Hymie’s mathematical model is near enough correct. Assuming these machines follow the European roulette model (with just zero and not zero and double zero as the US game has) then the House Advantage or “edge” is 2.7%. This edge is achieved because the odds paid for any single number is 35-1 (when in fact the true probability of any one number being spun is 36-1). A similar edge exists on the “even money” bets (payout is evens when the probability is 18/37). All the other group bets show a similar edge. This means that over a period, provided the spin is not fixed in any way, it should pay out £97.30 for every £100 staked. Staking £1 on single numbers on 111 spins should see three wins (111/37). This would see a return (including stakes) of £108. The £3 loss is the casino’s edge (3/111 = 2.7%).
But life ain’t like that as Woofgang has touched on. An individual punter would be quite fortunate to gain three wins in 111 spins. (Some might achieve three or more, but most would achieve less than three). So it is not quite so straightforward to suggest that for every £100 staked the punter should expect to lose only £2.30. If he placed £1,000 in bets (at the same value each) he might get closer to the average loss, £10,000 closer still and so on. To use a simple analogy imagine tossing a coin. On average you should win 50% of the time. But you might lose three times in a row (which nobody would deem unusual). But you’d be very unlucky to lose ten times in a row and even unluckier still to lose 100 times in a row.