Which of the numerous Roulette bets is the best one? Does something like that even exist? Let us match theoretical assumptions with a practical research that was carried out in 1972.
Firstly let us have a look on what the expected value says, i.e. what is our financial balance (profit/loss) going to be – according to the expectations – if we keep on playing Roulette in the long-term period. There are numerous betting possibilities in Roulette: a straight bet on a single number, bet on two numbers (split), three numbers (street) etc., or even-money bets such as red and black, high or low numbers. As the payouts are lower than the "true" odds based on the probability, the expected value for players is negative. In contrast a casino has positive expectations, since it gains what a player loses.
The long-term house edge, based on the expected value, and that creates house's profit, is the following. As for French Roulette it is 2.7% for all bets except of even-money bets, whereas the edge is a half of that 1.35% – only in case that the even bets are frozen if a zero comes up – thus the bets are not lost instantly as in American Roulette. The house advantage in American Roulette is much higher 5.26% (that is caused by a single extra number – the double zero).
What was said above indicates that if you e.g. play French Roulette, your average return will be $97.3 out of each $100 bet. On the contrary a casino gains those $2.70 out of the $100 bet (the calculations for the even-money bets in French Roulette and all bets in American Roulette are analogous), regardless of betting on a single number, two numbers or otherwise.
The expected outcome is still the same and therefore all the bets in Roulette are equally good or bad (except of the even-money bets in French Roulette – theoretically these are the best as they give the lowest edge to the house). Again, this deals with the long-term period, when you will likely be heading toward this state. Sure, in the short run you can win or lose much more based on your current luck.
Theoretically it does not matter, which kind of bet you use. However gentlemen Downton and Holder did a research in 1972 and their findings were quite surprising. Within the research they tested all bets in Roulette. They tried betting on single numbers only, then on two numbers only etc., and examined the returns of such changeless way of betting.
The best Roulette strategy according to the research was a straight bet or betting on single numbers! This is relatively surprising due to two reasons: 1) the expected value is still the same for all bets (–2.7%) and 2) the straight bet beat the even-money bets (red/black, high/low...) that were supposed to be the most advantageous for players (–1.35%). Just a little prove: the payout for a single number bet is 35:1, the probability to win is 1/37, we can lose 1 unit (a dollar for example) with the probability 1 – 1/37 = 36/37, the expected value is then 35 ˟ (1/37) + (–1) ˟ (36/37) = –2.7%. The result of the bet on two numbers (and all the other bets) with the payout 17:1 is the same: 17 ˟ (2/37) + (–1) ˟ (35/37) = –2.7%.
What are the findings of the research, how come the straight bet was the best in Roulette? Although it is not easy to tip a single number in Roulette, if you manage to do so (a few times during the course of play), you can enjoy the highest payout 35:1 that can help you grow your capital quickly. Then you can use it to enlarge your capital again or to cover potentially unsuccessful bets. In contrast there is a lower risk to ruin your capital if you bet on red/black or high/low numbers (→ see the test), but on the other side it is more difficult to grow your capital rapidly and to create a profit or a safety cushion for upcoming spins.