A few days ago, I won a small 5€ roulette bonus on a gambling site. Of course, I ended up losing it all in no time and was left with a bitter taste in my mouth.
Then, I remembered the famous Martingale method: the idea that doubling the bet after every loss will eventually win back everything plus a profit. It sounds tempting, but is it really that simple? I decided to delve into the topic and see if there was a better way I could have invested my 5€ bonus.
The principle is simple: always bet on red (or black, or any event with close to 50% probability). If the bet wins, start over with the initial bet. If it loses, double the bet for the next round. In theory, when finally winning, everything lost is recovered plus the initial bet.
Here’s a simple example of how the Martingale method works in practice:
| Round | Bet | Result | Total loss |
|---|---|---|---|
| 1 | 1€ | LOSE | 1€ |
| 2 | 2€ | LOSE | 3€ |
| 3 | 4€ | LOSE | 7€ |
| 4 | 8€ | LOSE | 15€ |
| 5 | 16€ | WIN | 15€ |
Total lost: 1€ + 2€ + 4€ + 8€ = 15€
Total won: 16€
Net profit: 16€ - 15€ = 1€
In general, assuming an infinite budget and unlimited betting capacity, the Martingale method will always result in a 1€ profit. But as the example shows, a series of consecutive losses can require astronomical bets. Doubling the 1€ bet 10 times in a row means the next bet should be 1024 times the initial bet. And what happens with another loss? And another?
This is the theory. In real life, casinos have maximum bet limits, and players have budget constraints. When hitting the table limit or wallet limit, the strategy collapses miserably.
Time to simulate it
I wrote a Python script to test different scenarios with various maximum spin counts, initial bets, and table limits.
import random
def martingale_simulation(spins, initial_bet, max_table_bet=1000):
current_bet = initial_bet
total_winnings = 0
max_bet_placed = 0
consecutive_losses = 0
max_consecutive_losses = 0
table_limit_hit = False
total_wins = 0
i = 0
# Flag to check if the last spin was won,
# to continue the loop until a win occurs
won_last = False
while i < spins or not won_last:
# Check if next bet would exceed table limit
if current_bet >= max_table_bet:
max_bet_placed = current_bet - (current_bet / 2)
table_limit_hit = True
break
# Simulate roulette spin (18 red, 18 black, 1 green)
result = random.randint(0, 36)
is_red = result in [1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36]
# Always bet on red
if is_red:
# Win!
total_winnings += current_bet
current_bet = initial_bet # Reset bet
consecutive_losses = 0
won_last = True
total_wins += 1
else:
# Lose
total_winnings -= current_bet
current_bet *= 2 # Double the bet
consecutive_losses += 1
won_last = False
# Update max consecutive losses
if consecutive_losses > max_consecutive_losses:
max_consecutive_losses = consecutive_losses
# Keep track of maximum bet
if current_bet > max_bet_placed:
max_bet_placed = current_bet
i += 1
return total_winnings, max_bet_placed, max_consecutive_losses, table_limit_hit, total_wins, i
# Run the simulation
rounds = 5
spins = 10000
initial_bet = 1
max_table_bet = 2500
round_balance = 0
for i in range(rounds):
winnings, max_bet, max_consecutive_losses, table_limit_hit, total_wins, spins_played = martingale_simulation(spins, initial_bet, max_table_bet)
round_balance += winnings
print(f"\n--- Round {i} Results after {spins_played} spins ---")
print(f"Total winnings: {winnings}€ in {total_wins} wins")
print(f"Maximum bet on table: {max_bet}€ in {max_consecutive_losses} consecutive losses")
if table_limit_hit:
print("Round stopped: table limit hit")
print(f"\nTOTAL BALANCE: {round_balance}€")First scenario: 10.000 spins with a ridiculously high table limit and 5€ initial bet. The expectation is to win the initial bet each time a win occurs.
spins = 10000
initial_bet = 5
max_table_bet = 1000000000The results match the expectation perfectly. Not bad if there’s at least 81.920€ available to stake on the table. The interesting observation is that long series of consecutive losses occur quite easily, but the final profit reaches 121.815€. Not bad at all.
--- Round 0 Results after 10000 spins ---
Total winnings: 24360€ in 4872 wins
Maximum bet on table: 40960€ in 13 consecutive losses
--- Round 1 Results after 10000 spins ---
Total winnings: 24540€ in 4908 wins
Maximum bet on table: 10240€ in 11 consecutive losses
--- Round 2 Results after 10001 spins ---
Total winnings: 24345€ in 4869 wins
Maximum bet on table: 5120€ in 10 consecutive losses
--- Round 3 Results after 10000 spins ---
Total winnings: 24160€ in 4832 wins
Maximum bet on table: 81920€ in 14 consecutive losses
--- Round 4 Results after 10002 spins ---
Total winnings: 24410€ in 4882 wins
Maximum bet on table: 40960€ in 13 consecutive losses
TOTAL BALANCE: 121815€Second scenario: Now testing with a more realistic table limit and a cautious initial bet of 1€. The 2000€ limit might not be entirely realistic, but it’s what I found online. When the table limit is hit, the round stops and the balance is printed.
spins = 10000
initial_bet = 1
max_table_bet = 2000The luck runs out this time. The simulation lost 5.665€ across 5 rounds.
--- Round 0 Results after 575 spins ---
Total winnings: -1792€ in 255 wins
Maximum bet on table: 1024.0€ in 11 consecutive losses
Round stopped: table limit hit
--- Round 1 Results after 2740 spins ---
Total winnings: -715€ in 1332 wins
Maximum bet on table: 1024.0€ in 11 consecutive losses
Round stopped: table limit hit
--- Round 2 Results after 1580 spins ---
Total winnings: -1302€ in 745 wins
Maximum bet on table: 1024.0€ in 11 consecutive losses
Round stopped: table limit hit
--- Round 3 Results after 3191 spins ---
Total winnings: -502€ in 1545 wins
Maximum bet on table: 1024.0€ in 11 consecutive losses
Round stopped: table limit hit
--- Round 4 Results after 1384 spins ---
Total winnings: -1354€ in 693 wins
Maximum bet on table: 1024.0€ in 11 consecutive losses
Round stopped: table limit hit
TOTAL BALANCE: -5665€I experimented with different initial bets and table limits, but the results didn’t improve significantly. The best outcomes occur with very low initial bets and the highest possible table limits.
Final experiment: Running 1.000 rounds of 10.000 maximum spins each, with a 1€ initial bet and 2.000€ table limit. The results remain disappointing.
The total loss reached 469.345€. Not exactly a winning strategy. See the full results here.
So, can I use it to become rich?
Well, no. The Martingale method could theoretically work, but only with unlimited budget and no table limits. In real life, casinos enforce maximum bet limits, and players face budget constraints. I think that the probability of winning using this method is likely no higher than simply betting on red or black the same amount all the time. Perhaps I’ll analyze the odds more deeply in a future post.