Garibaldi. This is a daunting number, but it's not surprising considering the enormous payouts.

When comparing this to other forms of gambling, such as roulette, it becomes clear that in any game, a higher chance of winning gives a lower payout.

When it comes to picking numbers, Garibaldi advises that if you want to avoid splitting the jackpot, you should pick unpopular numbers.

For instance, dates are often picked by other players, so avoiding them may increase your chances of not having to share the jackpot.

Or selecting a column of numbers on the ticket or playing sequential numbers won't increase your odds, but it might help you avoid sharing the jackpot if you do win.

The idea of playing every single number combination in a drawing has also been considered.

While this is not a practical choice for Powerball and Mega Millions, due to the huge number of possible combinations, he says it might work for smaller state-level lotteries.

There have been cases in New South Wales in 1986, Virginia in 1992, and with the Irish National Lottery, where syndicates bought a large portion of the tickets and ended up winning the jackpot.

When deciding where to play, Garibaldi points out that some states have a higher rate of return than others.

• He uses the example of Oregon in 1999, where there was an $18,000,000 jackpot, but not many tickets were sold. This scenario increases the chance of not having to share the jackpot if you win.

• In terms of a guaranteed lottery win, Garibaldi suggests a game where you bet on a four-digit number with repeated digits (like 1122 or 1212).

• Although the payout won't make you rich, your odds of winning are one in 1,667, which is significantly higher than in larger lottery games.

Garibaldi also discusses the case of Marge and Jerry Selbee, who won almost $8,000,000 playing the Massachusetts Cash Windfall.

In this game, when the jackpot got big enough, the value of smaller prizes was increased, making the overall investment worthwhile even if they didn't win the jackpot.

Garibaldi makes it clear that winning the lottery is a matter of luck more than strategy, but there are ways to speed up your chances.

His insights into lottery odds and number picking can be a helpful guide for those who enjoy the thrill of the game and the fantasy of what they would do if they won.

As he puts it, the real value of a lottery ticket may not be the potential jackpot, but the dreams it allows us to entertain.