Roulette odds are pretty easy to calculate because Roulette is a game of fixed odds. Each throw is unrelated to the previous throw, and no composite probabilities exist.
On an unbiased wheel of 38 slots, a probability for any slot playing out is 1/38. Based on this we can easily calculate the worth of all possible bets by deducing the house edge. As most of the bets don’t involve zero and double zero, we must take special care to not forget it.
For example, betting on red would result in the following calculation (given a 38 slot wheel):
Out of 38 slots, 2 are zeros, which leaves us with 36
Out of 36, half is red and another half is black. Only 18 of 38 possibilities win, therefore making the probability of this bet winning 18/38 (47.37%). There are 20 other possibilities to lose, 20/38 total.
You spend $1 on every lost game, and win $1 on every won game.
Out of 380 games (number taken to easen up the calculations) you will win $180 and lose $200. That is, you will lose $20.
$20/380 = 1/19, or 5.26%
The mathematics of roulette dictates that all bets, ultimately, have the same house edge, except for a very greedy composite zero – double zero – 1 – 2 – 3. If you try the experiment above, you will find that the house edge is 7.89% for this particular bet. For example, if you try the above calculation with a straight up bet, which pays off 35:1 but has a probability of 1/38, you will get the same numbers.
For the European wheel, the edge becomes 2.70%. As you can see, the additional zero on American wheel adds more than two percent to the house edge, which makes huge difference.
As the house edge is fixed on almost every single bet, it means that which bet you wager on doesnt really matter statistically because they all produce the same results. This leaves you room for bet management system and lucky guesses without prejudice.