Theoretical loss in a casino

What theoretical loss means in a casino

Every casino game has a built-in house edge, the share of each bet the casino keeps on average. Theoretical loss applies that edge to everything you stake over a session. From the casino's side the same number is called its theoretical win. Hannum and Cabot's textbook Casino Math treats the theoretical win as part of core casino maths, and the industry uses it to value a player's action without waiting for the dice or cards to settle.

The word 'theoretical' is the key. If you play £1,000 through a game with a 2.70% edge, your theo is £27 whether you finish £200 up or £200 down. It is the expected value of your play, turned into pounds and flipped to the casino's point of view.

The theoretical loss formula, step by step

The formula has four parts. Multiply them together and you have your theo for any session:

1. Multiply average bet by decisions per hour to get your hourly stake: £10 × 60 = £600.
2. Multiply by hours played to get your total staked, sometimes called turnover or action: £600 × 3 = £1,800.
3. Multiply total staked by the house edge: £1,800 × 2.70% = £48.60.
4. Divide by hours if you want an hourly figure: £48.60 ÷ 3 = £16.20 an hour.

Notice that the formula runs on turnover, not on the money you bring. Winnings are usually re-staked, so £100 can easily turn into £1,800 of bets over three hours. That is why theo can look large next to a modest starting balance. The Wizard of Odds house edge guide (opens in a new tab) defines the edge as the ratio of the average loss to the initial bet, which is exactly the multiplier the formula needs.

Theoretical loss worked out across casino games

Here is the formula applied to several games. House edges come from standard game maths; where a speed is shown, it comes from the developer's published round times or is stated as an assumption.

The baccarat rows use Evolution's published round times: about 48 seconds for its standard live Baccarat and about 27 seconds for Speed Baccarat. That gives 3,600 ÷ 48 = 75 rounds an hour against 3,600 ÷ 27, or about 133. The blackjack line uses the 0.62% Wizard of Odds figure for a six-deck, no-peek game where the dealer stands on soft 17 and doubling is allowed on 9 to 11 only. It assumes perfect basic strategy; real players who make mistakes give the casino more.

The pace of a live table depends on how many players are seated and how quickly they bet. Treat any hands-per-hour figure that isn't from a developer as a rough assumption and adjust it to your own play.

Why the same stake can carry a very different theo

The two baccarat rows above share the same bet, the same stake and the same 1.06% edge. The only change is speed. Speed Baccarat settles nearly 80% more rounds in an hour, so its theoretical loss is nearly 80% higher. Players often judge a game by the cost of a single bet and forget that the number of bets matters just as much.

Bet choice works the same way. The Banker bet costs 1.06% at eight decks, while a Tie paying 8 to 1 costs 14.36%. Swap £20 on Banker for £20 on Tie at the standard pace and the hourly theo jumps from about £15.90 to about £215.40 (£1,500 × 14.36%). Same table, same stake, more than thirteen times the cost. Our cost per hour page compares game speeds and edges side by side.

Theo in poker-style games: house edge against element of risk

Some table games let you add money during a hand. In these games the house edge is quoted against your opening bet (the Ante), not against everything you end up staking. Wizard of Odds uses a second figure, the element of risk, which divides the average loss by the total amount bet. For Caribbean Stud the house edge is 5.22% of the Ante but the element of risk is only 2.56% of total money wagered.

Either figure gives the same theo, provided you pair it with the right base. Take Ultimate Texas Hold'em, which the Wizard of Odds Ultimate Texas Hold'em analysis (opens in a new tab) puts at 2.185% of the Ante with optimal strategy and an average total wager of 4.15 times the Ante:

The trap is mixing them: applying the small element-of-risk percentage to just the Ante, or the bigger house edge to the total wagered. The first understates theo by about three quarters; the second overstates it about fourfold. Three Card Poker shows the same pattern, with an Ante and Play house edge of 3.37% and an element of risk of 2.01%.

Theoretical loss against what actually happens

Theo is an average, and single sessions spread widely around it. Take 1,000 bets of £5 on red at single-zero roulette. Total staked is £5,000, so theo is £5,000 × 2.70%, about £135. The standard deviation of the result is roughly £5 × the square root of 1,000, which is about £158.

