Let's take the lottery first. There are those people who decide on the numbers they want and they never, ever change those numbers. Their reasoning is that if not today then at some point they will win using those numbers. Last week a man in Staten Island won $17,000,000 dollars in the New York State Lottery. He had been playing the same numbers every week for twenty years. Of course, for every man like that there are probably 970 million people who will not win using this method. (A note: the man elected to get a lump-sum payment. He will be receiving about $5.6 million dollars. So he won the "big" prize and it's not as big a prize as he thought.)
Then there are the people who change their numbers every week. Their reasoning is that eventually they will "have" to find the winning combination. The law of averages says they are wrong.
Then there are the people who approach the lottery like a math problem to be solved. They research every winning number for X number of years. They look at who has won. They attempt to identify which numbers come up most often. They attempt to come up with a formula for a winning combination. And they win with no greater frequency then those who randomly choose a set of numbers.
I was at Waldbaums when someone brought in a winning lottery ticket to cash in. She was not particularly happy with her ticket--she had "only" won $300. "Wow" the rest of us thought. But for this woman only the mega jackpot would do. For her $300 was a paltry sum, a "consolation" prize. Seemed like a small fortune to the rest of us. She was typical of many lottery players who forget that there are many prizes in the lottery, some of higher denomination, some of lower, but all "winning" tickets.
Some people buy huge numbers of tickets from different vendors. Their reasoning is that the more tickets you have in the drawing, the better your chances of winning. Other people buy only one ticket. It's a bitochon issue for them.
Some people do not play the lottery at all. They reason that if they are fated to get a large sum of money, that money will find them somehow. Nothing they are going to do will get that money to them faster. Clearly they have never heard "You have to be in it to win it."
Substitute the terminology of shidduchim and you get a pretty fair description of how some people approach finding a mate.