Mathematical casino edge and expected value: table of main games New Zealand market (2026)

For each game in the casino, it is mathematically determined in advance how many percent of the wagered amount the casino will keep in the long term. This percentage does not depend on luck, the dealer or your mood — it is a property of the rules of the game. For blackjack it is 0.5%, for American roulette 5.26% — more than ten times as much. For the Sazka Sportka lottery, it is even around 50%. A player who bets € per hand in blackjack for one hour loses € on average. The same player will lose NZ$ 0on the same bets in American Roulette. In the lottery, for the same turn of NZ$ 0they will lose an average of NZ$ 0These numbers are not estimates — they are based on the rules of the game and apply equally to betting from the bus, playing at home in the living room or sitting at a table in a brick and mortar casino.

New Zealand player who goes to the casino once a month with a budget of € and plays slots with a return of 92 — 94%, in the long run donates 300 — NZ$ 10to the casino from each such visit. That's NZ$ 0per year. The same player with the same budget in basic strategy blackjack or baccarat loses on average only 25 — NZ$ 0per visit — 300 — NZ$ 40per year. The difference is 3,250 — € per year with identical time spent in the casino. That's one holiday weekend at the cottage, or buying oil and brake discs for the car. The choice of game is therefore not a matter of personal taste, but mathematically the most important decision of the player.

This article reviews the mathematical dominance of the main games available in licensed New Zealand casinos. For each there is a formula, a practical example in crowns and a comparison of variants so that you know what will cost you the least and the most in the long run. The data comes from published game returns, pay tables and official rules and is verified against several independent sources.

What is the mathematical advantage of the casino

The casino's mathematical edge is the theoretical percentage of each bet that the casino will keep over an infinite number of repetitions. It is expressed as a percentage. If a game has an edge of 2.7%, this means that for every € wagered on that game, the casino will on average keep NZ$ 100and return NZ$ 0to the players (in the form of winnings). The sum of the house edge and return to player (RTP) is always exactly 100%.

Predominance is not created by deception or trickery. It arises from a mismatch between the probability of winning and the payout ratio. In European Roulette, the probability of winning when betting on one number is 1/37 (about 2.7%). A fair payout should be 36 : 1 — if played with equal odds and a fair payout, the game would have an edge of 0%. However, the casino pays 35 : 1. This one crown saved on each hypothetical win constitutes the casino's mathematical advantage and works out to be exactly 1/37= 2.7%. For American Roulette, the odds are 1/38 (due to the added double zero), the payout remains 35 : 1, and the edge doubles to 2/38= 5.26%.

The same logic applies to every game. For a 96% payback slot, the paytable is set to return an average of 96 pennies for every crown bet. When rolling the game reels, the software already knows which symbols can fall and in what proportion — the resulting distribution is always such that it corresponds to the set return in the long term. Detail in article about random number generator and online slot machine audits .

Important — the advantage is a long-term average, not a guarantee: Mathematical advantage is manifested only with thousands and tens of thousands of bets. You can win even NZ$ 0in one hour of play on European Roulette, although its average edge is 2.7%. In the second hour, you can lose your entire budget. Short-term results are determined by variance (swing around the mean). Overhead is important especially when comparing games and budgeting — for the same turnover, the expected long-term loss is directly proportional to the advantage. Also look at article about budget management in an online casino .

Bet Expected Value — The Key Formula

The expected value (abbreviation EV) is the mathematical average result of the bet with infinite repetition. It expresses how much one bet costs you on a long-term average. The formula is simple:

Expected value= bet size × (-edge in decimal)

Examples for a NZ$ 10bet:

• European Roulette (edge ​​2.7%): EV= 250 × (-0.027)= -NZ$ 03 per bet.
• American Roulette (5.26% edge): EV= 250 × (-0.0526)= -NZ$ 201 per bet.
• Basic Strategy Blackjack (0.5% edge): EV= 250 × (-0.005)= -NZ$ 01 per bet.
• Baccarat on Banker (1.06% edge): EV= 250 × (-0.0106)= -NZ$ 03 per bet.
• Classic slot (4% advantage): EV= 250 × (-0.04)= -€ per spin.
• Bet NZ$ 0on Sazka Sportka (predominance 50%): EV= 25 × (-0.50)= -NZ$ 10 2 per lot.

