Table games: edges you can derive
Unlike slots, whose edge comes from a proprietary reel configuration, table game edges are derivable from the published rules. That makes them a useful teaching set, and it makes the arithmetic checkable.
European roulette. 37 pockets, numbers 0 to 36. A straight-up bet on a single number pays 35 to 1.
- Win probability = 1/37, return 36 units (35 profit plus 1 stake)
- Expected return per unit = 36/37 = 0.9730
- House edge = 2.70%
The edge comes entirely from the zero: a fair wheel would pay 36 to 1. Under standard rules every bet type on a single-zero wheel carries the same 2.70%, which is a neat result and is why bet selection on roulette changes volatility but never expectation. The exception is a table with a la partage rule, which returns half of an even-money stake when zero lands and so halves the edge on those bets to 1.35%.
American roulette. 38 pockets, with both zero and double zero, and the same 35 to 1 payout.
- Expected return = 36/38 = 0.9474
- House edge = 5.26%
Adding one pocket nearly doubles the edge. The double-zero layout also has one bet that breaks the equal-edge rule: the five-number bet on 0, 00, 1, 2 and 3 pays 6 to 1 rather than the 6.2 to 1 the formula implies, which gives it an edge of 7.89%. This is the clearest illustration in the whole subject of how a small rule change moves the economics.
Baccarat. In an eight-deck game the banker bet carries roughly a 1.06% edge, player roughly 1.24%, and the tie bet 14.36% at the usual 8 to 1, falling to roughly 4.8% where a casino pays 9 to 1 on the tie. The banker edge accounts for the commission, typically 5% on winning banker bets, without which the banker bet would favour the player. The spread between the main bets and the tie is the reason baccarat is simultaneously one of the lowest-edge and one of the highest-edge games on a floor, depending entirely on which bet is taken.
Blackjack. The edge depends on the rule set, and the dependencies are well documented. Playing with correct basic strategy, a typical multi-deck game with dealer standing on soft 17, double after split permitted and blackjack paying 3 to 2 sits at around 0.5% or a little below. Change blackjack to pay 6 to 5 and the edge rises by roughly 1.4 percentage points, which on a low-edge game is a multiple rather than an increment. Dealer hitting soft 17 adds roughly 0.2 points. Restricting doubling or resplitting adds more.
The general lesson from blackjack is that in a low-edge game, individual rule changes are proportionally enormous. A house edge moving from about 0.5% to 1.9% is close to a fourfold increase in the cost of playing, achieved by changing one payout.
Side bets, and why the edge sits there
Table side bets commonly carry edges several times those of the base game, which for the games above sits in the low single digits. The baccarat tie, at 14.36% against the banker bet's 1.06%, is the familiar example.
The reason is straightforward and worth stating without moralising. The base game is the attraction and is priced competitively because players compare it. The side bet is an optional add-on that most players do not evaluate, and it is where the margin per seat is made.
The arithmetic consequence is that a player taking every side bet converts one of the lowest-edge products on the floor into one of the highest. Since theoretical win for each hour of play is average bet multiplied by decisions per hour multiplied by house edge, and the side bet adds both to the average bet and to the blended edge, the effect on revenue per seat is substantial.
This is also why a casino's reported table hold percentage is a blend and cannot be read as a house edge. It reflects the mix of bets taken, and two properties offering identical games can report very different hold because their players bet differently. The denominator is different too: in Nevada, table hold is statistical win divided by statistical drop, broadly the cash and credit exchanged for chips at the table rather than the total amount wagered, and chips are bet over and over. That is why the Nevada Gaming Control Board reported a roulette win percent of 19.11% for the twelve months to June 2026, far above the 5.26% edge of even a double-zero wheel.
Sports betting: overround as the analogue
The sportsbook version of house edge is margin, and the mechanism is different in an important way.
Add up the implied probabilities of every outcome in a market. For a two-way market priced at 1.90 and 1.90 in decimal odds:
- Implied probability of each = 1/1.90 = 0.5263, or 52.63%
- Total = 105.26%
The 5.26% above 100 is the overround, and it is the theoretical margin on that market. Expressed as a share of turnover, which is the way sportsbooks usually quote it, the margin is the overround divided by the total: 5.26/105.26 = 5.0%.
Two structural differences from casino games matter.
Margin is per market and varies enormously. Margins are thinnest where competition and information are greatest: a study of five major European bookmakers' football odds from 2000/01 to 2016/17 found overrounds significantly lower in the first divisions of the top five leagues than in second divisions and smaller leagues, and falling steadily over the period. Player props and in-play markets are often priced wider still. A casino game has one edge; a sportsbook has thousands, and its blended margin depends entirely on what its customers bet.
Actual hold diverges from theoretical margin much more than in casino. In a casino game every round is an independent draw from a known distribution. In sports betting the book is exposed to correlated outcomes: if favourites win across a weekend, the sportsbook loses across many markets simultaneously. Actual hold is therefore a function of results as well as pricing, and the divergence can persist for months: DraftKings reported that customer-friendly sports outcomes, together with higher promotions, cut its sports net revenue margin to 6.8% in the second quarter of 2026, from 8.7% a year earlier.
Theoretical margin versus actual hold
This distinction causes more confusion in operator reporting than any other, and it is worth being able to explain crisply.
Theoretical margin is what the pricing implies: the overround built into the odds, weighted by expected turnover across markets.
Actual hold is what happened: win divided by turnover over a real period.
The gap between them has three sources.
Results. Favourites winning is the classic case. Because recreational money concentrates on favourites, a weekend of favourite wins produces a low or negative hold across the book.
Customer mix. A book with a high proportion of sharp customers holds below its theoretical margin, because those customers systematically take the better side of mispriced markets. A book serving mostly recreational multiples holds above it, because accumulator margin compounds across legs.
Product mix. In-play and prop markets typically carry higher margin than headline match markets, so a shift in what customers bet moves the blended figure without any pricing change.
The compounding point deserves its own note. On an accumulator, margins multiply rather than add. A four-fold built from legs each carrying 5% margin has a combined theoretical margin of approximately 1 minus 0.95 to the power of four, which is around 18.5%. This is why sportsbooks promote multiples heavily, and why a book's blended hold tracks its multiples mix closely. Flutter, for example, attributed a 60 basis point rise in its US structural sportsbook revenue margin, to 14.2% in 2025, partly to greater same game parlay penetration.
Comparing verticals honestly
Putting a casino game and a sports market side by side requires care, because the denominators differ.
A casino game's house edge applies to every unit staked, and units are staked repeatedly at high frequency. A sportsbook's margin applies to each bet placed, and bets are placed far less often. That is why a 4% slot and a 5% sports market are not comparable propositions: the slot's edge can be applied several hundred times an hour and the sports margin perhaps a handful of times a week. In Britain, online slots must allow at least 2.5 seconds between the start of one game cycle and the next, which still permits up to 1,440 spins an hour.
The comparable measure, again, is expected loss per hour or per unit of time, which returns to the formula from the first lesson. Any comparison of verticals that stops at the edge or the margin has stopped one step too early.