I have used a similar example in Statistics class when learning about the central limit theorem: for a better chance to win the lottery, buy more tickets to get closer to certainly winning.

Bernard Marantelli had a plan in mind. He and his partners would buy nearly every possible number in a coming drawing. There were 25.8 million potential number combinations. The tickets were $1 apiece. The jackpot was heading to $95 million. If nobody else also picked the winning numbers, the profit would be nearly $60 million.

Marantelli flew to the U.S. with a few trusted lieutenants. They set up shop in a defunct dentist’s office, a warehouse and two other spots in Texas. The crew worked out a way to get official ticket-printing terminals. Trucks hauled in dozens of them and reams of paper.

Over three days, the machines—manned by a disparate bunch of associates and some of their children—screeched away nearly around the clock, spitting out 100 or more tickets every second. Texas politicians later likened the operation to a sweatshop…

Over the years, Ranogajec and his partners have won hundreds of millions of dollars by applying Wall Street-style analytics to betting opportunities around the world. Like card counters at a blackjack table, they use data and math to hunt for situations ripe for flipping the house edge in their favor. Then they throw piles of money at it, betting an estimated $10 billion annually.

How representative sampling works: get a large enough sample with characteristics that mirror that of the larger population and you can have confidence that the sample results are within several percentage points of results if you measured the same things for the whole population. And as your sample size increases, you get closer and closer to the characteristics of the whole population.

Buying one lottery ticket means the buyer has really small odds of winning. Super small. Buy more tickets and the odds of winning increase. Buy nearly all the tickets and your odds go way up. Buy them all and you win.

It sounds like the gamblers above compare the cost of buying all the tickets to the jackpot and go all in when there is a large enough gap. But the central limit theorem suggests they could drastically increase their odds without buying every ticket; might that be worth it financially?