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The Maths behind gambling systems (and why it doesn’t work)

If you’re hoping to make it big in the world of casino gambling, you’ve got to have your head screwed on, lady luck in your corner and a fool proof, iron-clad system in place! The system is the core of how you make your money back after all; so, with so many people champing at the bit to use them, they’ve got to be good. Right?

Well, not quite, the problem with gambling systems is that… they really aren’t going to work. The core of any gambling system is rooted in a fallacy that means it’s most likely going to end up costing you a lot of money rather than securing that life-changing jackpot. No amount of clever play with your casino bonus from Betfair will make up for the flaws in your gambling system.

Let’s start at the beginning: the key element behind all these systems is the assumption that what came before can affect what’s coming up. That’s normally expressed by saying something like “It’s come up red the last five times, it’s got to come up black next time.” This is what’s traditionally called the gambler’s fallacy, it’s the belief that prior events will affect future outcomes. There was one famous occasion in 1913 where a game of roulette in a casino in Monte Carlo had the ball land on black 26 times in a row. The odds of this happening are something like 136 million to 1 but there were numerous players who bet on red because they believed it was overdue and would land in that pocket the next time the ball rolled. Mathematically, it’s easiest to explain with coin flips and a simple 50:50 chance: if you flip a coin the odds of it landing heads or tails is 50:50. So, if after the first flip it lands on heads and you flip it again, what are the odds it lands on heads? It can be tempting to say the odds will be ¼ but this is only true if you’re looking at the odds of flipping heads twice. If all you’re asking is what will the coin land on for this spin, it’s still a 50:50 chance. This is the core of the gambler’s fallacy, while the probability of flipping two heads in a row is 1 in 4, the odds of each individual flip remains 50:50. This holds true for any gambling situation, such as the roulette wheel above.


Now, when it comes to gambling systems, the majority will be focused on how you mitigate the eventual results of a loss and how to limit the losses you’re going to incur. This will usually take the form of either a progressive or negative progressions style of play. For a progressive, when you win you double your stake, but after a loss you reset to the lowest amount again which means you’ll make plenty of money on your hot-streaks and then have plenty when you start losing. The other version, a negative progression system, is where you double your stake after you lose instead. The latter is normally called the Martingale system and it’s really popular with quite a few gamblers who fall for the fallacy we were talking about earlier.

The problem here is that the Martingale is doubling the stake on the expectation that it will eventually pay off when the gambler wins again. If they lose 1 game, then lose 2 then lose 4 but eventually win 8, they should be back where they started, shouldn’t they? The problem is that this only works if you have both infinite time and money. Any gambler playing against the casino, who expects to win through maths, is going to be sorely disappointed as the probability that they will win might require them to wait for a good long while. Given an infinite timeframe, the probability of a result becomes 1 but if you’re limited to, say, an hour, then it’s pretty much just down to chance. Put simply, you need huge amounts of time and money to guarantee you’ll win, the casino will almost definitely have more of both. This holds true for the positive progression system too, if you lose a significant number of times in a row, all the profits you’ve made will vanish along with your chips. This holds true for just about any system, predicting events that are, by design random, is a recipe for disaster.

This is the inherent flaw in pretty much every gambling system because the spin of the roulette wheel and the fall of the dice aren’t going to change based on what came before. That’s not to say these systems are going to be detrimental to your play, if you have a healthy enough bank balance then few gambling systems will leave you destitute but the maths says they simply won’t see you making a major profit.

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