With 100 bets of NZ$ 10(turnover NZ$ 0) the expected loss is:

• Basic Strategy Blackjack: NZ$ 0
• Baccarat (Banker): NZ$ 10
• European Roulette: NZ$ 30
• Classic slot (RTP 96%): €
• American Roulette: €
• Lower Payout Slot (RTP 92%): €

The difference between blackjack (NZ$ 0) and the worst slot machine (€) is 16 times — with the same turnover, the same time spent in the casino and the same number of bets. This is the main reason why the choice of game affects the long-term result the most. Detail in of the article about the real return of New Zealand slots and in article on return and volatility .

How much do you realistically lose per hour of play?

Predominance is given as a percentage of turnover. In order to know how many real crowns this means per hour, two factors need to be added: the average bet and the pace of the game. Here are model calculations for common New Zealand scenarios (average bet NZ$ 0and NZ$ 0corresponding to a typical slot player and table player):

A practical view for New Zealand players: The average net monthly salary in New Zealand is around NZ$ 0A player who spends 3 hours in an online casino every weekend spends around 156 hours at the casino every year. Playing a classic slot machine with an edge of 4% and an average bet of NZ$ 0at a rate of 500 spins/hour, such a player loses on average 156 × NZ$ 30= NZ$ 0per year. At the same time and the same turn in basic strategy live blackjack, he would lose €. The difference is more than two net monthly salaries.

Big table of casino advantage for all games

The table covers all categories of games available on the New Zealand regulated market, from the best to the worst from a player's perspective. Green color= very low prevalence, orange= medium, red= high prevalence (better to avoid):

Blackjack — the lowest edge in table games

Blackjack is the game with the lowest house edge among traditional games. video poker with the right strategy has even lower but is less widespread. Knowing the basic strategy (card with decisions for each combination of the player's cards and the dealer's card) the advantage is 0.3 - 0.8% depending on the variant. Without a strategy, it can grow to 1.5 — 3%. Comprehensive analysis of rules and strategy in article on basic blackjack strategy and in article about blackjack New Zealand .

Factors that affect the dominance of blackjack:

• Number of card decks: 1 deck (0.15%) → 2 decks (0.40%) → 4 decks (0.60%) → 6 — 8 decks (0.70 — 0.80%). Online live blackjack typically uses 6 or 8 decks.
• Dealer rules on soft 17: Dealer stands on soft 17 (ace + 6)= lower advantage for player. The dealer takes another card on a soft 17= advantage higher by 0.20%.
• Blackjack payout: 3 : 2 (standard, 0.5% edge). 6 : 5 (predominance higher by 1.4%). Always look for tables with a 3 : 2 payout and avoid 6 : 5 — the difference is huge.
• Surrender: Surrender for losing half of the bet reduces the advantage by 0.07%.
• Double the bet: Being able to double the bet on any two cards reduces the advantage by 0.25% compared to the rule where you can only double on 10 and 11.
• Splitting a pair: The option to split a pair and play two hands reduces the edge by 0.1 — 0.2%.

For New Zealand players, the main message is simple: blackjack only pays off with basic strategy. It's an expensive game without it. Detail in article on side bets in live blackjack — most of them have a prevalence of 6 — 18% and it is better to avoid them.