In plain terms, about two-thirds of such sessions would end somewhere between a win of about £23 for the player and a loss of about £293. The theo of £135 sits in the middle, and a minority of players will finish ahead. Casino Math makes the same point with an American double-zero example: 1,000 bets of $5 on red give the casino an expected win of $263.16 with a standard deviation of $157.89. Our variance and standard deviation page explains why the spread grows more slowly than the expected loss.

Over many sessions the averages win out. Expected loss grows in direct proportion to the number of bets, while the spread only grows with its square root. That is why theo is reliable for the casino, which sees millions of bets, and much less predictable for one person on one night.

Theo is not the same as hold

Wizard of Odds draws a clear line between the house edge and hold. The house edge is the expected loss relative to the initial bet, assuming optimal or near-optimal strategy. Hold is the share of chips sold that the casino actually keeps over a period such as a shift, and it depends on how people really play, including how often they re-bet winnings and how many mistakes they make.

Theo sits on the house-edge side of that line: it is a forecast from the maths. Hold is a measured result. A table can hold far more than its theo on a quiet night and far less on a lucky one. Over long periods, the gap between theo and actual results shrinks as a share of money staked, which is the law of large numbers in action.

How casinos use theoretical loss, and the UK rules around it

Because theo values a player's action without waiting for results, casinos use it to rank customers and decide on rewards. Casino Math covers complimentaries, or comps, in their own chapter, and our casino comps page explains how they work. No reliable source publishes a standard share of theo that UK casinos return as rewards, so be wary of any figure quoted as typical.

In Great Britain, rewards aimed at high-spending customers are tightly controlled. Rules announced on 30 September 2020 and in force from 31 October 2020 require an operator, before treating someone as a VIP, to confirm their spending is affordable and sustainable, look for signs of harm or vulnerability, and hold up-to-date identity, occupation and source-of-funds evidence. Checks continue afterwards, and a senior executive with a Personal Management Licence must oversee each scheme. The Commission's announcement on VIP customer rules (opens in a new tab) sets this out, and our VIP schemes page covers what it means for players.

How to work out your own theoretical loss before you play

Theo is just as useful to you as to the casino. Treat it as the expected price of a session and budget for it:

1. Pick the game and the exact bet, then find its house edge or RTP in the help screen.
2. Decide your stake per bet and estimate how many bets you will make in an hour.
3. Multiply stake × bets per hour × hours × house edge to get your theo.
4. Set your session budget well above theo, because real results swing either side of it.
5. Use deposit limits, reality checks and time-outs to keep the session to plan.

Our house edge and cost-per-hour calculator does the arithmetic for you, and the session budget calculator turns it into a spending plan. For the limits themselves, see how to set deposit limits.

Theoretical loss myths and misunderstandings

For the bigger picture of how these margins add up for operators, read how casinos make money, or return to the casino maths hub for related topics.

Theoretical loss and casino bonuses

Bonus wagering is turnover too, so the theo formula applies to it. These are mainly slot offers, and table and live games are often excluded from wagering or count for less, so check the terms. Casumo offers new customers aged 18+ who opt in a 50% bonus up to £100 on a first deposit of at least £20; wager the bonus 10x within 7 days, with a £5 maximum bet while it's active, and game, play and payment restrictions apply. A full £100 bonus means £1,000 of wagering, and on a 96% RTP slot that turnover carries a theo of about £40.

10bet gives new UK customers aged 18+ a 100% match up to £25 when they choose the casino welcome bonus at sign-up and deposit within 7 days; the bonus is wagered 10x on slots within 3 days, bonus winnings are capped at £1,000, and Skrill and Neteller deposits don't count. Coral's offer (18+, new players, 1 October 2026 to 1 February 2027) is deposit and bet £10 or more on slots to get 100 free spins at 10p each on selected games, accepted within 48 hours and valid for 7 days, with no wagering on winnings; Neteller, PayPal, Paysafe, Skrill, prepaid cards and certain debit cards are excluded.

18+. Every casino game has a built-in house edge, so over time you should expect to lose what you stake. Set a budget before you play and stop when it’s gone: safer gambling tools and support. Free, confidential help: National Gambling Helpline 0808 8020 133.