To start with we would take a closer look at the nature of the house edge.
Simply saying it is a difference between the real roulette odds and the odds that players are paid by casino when they win. The difference exists due to the fact that there is a one (European roulette) or two (American roulette) zero positions on the roulette wheel.
Mathematical explanation learn
Thereby, initially every casino has an advantage over the gamblers and it is very easy to prove mathematically:
Assume that players bet inside and stake on single numbers. Then, the probability of their win is 1/37 (European) or 1/38 (American) for each wheel spin but the reward expected is only 35. For instance, if you bet $1 on some number and win, you get your gain of $35 and keep your original investment of $1. In European version the difference is $37-$35-$1=$1 and in American one $2=$38-$35-$1. In order to get true odds we need to divide 1 and 2 by 38 and thus, we get 2.703% house edge for European roulette and 5.263% for American one. In reality these percents mean that if you place bets for $100 000 during a sufficient period of time you will lose $2 703 or $5 263.
For the sake of validity it is worth to mention that in the short run (several hundred spins) and in the medium run (a few thousands of spins) these values of house edge will be biased because of standard deviation.
The 'En Prison' or the 'La Partage' rules
Furthermore, there are some roulette rules that could soften such an injustice:
- the 'En Prison' rule is valid for even-money stakes only and is used not in all casinos. It says that in case of zero position the players are allowed to withdraw a half of their bet or, alternatively, they can keep the roulette bets and continue the game. In the latter case, if the outcome is zero for a second time, then the gamblers lose the whole bet;
- the 'La Partage' rule has a lot of common with 'en prison' rule with a difference that here players have no option to keep the bet for further game and just lose the half of it, not the whole amount.
Both the rules are suitable only for even-money outside betting on Red/Black, Odd/Even and High/Low; additionally the outcome should be zero. Anyway, the rules are designed so they decrease the house edge essentially, notably the house edge for European roulette is now only 1.35% and for American one 2.63%.
The main conclusion that one can make from the computations above is that you always should try to play European roulette and ask whether the 'En Prison' or the 'La Partage' rules are applicable. Anyway, in the long run it is a casino that makes profit and the best advice for gamblers ever is not to miss the moment when to stop in order to stay a winner.