Roulette — European vs. American vs. french

The most important decision in roulette is choosing the right variant. The three variants on the New Zealand market differ in only one detail — the number of zeros on the wheel — and that detail doubles the player's loss:

Practical example — bet € for one hour of play (about 60 spins) in individual variants:

• French Roulette (outside bets): 2500 × 60 × 0.0135= € expected loss
• European Roulette: 2500 × 60 × 0.027= € expected loss
• American Roulette: 2500 × 60 × 0.0526= € expected loss

The difference between French and American roulette at the same time and the same stakes is almost 4 times. Detail in article about European, French and American roulette , in article about roulette New Zealand and in tips for playing roulette .

Beware of betting systems in roulette: Martingale, Fibonacci, D'Alembert or any other system does not reduce the advantage of roulette. Roulette remains 2.7% or 5.26% no matter how you split the bets. The systems just change the distribution of losses — more small wins, but sometimes a huge loss. Detail in article on betting systems in roulette .

Baccarat — a little-known game with a very low edge

Baccarat has a rather marginal position in New Zealand casinos (many players have never played it), but mathematically it is the second best table game after blackjack. The rules are simple — no strategy, just a choice between three bets:

Rule #1 in baccarat: always bet on the banker. Even with a 5% fee, it has the lowest advantage. A draw bet never pays off — the 14.36% advantage is comparable to worst bets in Sic Bo and craps and worse than any decent slot machine. Detail in article about baccarat in an online casino .

Poker vs Casino (Three Card, Casino Hold'em, Caribbean Stud)

These games are played by the player against the dealer (unlike the classic texas hold'em , where you play against other players). They require minimal strategy, but the house edge is higher than classic blackjack:

• Three Card Poker (Ante + Game): 3.37% with the right strategy. Even 7% without a strategy.
• Casino Hold'em: 2.16% with the right strategy. The lowest edge among casino pokers.
• Caribbean Stud Poker: 5.22%. Higher because of the passive nature of decision making.
• Pai Gow Poker: 2.84% with the right deal strategy.

In all of these games, the side bets are significantly worse — 5 advantage — 25%. Detail in article on strategy in casino poker . For a player in New Zealand who wants to play "real" poker, classic texas hold'em against other players is more advantageous — there the casino only takes a fee from the table (rake) of around 2.5 — 5% without any personal participation. Detail in Texas Hold'em guide , in article about Poker New Zealand and in advanced Texas Hold'em strategy .

Slot machines and video poker

Machines (slots) are the most popular category in New Zealand online casinos. They make up about 70 — 80% of the turnover and generate most of the operators' income. Predominance ranges widely:

• Classic fruit slots (Kajot Games, SYNOT TIP, Apollo Games): return 95 — 96%, edge 4 — 5%. Low volatility, frequent small wins.
• Modern video slots (Pragmatic Play, Play'n GO, NetEnt): return 94 — 97%, edge 3 — 6%. Moderate volatility.
• Megaways and high volatility slots: return 94 — 96.5%, edge 3.5 — 6%, but very high swings (occasional wins with a high multiplier, long streaks without a win).
• Progressive jackpot slots: return 88 — 94% (part of the bet goes to the common jackpot), edge 6 — 12%.
• Versions with lower returns: 88 — 92% (8 — 12% advantage) — the same game sometimes deploys these "strangled" versions. Avoid.

You can find out the current return of a specific machine in its paytable. Detail in instructions on how to read the pay table of the machine , in of the article about the real return of New Zealand slots , in explanation of volatility and in article about Megaways slots .

Video poker with the right strategy has the lowest edge in the casino — Jacks or Better with a full 9/6 paytable only has an edge of 0.46%. That's less than blackjack. Unfortunately, full paytables are rare — most New Zealand online casinos offer "strangled" versions of 8/5 or 7/5 with an edge of 2.7 - 5%. Detail in video poker strategy and paytables article .

