A fairly conservative roulette player once compared the probability of the outside, even-money bets hitting as being similar to a pendulum. He theorized that the odd/even, red/black/, and high/low bets would hit with some regularity on either side, but rarely did one side hit 10 times more than the other in any session of play.
To visualize his thinking, he suggested a swinging pendulum, where Red was on one side, numbered 1 to 10, and Black was on the other, also numbered 1 to 10. In a perfect world, the pendulum would swing to Red, then to Black, then to Red, then to Black, as each colored number hit. Of course in the real world, at any one time in the past few spins of the roulette ball, either color may have hit more than the other. Perhaps in the past 10 spins Black has won 7 times and Red just 3, so the pendulum, or pointer, would register at 4 on the Black side. Another hit on Black would raise the number to 5. Two hits to Red thereafter would lower the pointer to 3, and so it would go.
Using this logic, Wells suggested a bankroll of 145 units, and a starting wager of 10 units on whichever even-money bet is chosen. Like the d’Alembert system, after each win, the wager is reduced one unit, and after each loss, the wager is increased one unit. Starting at 10, if every spin produces a loss, the bankroll is exhausted in 10 bets. However, since this rarely happens, the numbers move up and down, or back and forth, just as a pendulum does. Wells considered his session to be finished if his stake fell to 0 or rose to 20.
In this manner, if he won 10 straight wagers, his win was 55 units (10 units bet, then 9, then 8 etc.), and if he won a few and lost a few over the course of a long period of play but his wager eventually fell to 0, his win was quite substantial. With this method, any series of wins early on produces a nice win, but a series of losses early on leads to a long session of trying to get back to even, or the eventual collapse of the bankroll. Like the d’Alembert, the Wells system can produce a profit with less winning hits than losses, provided the wins come at the correct time, generally the best aspect of the systems.
To guard against the loss of 145 units, the Wells Pendulum has been revised over time into two separate betting schemes. The first, is simply to start the wagering at 5 units and hope to get ahead five wins and take down a small profit of 15 or more before starting over. This means each session of wagering needs only start with a table bankroll of 45. When a hit occurs at 5, the bet is reduced to 4, then three if it hits again…when the bet gets to zero, you quit.
The second scheme is to start with a table bankroll of 110 units and try to double-up before quitting. Since this method either wins 110 units or loses 110 units, it would appear to be much more likely to produce a long-term profit. Of course with all roulette wagering, the house retains the edge and the player hopes to profit from a good series of wins, or to reduce loses during a bad series.
To play the double-up method, imagine that you are going to bet both Black and Red using the Wells Pendulum system. On the first spin, you would have 10 units on each, but since there is no profit in such a wager, you wait and see the result before making your first wager. And, you will then make a wager equal to the difference between how much you would bet on each color.
Suppose Black is spun, then with the original system you would have bet 9 units on Black (reducing your wager by 1 unit after a win), and 11 units on Red (raising your wager by 1 unit after a loss). The difference is 2 units, and this should be wagered on Red (the color that did not win last spin). Should Black again spin, the original wagers would be 8 units on Black, and 12 units on Red, so now the next spin requires a bet of 4 units on Red. Let us assume another Black is spun, so the original wagers would have been Black 7, Red 13, a difference of 6, so 6 units is now wagered on Red. You may need a pencil and paper to understand and keep track of this betting method at first, but don’t fret, the pattern is actually quite simple.
With those two imaginary bets starting at 10 units, each loss lowers one bet a unit and raises the other by one unit, thus a 2-unit increase is necessary for the next wager. Each win reduces the previous losing color’s bet by a unit and raises the other by a unit, so a 2-unit reduction is necessary for the next bet. In practice, this betting method is the same as following a progression of 2-unit changes and a risk of having the pendulum swing 10 wagers to lose 110 units (2,4,6,8,10,12,14,16,18,20).
If you are playing with a single zero (we hope) and have European rules that include En Prison or La Partage, simply take the ½ refund when zero spins and make the same wager as your last spin. This will set your overall win back slightly, but following the same pattern your overall loss or win will be the same each time a zero spins (example: you have a bet of 6 and zero spins, take the three chips back and add another three to the same wager).
Playing long enough to see a 110 unit win is sometimes impractical, so the modified Wells Pendulum roulette system is easily adapted to a timed session. Play for an hour and check your results! For sessions where things are going well, consider a small increase in wagers for a new session, such as 3 units instead of 2. Take down part of your win, set a new bankroll of 165, and If you catch back-to-back winners, your overall growth in bankroll will be substantial!