What is a betting system?
A betting system is a fixed rule for what to bet or how much to stake, followed the same way every time. A staking system cannot beat the book on its own, because changing the size of your bets does not change the price you are betting into.
Two kinds
There are staking systems, which tell you how much to bet, and selection systems, which tell you what to bet. The best known staking system is the Martingale: double the stake after every loss. Flat betting and betting a fixed percentage of your bankroll are staking systems too. Selection systems are rules found in past results, such as backing every home underdog coming off a loss.
In some countries a "system bet" means something else again: a set of small parlays written from one list of picks. Here that is called a round robin.
The doubling system
Start with $10 at even money. Win and you are $10 ahead. Lose and you bet $20, then $40, and so on, so that the first win gets everything back plus $10.
Now lose seven in a row. You are down $1,270 and the eighth bet is $1,280, which means you are risking $2,550 in all to finish $10 ahead, and that is the kind of bet I'd have been glad to write all day long.
Seven straight losses on a coin flip happens one time in 128. Play enough rounds and it arrives. Then your bankroll runs out, or the book's bet limit stops you from doubling again (that is what the limit is for). At -110 it is worse, because every win pays less than the stake.
Why selection systems fade
Search enough past seasons and you will find rules that would have won. Most of them won by chance, and chance does not repeat on request. The ones that were real don't last either, because books read the same results and the line adjusts until the edge is gone.
What I'd use instead
Dull staking. Bet the same amount, or the same small share of your bankroll, on every play; I'd keep one bet to 1 or 2 percent of the bankroll, and under 5 always. It will not make a losing bettor win. It keeps a winning one alive through the bad runs, and it makes a losing one lose slowly. Never raise a stake to recover a loss.
The bankroll guide has the numbers. For the part that decides whether you win, see what a betting strategy is. As for any system for sale, I'd treat it as a product, because the seller's edge is the sale.
The price decides whether you win. A staking system only decides how fast you find out.
Related questions
What is a sports betting strategy?
A sports betting strategy is a plan for which bets you make, at what price and for how much. The ones that hold up rest on two things: getting a better price than the bet deserves, and keeping stakes small enough to survive the losing runs.
What is the vig?
The vig is the bookmaker's cut, built into the price. At the standard -110 you lay $110 to win $100, and that extra $10 is how the book gets paid.
How do betting odds work?
Betting odds are a price. They tell you what a bet pays and, read the other way, how often it has to win. Odds of -200 mean you risk $200 to win $100. Odds of +150 mean you risk $100 to win $150.