Live games and televised rounds (Crazy Time, Lightning Roulette, Monopoly Live)

Live TV rounds (English game shows) from the provider Evolution Gaming are a newer but very popular category. The advantage depends on the specific bet and can range from decent to very bad in the same round:

• Crazy Time: 3.82 - 6.55% by segment (lowest on number 1 bet, highest on bonuses like Coin Flip and Pachinko).
• Lightning Roulette: 2.90% on a specific number bet, 2.70% on outside bets (Lightning mechanics add random multipliers without changing the mathematical advantage).
• Monopoly Live: 2.55 — 5.17% by segment.
• Mega Wheel (Pragmatic Play Live): 3.69 — 4.15%.
• Funky Time, Crazy Coin Flip, Dream Catcher: 3.5 — 6%.

For all live televised rounds, always check for the lowest edge bet (typically the surest numbers or outside bets) — bonus segments sometimes pay huge multipliers, but their average returns are lower. Detail in Crazy Time article and live TV rounds , in article on live game dominance . A very interesting alternative is Crash game Aviator — with a careful strategy, a return of around 97% can be achieved.

Sports betting and bookmaker margins

For sports bets, the "casino advantage" is not stated, but the "bookmaker's margin" (English overround — odds that add up to more than 100%). The principle is the same — a percentage of each amount bet, which the office will keep for a long time. Typical margins on the New Zealand market:

• Top matches (Champions League, home derby): 3 — 5%
• Regular matches in the top leagues (5 strongest European league competitions): 5 — 8%
• Minor leagues and fringe sports: 8 — 15%
• Special bets (number of corners, half-time goals, number of cards): 10 — 20%
• Live bets (during the match): 6 — 12%, the office includes a reserve for unforeseen events in the course
• Value bets: can also have a negative margin for the office if you find the wrong rate

Detail in of the article on the odds and margin of the betting office and in value betting article . Practical difference: if you bet € per week in the top leagues with an average margin of 6%, you will lose on average around € (52 x 2500 x 0.06) per year in the long term. When betting on fringe sports with a margin of 15%, it is already NZ$ 0per year with the same turnover.

Betting systems and the casino's mathematical edge

One of the most widespread myths among players is that the betting system can beat the casino's edge. The truth is the opposite: no betting system reduces the mathematical advantage. The edge affects every single bet the same, regardless of how much more or less you put into it.

The most famous betting systems and why they don't work:

• Martingale (doubling after loss): After each loss, you double the bet to make up for the previous losses plus one unit of profit with the next win. It looks invincible, but it has two problems: 1) After 8 losses in a row with an initial bet of NZ$ 10the system asks for a bet of NZ$ 0The probability of 8 losses in a row in roulette is 1 : 256, but this situation happens occasionally and the player either fails to pay or hits the table limit. 2) Even if this does not happen, the casino's edge in roulette (2.7% or 5.26%) is not reduced. The player just changes the distribution of losses — most streaks end in a small win, but the occasional huge loss exactly offsets the gain.
• Fibonacci (bet sequence 1, 1, 2, 3, 5, 8, 13...): A milder version of the Martingale. It grows more slowly on a losing streak, but will still eventually hit the table limit or the player's budget.
• D'Alembert (+1 after loss, -1 after win): The most cautious system. It loses more slowly, but it also doesn't reduce dominance — it just reduces swings.
• Paroli (double after a win): A positive variant of the Martingale — uses a winning streak instead of a losing streak. It changes the distribution of results, but does not reduce dominance.
• Labouchere (cancel system): A complex system based on canceling numbers from a list. Loses gradually in losing streaks, but doesn't beat dominance mathematically.

The main idea: the betting system is a tool to distribute the capital during the game, not to change the mathematical odds. If you want to realistically reduce the loss, the only way is to change the game — not change the system. Detail in article on betting systems in roulette and in article on cognitive distortions in gaming (there it is explained why betting systems intuitively seem more successful than they actually are).

Bonuses and the casino's mathematical advantage

Welcome bonuses and other promotions can temporarily reduce or even completely erase the casino's advantage — but only under specific conditions. Most players will not reach them because the bonus has wagering rules, which means that the net value of the bonus is often lower than it appears.

