European Roulette Strategies: Martingale, D’Alembert, Fibonacci, James Bond

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European Single Zero Roulette Payout Table

Bet name Winning Numbers Payout Odds Expected value
(on a $10 bet)
0 0 35:1 1:36 -$0.27
Straight up Any single number 35:1 1:36 -$0.27
Split any two adjoining numbers vertical or horizontal 17:1 1:17 12 -$0.27
Street any three numbers horizontal (1, 2, 3 or 4, 5, 6, etc.) 11:1 1:11 13 -$0.27
Corner any four adjoining numbers in a block (1, 2, 4, 5 or 17, 18, 20, 21, etc.) 8:1 1:8 14 -$0.27
Six line any six numbers from two horizontal rows (1, 2, 3, 4, 5, 6 or 28, 29, 30, 31, 32, 33 etc.) 5:1 1:5 16 -$0.27
1st column 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 2:1 1:2 112 -$0.27
2nd column 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35 2:1 1:2 112 -$0.27
3rd column 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 2:1 1:2 112 -$0.27
1st dozen 1 through 12 2:1 1:2 112 -$0.27
2nd dozen 13 through 24 2:1 1:2 112 -$0.27
3rd dozen 25 through 36 2:1 1:2 112 -$0.27
Odd 1, 3, 5, …, 35 1:1 1:1 118 -$0.27
Even 2, 4, 6, …, 36 1:1 1:1 118 -$0.27
Red 1, 3, 5, 7, 9, 12,
14, 16, 18, 19, 21, 23,
25, 27, 30, 32, 34, 36
1:1 1:1 118 -$0.27
Black 2, 4, 6, 8, 10, 11,
13, 15, 17, 20, 22, 24,
26, 28, 29, 31, 33, 35
1:1 1:1 118 -$0.27
1:18 1, 2, 3, …, 18 1:1 1:1 118 -$0.27
19 to 36 19, 20, 21, …, 36 1:1 1:1 118 -$0.27

The Martingale Strategy

1

Double your bet after a loss. If the next bet wins, you reclaim your losses + profit equal to your first bet.
Example:

Bet Result Math Balance
$10 Lose $0-$10 -$10
$20 Lose -$10-$20 -$30
$40 Lose -$30-$40 -$70
$80 Win -$70+$80 +$10
  • Betting black or red, odd or even, or numbers 1-18 or 19-36 is nearly 50:50 odds. If you double your bet and win, you will recover all your losses + profit equal to your first bet. Continue doubling your bet after consecutive losses until you win.
  • Remember Gambler’s Fallacy. For example, the odds of getting a black number is almost 50% every spin, regardless if previous spins have produced all black numbers. The roulette wheel doesn’t remember each spin’s result.
  • Be careful if you lose multiple times. Doubling your bet may reach the table maximum, causing the strategy to fail. Modify your strategy before reaching the table maximum. Alternatively, your first bet should be very small.
2
Find a roulette table with a small minimum bet and a high maximum bet. 
3
Bet a small amount on black or red, odd or even, 1-18 or 19-36. European roulette tables have 37 numbers including the 0. The 0 decreases the probability of a black or red number slightly below 50:50.
4
Repeat your bet if you win. Do not double winning bets.
5
Double your bet if you lose. Repeat your choice of black or red, odd or even, numbers 1-18 or 19-36.
6
If you recover your losses, return to your starting bet and continue. Leave the casino if you feel unlucky, remember you have profited!
7
Repeat these steps until you have met your profit goal. If you reach the table maximum bet before recovering your losses, modify your bet or quit. The Martingale Strategy is expensive if you are unlucky.

Inverse Martingale Strategy

Double your bet after a win. If the next bet loses, you lose your winnings – losses equal to your first bet.
Example:

Bet Result Math Balance
$10 Win $0+$10 +$10
$20 Win +$10+$20 +$30
$40 Lose +$30-$40 -$10
$10 Win -$10+$10 $0
$20 Win $0+$20 +$20
  • Betting black or red, odd or even, or numbers 1-18 or 19-36 is nearly 50:50 odds. If your next bet loses, you will lose your winnings – losses equal to your first bet. Do not double your bet after consecutive losses. Return to your first bet and wait until you win.
  • Remember Gambler’s Fallacy. The odds of getting black number is almost 50% each time, regardless if previous spins have produced all black numbers. The roulette wheel doesn’t remember each spin’s result.
  • Be careful if you win many times. Doubling your bet may reach the table maximum, causing the strategy to fail. Modify your strategy before reaching the table maximum. Alternatively, your first bet should be very small.
2
Find a roulette table with a small minimum bet and a high maximum bet. 
3
Bet a small amount on black or red, odd or even, 1-18 or 19-36. European roulette tables have 37 numbers including the 0. The 0 decreases the probability of a black or red number slightly below 50:50.
4
Double your bet if you win.
5
Do not double losing bets. Repeat your choice of black or red, odd or even, numbers 1-18 or 19-36.
6
If you lose, return to your first bet amount and continue. If you win again and feel unlucky, leave the casino. Remember, you have profited!
7
Repeat these steps until you have met your profit goal. If you reach the table maximum after multiple wins, modify your bet or quit. The Inverse Martingale Strategy is expensive for the casino if you are lucky!

