A £27.03 expected loss can describe a session in which losing exactly £27.03 is impossible. For 100 fixed £10 wagers on red in independent spins of a single-zero roulette wheel, under the ordinary full-loss-on-zero rule, the average loss is about £27.03. The actual net result moves in £20 steps.
There is no contradiction. The average weights every possible result by its probability. One completed session produces just one of those results.
This article works through that finite-session calculation. Our RTP explainer covers what a game's published percentage measures; the question here is what happens when an expectation is applied to a fixed number of wagers. The example is a mathematical model, not a recorded session or a recommendation to stake these amounts.
Start with the amount wagered, not the deposit
For this calculation, the wheel has 37 equally likely pockets: 18 red, 18 black and one zero. A red wager pays even-money profit when it wins and loses its full stake otherwise. We assume independent completed spins, a constant £10 stake and exactly 100 rounds. There are no bonuses, fees, multipliers, refunds on zero or changes of bet.
The Venetian's published roulette rules distinguish a single-zero wheel from other configurations and list even-money payouts on red or black. Those are the conventional features used in our model. They do not identify the rules of every roulette product.
Each winning £10 wager returns £20 in total, including the £10 staked. Its net result is plus £10. A losing wager returns nothing, leaving minus £10. The expected net result per spin is therefore (18/37 × £10) + (19/37 × minus £10), or minus £10/37. Dividing that expected loss by the £10 stake gives a house edge of 1/37, about 2.70%.
Across 100 such wagers, the total staked is £1,000. Multiply that turnover by the unrounded edge: £1,000/37 gives an expected loss of about £27.03. Using a rounded 2.70% would give £27 instead; the small difference is rounding, not an extra charge.
The £1,000 is the sum of stakes placed. A deposit is money entering an account. Reusing returned money can create stake volume beyond the original deposit, so multiplying the edge by a deposit alone does not calculate the expectation of an unknown session.
For the examples below, assume £1,000 is available at the start. That makes every one of the 100 fixed £10 wagers fundable, even along the path that loses all of them. This is an accounting assumption, not a suggested gambling budget. Stopping early, running out of funds or changing the stake would create a different model.
The actual ledger cannot show the average loss
Let W be the number of winning red wagers in the 100 rounds. There are 100 minus W losses. The net result is £10 × W minus £10 × (100 minus W), which simplifies to £20 × W minus £1,000.
With 40 wins, the session loses £200 and the assumed starting £1,000 becomes £800. With 50 wins, it breaks even and finishes at £1,000. With 60 wins, it gains £200 and finishes at £1,200. These are possible model outcomes, not forecasts.
Every additional win replacing a loss improves the result by £20: a minus £10 result becomes plus £10. That is why the completed-session result must be a multiple of £20, between minus £1,000 and plus £1,000. A £27.03 loss is not on that list.
The mean still belongs to the distribution. The Gambling Commission's player guide describes house edge as the percentage the casino expects to retain on average, given normal patterns of play. It does not describe a fixed deduction from every person's balance.
A negative expectation still permits a session ahead
Under these assumptions, each spin wins with probability 18/37. Counting the wins over 100 independent trials gives a binomial distribution. We calculated the probabilities for all 101 possible win counts, rather than generating a batch of simulated sessions.
| Session result | Red wins out of 100 | Calculated probability |
|---|---|---|
| Finishes below the starting balance | 0 to 49 | 56.79% |
| Finishes at the starting balance | Exactly 50 | 7.67% |
| Finishes above the starting balance | 51 to 100 | 35.53% |
Percentages are rounded to two decimal places, so the displayed values sum to 99.99%. The unrounded probabilities sum to 100%. The corresponding expected loss, calculated over the same complete distribution, is £1,000/37.
The 35.53% describes finishing ahead after exactly these 100 wagers. It is not the chance of being ahead at any point during them, the chance of winning at least one spin, or a personal forecast for a different game. Someone can lead partway through a sequence and finish behind.
There is also no promise that exactly 35 or 36 of the next 100 people would finish ahead. Even a set of sessions is subject to variation. The percentages describe the specified probability model, not a quota assigned to a group of players.
More rounds increase exposure; they do not repay a shortfall
Ten wagers of £10 in this model produce £100 of turnover and an expected loss of about £2.70. One hundred produce £1,000 and about £27.03. The rate is unchanged while the expected amount lost grows with the number of wagers.
Earlier losses do not alter the next spin's 18/37 chance of red under the independence assumption. If the first 50 wagers have lost £100, another 50 wagers have an expected additional loss of £500/37, about £13.51. Conditional on that first-half result, the expected final loss is about £113.51, not a correction back to £27.03.
The calculation at the start of the session averaged over all possible first halves as well as all possible second halves. Once the first-half result is known, it is an actual loss in the ledger. The unchanged probability of future spins does not erase it.
This model says nothing about an unknown machine's full payout distribution. Our slot volatility explainer shows why the same average return can accompany very different payout patterns. You cannot transplant the probabilities in this roulette table into a slot simply because its percentage looks similar.
An expectation is not a maximum loss
The house edge supplies a rate for an expectation under stated assumptions. It does not cap what can be lost. In the fixed session above, losing all 100 wagers would exhaust the entire assumed £1,000, despite the much smaller expected loss.
Game rules matter before any percentage is applied. Our roulette rules explainer covers other wheel configurations and payouts. A partial refund on zero changes this model; a multiplier feature can require probabilities not disclosed in an ordinary paytable.
A real account record gives the money actually staked and returned. A theoretical expectation gives the probability-weighted average under a defined model. In this example, £27.03 is a valid rounded expectation, but it cannot be the loss written in the completed 100-spin ledger.