Model Example — welcome bonus 100% up to € with 35x spins:

• Deposit: €. Bonus credit: €. Total game balance: €.
• Spinning 35 times the bonus= 35 × €= NZ$ 0turnover required before withdrawal.
• Playing slots with an average edge of 4%, the expected loss on a NZ$ 0turnover is: NZ$ 100× 0.04= €.
• The bonus has a theoretical value of €, but the expected spin loss is €. Net bonus value: -€.
• The bonus only makes sense if you play the game with an edge below 2.86% (€/NZ$ 0= 2.86%). Such games are typically excluded from spins or only count for 10-20%.

The actual value of the bonus is calculated according to the formula: bonus value - (turnover per spin x average advantage of allowed games). If the result is positive, the bonus is mathematically worth taking. If it's negative, the bonus is expensive and should be taken just for the fun of it, not the profit.

For New Zealand players, it is also important to monitor the spin time limit (most are 7 — 30 days), the minimum bet during the spin (typically NZ$ 0max) and excluded games. Detail in article about the conditions of spins in New Zealand casinos , in analysis of the value of the bonus conditions , in overview of games suitable for spinning and in article about the most common mistakes players make with bonuses .

Lotteries and scratch cards — the worst return on the market

Many New Zealand players do not realize that the state lottery has a drastically worse mathematical advantage than any casino game. With Sazko Sportka, Eurojackpot and Šťastný 10, the revenue after deduction of taxes, operating costs and funds is distributed among the players in a ratio of approximately 50%, which corresponds to a predominance of around 50%.

Why is the lottery so expensive? Part of the revenue from Sazka goes to the state budget, to sports, culture and charity. The casino pays a significantly smaller portion of the turnover as tax (typically 22-27% of the gross revenue, which is only a few percent of the turnover). Another reason is the huge jackpot — you can win 3 billion crowns with the Eurojackpot, but the chance is 1:140 million. If the game had a higher return, the jackpot would never reach that high.

A practical comparison: a player who spends NZ$ 10per week on Eurojackpot tickets donates an average of NZ$ 0per week= € per year to the organizer in the long term. The same player who plays for NZ$ 10a week on a 96% return slot loses € a week= NZ$ 30a year. The lottery costs 12 times more for the same "feeling of a chance to win". The same logic of the lottery economy applies to Ken directly in the casino, where the advantage is usually 20 - 30% - we detailed it in the article about Bingo and Ken in the online casino . Detail in overview of types of gambling games .

Effect of pace of play and frequency on overall loss

The advantage is given as a percentage of the turnover unit. But the speed at which you go through a turn in the game determines how much you actually lose per hour. The online slot machine can perform 500 — 800 spins per hour (one spin takes 3 — 6 seconds, autoplay even faster). Classic live roulette can handle 30 — 40 spins per hour (croupier, betting, payout). With the same bet of NZ$ 10and an edge of 4%, a slot machine player loses NZ$ 0per hour, while on live roulette, with an edge of 2.7%, only NZ$ 300— NZ$ 10

NZ$ 0online slot costs 15-30 times more per hour than NZ$ 0live blackjack — a combination of higher odds and a much faster pace. For the long-term player, choosing between a slot and a live table game is a significantly bigger difference financially than the superiority alone suggests.

Trick to lose less in the same game: Turn off autoplay, play slower, take breaks. The same slot with a 4% edge costs NZ$ 10at 200 spins per hour, NZ$ 40at 800 spins per hour. The difference is 4x — without having to change your game, bet or strategy. Just click less. For table games (blackjack, baccarat) the pace is automatically set by the croupier, so this trick doesn't work there. Detail in game journal article — when you record your bets, you have an accurate overview of how many turnovers you really go through and what the loss is.