The D’Alembert Strategy

1
The D’Alembert strategy is different from the Martingale strategy. D’Alembert strategy changes your bet using Arithmetic factors instead of geometric factors. You increase your bet by 1 each time you lose. You decrease your bet by 1 each time you win. 1 is always the minium bet in the sequence. You do not double winning or losing bets.

This strategy benefits the player because roulette table maximum amounts are rarely reached. Players can also make larger first bets because they will not need to double any subsequent bets. Players can enjoy playing roulette for much longer time periods. The D’Alembert strategy slows the game to a comfortable pace..

Example, using $10 increments:
Bet Result Math Balance
$10 Lose $0-$10 -$10
$20 Lose -$10-$20 -$30
$30 Lose -$30-$30 -$60
$40 Win -$60+$40 -$20
$30 Win -$20+$30 +$10
$20 Win +$10+$20 +$30
$10 Win +$30+$10 +$40
2
Bet a small amount on black or red, odd or even, 1-18 or 19-36. European roulette tables have 37 numbers including the 0. The 0 decreases the probability of a black or red number slightly below 50:50.
3
Increase your bets by one after a loss, and decrease them by one after a win. An equal number of wins and losses still makes a profit.
  • Example results and balance, 2 losing bets and 2 winning bets:
    # Bet Result Math Balance
    1 $10 Lose $0-$10 -$10
    2 $20 Lose -$10-$20 -$30
    3 $30 Win -$30+$30 $0
    4 $20 Win $0+$20 $20
4
Remember, you will profit even if the number of losing bets equals the number of winning bets. Players should leave the casino after making a profit.

The Fibonacci Roulette Betting Strategy

1
The mathematician Leonardo Pisano Bigollo discovered Fibonacci numbers. This sequence is popular in stock market technical analysis and appears unexpectedly in mathematical studies. Here is the Fibonacci number formula, with two required starting values:

Fn = Fn-1 + Fn-2 with starting values of F1 = 1, F2 = 1.
E.g. 1, 1, (F3 = F1+F2), (F4 = F2+F3), etc.
The first 15 Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610.
  • After a loss, bet the next number in the series. E.g. you lose betting 13, the next bet is 21.
  • After a win, the next bet is equal to two steps back in the series. E.g. you win betting 8, the next bet is two steps back to 3.
  • You can profit by losing more spins than you’ve won. Be careful, the further you go through the sequence, the more money you lose.
2
Bet a small amount on black or red, odd or even, 1-18 or 19-36. European roulette tables have 37 numbers including the 0. The 0 decreases the probability of a black or red number slightly below 50:50.
3
If you lose, keep going through the sequence.  Example, using $10 increments:
# Bet Result Math Balance
1 $10 Lose $0-$10 -$10
2 $10 Lose -$10-$10 -$20
3 $20 Lose -$20-$20 -$40
4 $30 Lose -$40-$30 -$70
5 $50 Lose -$70-$50 -$120
6 $80 Win -$120+$80 -$40


4
When you win, move back two numbers in the sequence. Example continued from part 3, using $10 increments. Note we move two steps back in the sequence to $30 after a $80 win, spin #6.
# Bet Result Math Balance
4 $30 Lose -$40-$30 -$70
5 $50 Lose -$70-$50 -$120
6 $80 Win -$120+$80 -$40
7 $30 Win -$40+$30 -$10
8 $50 Win -$10+$50 +$40
9 $20 Lose +$40-$20 +$20

The James Bond Strategy

1
The "James Bond" Strategy is named for a fictional Western movie character. James Bond was an imaginary British Secret Service agent assigned to fantastic missions. He often visited casinos in Monte Carlo. This strategy features the column bet. Our example assumes you have $200 to wager.
2
Place $140 on high numbers (19-36).
3
Place $50 on six numbers 13-18.
4
Place $10 on 0 for insurance.
5
Numbers 1-12 are unlucky because you will lose the entire bet. After a loss, revert to the Martingale Strategy. Double your wager to balance the loss.
Any other numbers besides 1-12 return a profit.
  • If numbers 19-36, you win $80.
  • If numbers 13-18, you win $100.
  • If number 0, you win $160.
Sources: 1. Wikipedia, Martingale Probability Theory 2. Wikipedia, Fibonacci Numbers 3. Wikipedia, D’Alembert 4. Wikipedia, James Bond Monte Carlo Casino