From the glitz, glamour and bright lights of Las Vegas to a small, smoky room in the corner of your local pub, the allure of the flutter is designed to be a tantalising one.
Whether it’s a poker machine or a table-based game of chance or skill, for a bit of harmless fun or a genuine attempt at a jackpot, Australians blow millions on legalised gambling each year. And if you walk away with your pockets empty, assured that ‘the house always wins’, you’re right, and here’s how they do it.
Casinos thrive not because every gambler loses every night, but because of the mathematics embedded in the design of every game they offer.
At the core of this system is a concept known as the ‘house edge’ – a small, statistical advantage built in to ensure the casino’s profitability over time, even though individual players may win big on any given day.
The house edge is defined as the ratio of the average loss to the initial bet a player makes. It expresses, as a percentage, how much the casino expects to retain from bets in the long run after millions of wagers have been made over weeks or months, not from the takings on any one night.
The house edge does not determine the outcome of a single bet. Instead, it plays out over many bets. Each casino game – from roulette to the pokies to table games like blackjack and craps have a particular house edge that reflects its rules and payoffs. Over a large number of bets, the law of large numbers ensures results converge toward the expected mathematical outcomes. Short-term wins and losses average out, leaving the casino’s advantage intact. This is why casinos can absorb daily payouts and still come out ahead over months and years.
For those with more time and sufficient interest, YouTube offers a number of lengthy university lectures unpacking Gambler’s Ruin more effectively. But for those with less time, here’s a version of it explained in one minute.
Roulette looks deceptively fair. Bets on red or black appear to offer near-even odds. But an Australian roulette wheel has 38 pockets (18 red, 18 black, and two marked zero), the true probability of winning a red/black bet is about 47.37% – not 50 per cent. The zeros don’t pay out, yet they are included in the spin results. This creates a house edge of approximately 5.26% on such bets.
European wheels have a single zero pocket, which reduces the house edge to about 2.7%, but the principle is the same: the casino pays out winners as if the odds were even, yet the actual odds are always tilted slightly in its favour.
Not all games are created equal. According to data from Wizard of Odds, house edges differ significantly across popular casino games.
This range shows how some games – like blackjack and some table bets – can offer relatively low house edges, while others such as slots and keno can be much harsher for players.
Casinos are not especially concerned about who wins or loses in the short term. What matters to their business model is aggregate play – the cumulative effect of millions of bets. The law of large numbers predicts that as the number of wagers increases, the actual results will closely approach the expected mathematical results. Over thousands or millions of spins or hands, the house edge nearly guarantees the casino’s expected profit.
Another aspect of gambling math is what’s known as the Gambler’s Ruin problem. This is when a player with a finite purse competes against an opponent with effectively unlimited resources, that being the casino. The player is statistically certain to go broke eventually, even if the game is fair. When the house also has a statistical edge, ruin becomes even more inevitable.
Consider a hypothetical player who aims to win modestly, say $100, by betting $1 at a time on red or black in roulette. No matter how much money the player arrives with, the chance of reaching that goal before exhausting their money is extremely low – next to zero. The longer the player continues to make bets, the more the house edge works against them. In a classic analysis, the probability of gaining $100 before losing $100 million with this approach is less than one in 37,000 – effectively negligible.
Even betting systems that adjust stake sizes based on wins or losses cannot overcome the house edge in the long run. While certain strategies may temporarily heighten the excitement or reduce volatility, they do not change the underlying expected loss imposed by the math.
There are ways to improve short-term probabilities. Lowering your target, by aiming to win $10 instead of $100, reduces the number of bets needed, which lessens exposure to the house edge and gives a better-than-even chance of success in the very short run.
Betting a single larger sum at once can also yield a higher immediate probability of hitting a target than making many small wagers.
However, these approaches do not alter the fundamental maths of the house edge – they merely reduce the number of trials over which it can assert itself.
Across all casino games, the house edge reflects the average gross profit a casino expects to retain per bet over the long term. While players can and do win in the short term, and some games have lower edges than others, the cumulative effect of repeated play tilts the financial outcome in the casino’s favour.
That is why, despite occasional jackpots and winning streaks, casinos remain profitable. The underlying odds are structured so that, over time, the house advantage prevails – a mathematical certainty in the long run.