Myths about the mathematical superiority of the casino

There are a lot of misconceptions surrounding the dominance of the casino. Here are the most common ones:

• "A slot machine that hasn't paid out for a long time must pay out soon." No. Each spin is independent. The machine has no memory. The probability of winning is the same in each round — regardless of previous results. This is a classic case of the gambler's fallacy.
• "The bigger the bet, the better the chance of winning." No. The probability of winning does not change. Only the size of the win and the size of the potential loss change — proportional to the bet. With a bet of NZ$ 10you have the same chance of winning as with a bet of NZ$ 0only the win and loss are 10 times greater.
• "Black hasn't fallen in roulette for a long time, so now it must." No. Even if red has fallen 10 times in a row, the chance of black on the next spin is still 18/37 (48.6%). He doesn't remember the bike. This myth became famous in 1913 in Monte Carlo, when black fell 26 times in a row in roulette, and players who bet on red with the vision of "evening" lost millions of francs.
• "The betting system defeats the dominance of the casino." No. No system beats math superiority. It only changes the distribution of losses — more small wins vs. The occasional big loss.
• "Online casinos are controlled, results are rigged." No. Licensed New Zealand casinos (Tipsport, Fortuna, Chance, SYNOT TIP, Sazka, Forbes, eCasino, Maxa, VsadAHrej, 69Games, Admiral, Tokyo, Bonver, Kartáč) have independently audited random number generators and the gambling regulator regularly checks the return of games. Detail in article about audits of online machines and in overview of the gambling regulator .
• "There is a winning strategy for slot machines." No. In slot machines, no strategy is possible to change the upper hand. The only thing you can influence is the choice of a machine with a higher return and the pace of play. Detail in article about myths surrounding slot machines .
• "The higher return game is always the best option." Not quite. While lower upside is usually better, the volatility of the game must also be considered. A highly volatile game with a 96% return can drain your budget faster in the short term than a game with a 94% return and low volatility. Detail in article on return and volatility .

How to choose a game by goal

After going through all the numbers and tables, the decision is usually easier than it seems. It depends on what you want from gaming:

Detail in article about choosing an online casino according to the type of player , in glossary of terms , in curiosities about casinos and in comparison of classic and progressive jackpot .

Practical summary: If you want to play the casino for a long time with minimal loss, play blackjack with basic strategy or baccarat on the banker. With the same turnover of NZ$ 0the expected loss is NZ$ 0(blackjack) instead of € (average slot machine) or € (American roulette). If you prefer slots for simplicity and big hit potential, look for those with a 96%+ return and avoid the lower return versions. Slots with a return of 88 — 92% cost 3 times more than slots with a return of 96%. And avoid the lottery if you want to maximize your "time in the game" on a given budget — for the same bet of NZ$ 10you get 15 minutes of exciting casino play, while the Eurojackpot draw takes a few seconds.

Related topics

• Blackjack: basic strategy (chart)
• Blackjack New Zealand
• European, French and American roulette
• Roulette New Zealand
• Tips for playing roulette
• Betting systems in roulette
• Baccarat in an online casino
• Casino Poker — Strategy
• Video Poker Strategy and Paytables
• Return and volatility of slot machines
• Real payback New Zealand slots
• Volatility of slot machines — explained
• How to read a slot machine paytable
• Myths about slot machines
• Megaways slots
• How Aviator works (Crash game)
• Crazy Time and live TV rounds
• Dominance in live casino games
• Side bets in live blackjack
• Bookmaker odds and margins
• Value betting
• Conditions for rolling out bonuses
• The value of the bonus terms
• Budget management in an online casino
• Online casino game log
• Cognitive distortions in gaming
• Glossary of online casino terms
• Choosing an online casino according to the type of player
• Online casino game providers — which studios have a higher RTP
• Loyalty programs and VIP clubs of casinos — when a refund actually reduces the casino's edge
• The most common mistakes players make with bonuses — how the math plays against the player even with the bonus

❓ Casino Predominance FAQ

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