How to calculate expected value in casino games

Every wager in a casino carries a mathematical fingerprint. Expected value, or EV, is the average outcome a game returns over millions of hands or spins. It is the most useful number a player can learn before risking money, whether on a pokie in Melbourne or at a baccarat table in Sydney.

Australian players are increasingly curious about the maths behind their favourite games. With Crown Melbourne and The Star Sydney anchoring the scene, plus thousands of pokie machines in clubs and hotels nationwide, understanding EV separates casual fun from costly habit. Local payout rules and taxes shape how the maths plays out.

This guide walks through the core principles of expected value, shows how to apply it across game types, and explains why short-term luck can mislead even seasoned players. You'll also find a table comparing common Australian casino favourites and the realistic returns you can expect.

The core formula and what it means

Expected value is a weighted average. You multiply every possible outcome by the probability of that outcome, then add the results. In casino terms, this tells you what you would win or lose on average per dollar bet if you played the same wager millions of times.

The formula looks like this: EV = (Probability of Winning × Amount Won) − (Probability of Losing × Amount Lost). A positive EV signals a profitable bet, while a negative EV shows a losing one long term. Nearly every casino game carries a negative EV, which is how the house makes money. For the conceptual side, see the role of EV in gambling strategy.

A simple example: bet AUD 10 on a coin flip, win AUD 20 on heads or lose AUD 10 on tails. With 50/50 odds, the EV is (0.5 × 20) − (0.5 × 10) = AUD 5, a positive expected value. No casino would offer this, but it shows how the maths work.

House edge and return to player explained

Two concepts appear alongside EV: house edge and return to player, or RTP. House edge is the casino's average profit as a percentage of your wager; RTP is the percentage returned to players over time. They sum to 100 percent, so a 5 percent edge equals 95 percent RTP.

Australian pokie machines display RTP, and state regulators audit these figures. Pub and club pokies run 85–92 percent RTP, tighter than the 95 percent or higher common in many overseas-licensed online versions.

Game Type	Typical House Edge	Typical RTP	Notes for Australian Players
European Roulette	2.7%	97.3%	Single zero; common at Crown Melbourne
American Roulette	5.26%	94.74%	Double zero; less common locally
Blackjack (basic strategy)	0.5%–1%	99%–99.5%	Rules vary; check soft 17 rule
Punto Banco Baccarat	1.06% (banker)	98.94%	Popular in Sydney high-roller rooms
Pokies (pub/club)	8%–15%	85%–92%	Lower RTPs legal under state rules
Online Pokies (overseas)	3%–5%	95%–97%	Licensed by offshore regulators

This table shows that game choice dramatically affects your expected outcome. Choosing European over American roulette, for example, nearly halves the house edge on every spin.

Applying EV to table games

Table games like blackjack, baccarat, and roulette offer excellent opportunities to calculate EV because their rules are fixed and outcomes are transparent. You can often work out the expected value of a specific bet in minutes with a calculator.

Backing the banker in punto banco carries a house edge of roughly 1.06 percent, so every AUD 100 wagered long term costs about AUD 1.06. The player bet edges higher at 1.24 percent, while the tie bet is a trap with an edge over 14 percent. Knowing these numbers before sitting down separates a sharp session from an expensive one.

Blackjack adds a wrinkle: EV depends on your decisions. Perfect basic strategy can push the house edge below 0.5 percent, but deviating on a few hands can balloon it to 2 or 3 percent. Many Australian players keep a strategy card handy at Crown or The Star, where multi-deck shoes are standard.

EV calculations for pokies and slot machines

Pokies present a different challenge. The maths is the same in principle, but the sheer number of symbol combinations, scatter pays, and bonus features makes hand-calculating EV nearly impossible. Players rely instead on the published RTP, which the software uses to determine long-term payouts.

A 90 percent RTP pokie returns AUD 90 for every AUD 100 wagered across millions of spins. Short term, results swing wildly: a player might hit a AUD 500 bonus on a AUD 1 spin, or burn through AUD 50 without a feature. This is why casual players misjudge EV, as short sessions are dominated by variance, not the underlying average.

Check whether the pokie has a bonus buy option, common online. These usually carry a lower RTP than the base game, often 2 to 4 points lower, because you pay a premium to skip to the bonus. Read the help screen before committing.

Variance, standard deviation, and bankroll planning

EV shows where you end up long term, but not the journey. Variance measures how far results deviate from expected value in a session, and standard deviation quantifies that. High-variance games like progressive pokies swing wildly; low-variance games like baccarat even-money bets ride smoother.

Smart bankroll planning accounts for both. A common rule is to bring 50 to 100 base bets for a low-edge table game, and 200 to 300 for a high-variance pokie session. This cushion lets the maths play out without busting in a cold streak. For a detailed walkthrough, this practical guide on how to calculate EV in real betting situations is well worth a read.

Mistakes players make when estimating EV

The most common error is confusing short-term wins with long-term expectation. A AUD 500 jackpot on a 90 percent pokie does not make the machine "hot" or "due"; each spin is independent, and the next still carries a 10 percent house edge.

Another mistake is ignoring side bets. Many Australian blackjack tables offer "perfect pairs" or "21+3" wagers that look tempting but carry a 5 to 10 percent house edge. The progressive side bet on Caribbean stud or three-card poker drains bankrolls fast. Always check the EV of every wager, not just the main one.

Finally, players forget comps and loyalty perks. Cashback and point conversion can reduce the house edge by a few tenths of a percent. At Crown Melbourne, regulars can shave 0.2 to 0.5 percent off their effective loss rate, which over hundreds of hours adds up to real money.

Understanding EV turns gambling from guesswork into an informed decision. Choose low-edge games, manage your bankroll for variance, and remember the house always wins long term. Set a budget, treat wins as bonuses, and walk away when the fun stops.