Gambling Science: Why the house will always win in the long run
Undoubtedly you have heard the phrase "the house always wins" when it comes to casino gambling. But what does that actually mean? And why is that said?
After all, people do hit jackpots, people have great runs at table games, people win repeatedly in the sport books, people win at the other games. And casino games are supposed to be fair – so what guarantees the casino still comes out ahead?
The answer lies in a simple but powerful mathematical idea called "the house edge": a small, systematic statistical advantage built into every single casino game. It's the invisible force that ensures the numbers will always tilt toward the house in the long run.
So, let's unpack and quickly take apart the science behind that edge: how it's constructed, and how it plays out over repeated bets.
Roulette: the clearest place to see the house edge at work
Roulette looks like one of the fairest games in the casino. A spinning wheel with numbered pockets, half colored red and half colored black, and a single ball sent spinning around the outside to eventually land in one pocket at random. If you bet the ball will land in a red pocket (or a black one), it feels like a 50–50 gamble.
But the real odds are a little bit different. In most Australian casinos you'll find 38 pockets on the roulette wheel: 18 red, 18 black, and two "zero" pockets marked 0 and 00. (In Europe roulette wheels have 37 pockets, with only a single 0.)
The zero pockets are what creates the house edge. The casino pays out as if the odds were 50–50, however if you get the color right, you get back the same amount you bet. Which most believe that is a 50-50 chance, but in reality, on a wheel with two zero pockets your chance of winning is 47.37%.
When you bet on a color, the house has a 5.26% edge – meaning gamblers lose about five cents per dollar on average. A single-zero wheel is slightly kinder to the gambler at 2.7%.
You don't see the house edge in the course of a few spins, one-two or three shoes of cards, a few hours at a slot machine, etc. But casinos don't rely on a few spins, a few shoes or a few hours at a machine. Over thousands of bets, the law of large numbers takes over. This is a fundamental idea in probability that implies the more times you repeat a game with fixed odds, the closer your results get to the true mathematical average. The short-term ups and downs flatten out, and the house edge asserts itself with near certainty.
The law of large numbers is why casinos aren't bothered by who wins this spin or that shoe of cards, or even tonight, or win for several nights or even more. They care about what happens over the next million bets. They don't care about the winners (unless they are obviously cheating), they only care that there are enough losers. Please read the Wiki for a great detailed run down of 'the law of large numbers', that will help you understand this super important info as to what I just mentioned.
CLICK ON THE WIKI:
https://en.wikipedia.org/wiki/Law_of_large_numbers
Simply a great detailed explanation. OPENING: "In probability theory, the law of large numbers is a mathematical law that states that the average of the results obtained from a large number of independent random samples converges to the true value, if it exists. More formally, the law of large numbers states that given a sample of independent and identically distributed values, the sample mean converges to the true mean."
And once you understand that, you will be able to adjust your play, gain advantages and use a Money Management Method that benefits you whether you are winning or losing.
The Gamblers' Ruin problem
Another way to see why the house always wins is through the so-called Gambler's Ruin problem.
The problem asks what happens if a player with a limited bankroll keeps betting against an opponent with effectively unlimited money (even in a fair game). Say baccarat with 50-50 banker-player wagering with no commission or side bets.
The mathematical answer is blunt: the gambler will eventually go broke if he continually wagers every hand or a large number of hands per shoe, plays everyday or nearly everyday. Period, with absolute certainty.
In other words, even if the odds are perfectly even, the side with finite resources loses in the long run simply because random fluctuations will push them to zero at some point. Once you hit zero, the game stops, while the house is still standing.
You have to fully understand the following without any doubts, "In statistics, gambler's ruin is the fact that a gambler playing a game with non-positive expected value will eventually go bankrupt, regardless of their betting system. The concept was initially stated: A persistent gambler who raises his bet to a fixed fraction of the gambler's bankroll after a win, but does not reduce it after a loss, will eventually and inevitably go broke, even if each bet has a positive expected value."
Casinos, of course, stack the odds even further by giving themselves a small edge on every bet. That tiny disadvantage, combined with the fact the house never runs out of money, makes ruin mathematically inevitable.
The more bets you make, the worse your chances
Say you walk into a casino with a simple goal. You want to win $100, and you plan to quit as soon as you hit that target.
Your approach is to play roulette, betting $1 at a time on either red or black.
How much money do you need to bring to have a decent chance of reaching your $100 goal? A thousand dollars? A million? A billion?
Here's the surprising truth: no amount of money is enough.
If you keep making $1 bets in a game with a house edge, you are practically certain to go broke before getting $100 ahead of where you started, even if you arrive with a fortune.
In fact, the probability of gaining $100 before losing $100 million with this strategy is less than 1 in 37,000.
You could walk in with life-changing wealth and still almost certainly never hit your modest $100 goal. (The full mathematical explanation is spelled out in, 'the law of large numbers', I referred to above.
Betting bigger may give you a fighting chance
So how do you create a real chance of success? You must either lower your target or change your strategy entirely.
If your target were only $10, you'd suddenly have over a 50% chance of going home happy, even if you started with just $25. A smaller goal means fewer bets, which means less opportunity for the house edge to grind you down.
Or you can flip the logic of Gambler's Ruin: instead of making hundreds of small, disadvantageous bets, you can make one big bet. Or several depending on your knowledge and bankroll in regards to what you are attempting.
If you put $100 on red all at once, your chance of success jumps to roughly 47%. This is far higher than the near-zero chance of trying to grind your way up with $1 bets.
The long-run strategy is mathematically doomed, while the short-run strategy at least gives you a fighting chance.
A small house edge adds up
Roulette is the clearest place to see the house edge, but the same structure runs through every casino game. Each one builds in a varying degree of statistical tilt or bias.
Some games, like roulette, have fixed, rule-based house edges that don't change from one player to the next. But others, like blackjack, have a variable house edge that depends on how the game is played. But no game is exempt from the underlying structure.
Small edges don't stay small when you expose yourself to hundreds or thousands of bets. In the long run, the variance fades, and the outcome converges to the house's advantage with almost certainty. Again, maybe not in a session or two or three or even five. But the house's advantage will always outweigh yours, always.
That's why the house always wins. Because mathematics never takes a night off. Never ever.
Win you win, there is no charge to color up and leave. By the way, you can opt-out anytime.