Martingale System

Martingale is gambling's most famous and most dangerous illusion. The premise is intoxicating: double your bet after every loss, and when you finally win, you'll recover everything plus profit. It works—until it doesn't. The system creates a seductive pattern of frequent small wins that mask inevitable catastrophic losses. Casinos don't fear Martingale; they welcome it. The math guarantees their edge remains intact regardless of how bets are sized.

How Martingale Works
The Mathematics
Why Martingale Fails
Simulation Results
Martingale Variations
Psychological Traps
The Bottom Line

How Martingale Works {#how-it-works}

The Basic Principle

\text{Next Bet} = 2 \times \text{Previous Bet} \text{ (after loss)}

\text{Next Bet} = \text{Base Bet} \text{ (after win)}

Step-by-Step Example

Starting with $10 base bet:

Round	Bet	Result	Running P/L	Total Risked
1	$10	Lose	-$10	$10
2	$20	Lose	-$30	$30
3	$40	Lose	-$70	$70
4	$80	Lose	-$150	$150
5	$160	Win	+$10	$310

Result: You risked $310 to profit$ 10.

Why It "Seems" to Work

After a win, you've recovered all losses plus 1 unit profit:

\text{Profit} = \text{Winning Bet} - \sum(\text{Previous Losses}) = \text{Base Bet}

Losses Before Win	Total Recovery	Net Profit
0	$10	$10
3	$70 +$ 80	$10
5	$310 +$ 320	$10
7	$1,270 +$ 1,280	$10

Same profit regardless of losing streak length—this is the seduction.

The Mathematics {#math}

Exponential Growth of Bets

\text{Required Bet after N losses} = \text{Base Bet} \times 2^N

Losses	Bet Required	Cumulative Risk
1	2 units	2 units
3	8 units	14 units
5	32 units	62 units
7	128 units	254 units
10	1,024 units	2,046 units
15	32,768 units	65,534 units

A $10 base bet becomes$ 327,680 after 15 losses.

Probability of Losing Streaks

P(\text{N consecutive losses}) = (1 - P_{win})^N

European Roulette (red/black, 48.65% win):

Streak	Probability	1 in X
5	3.45%	29
7	0.86%	116
10	0.13%	784
12	0.03%	3,107
15	0.004%	24,380

Expected Number of Streaks

\text{Expected Streaks} = \text{Total Bets} \times P(\text{Streak})

Bets	Expected 7+ Streaks	Expected 10+ Streaks
100	0.86	0.13
500	4.3	0.64
1,000	8.6	1.28
10,000	86	12.8

After 1,000 bets, you'll likely have experienced a 10+ losing streak.

The Fundamental Math Problem

\text{EV (Martingale)} = \text{EV (Flat Betting)} = -\text{House Edge} \times \text{Total Wagered}

Critical insight: Martingale doesn't change expected value—it only changes result distribution.

Why Martingale Fails {#why-it-fails}

Failure Point 1: Table Limits

Casino	Min Bet	Max Bet	Max Doubles
Low-limit	$5	$500	6-7
Standard	$10	$2,000	7-8
High-limit	$25	$10,000	8-9

**After 8 doubles at $10:**$ 2,560 required, exceeds $2,000 limit. Game over.

Failure Point 2: Bankroll Exhaustion

Required bankroll for N losing streak survival:

\text{Bankroll Needed} = \text{Base Bet} \times (2^N - 1)

Streaks to Survive	Bankroll Needed ($10 base)
5	$310
7	$1,270
10	$10,230
12	$40,950

Surviving 10 losses requires 1,000x your base bet in reserve.

Failure Point 3: Risk/Reward Imbalance

Outcome	Probability	Result
Win within 10 bets	99.87%	+$10
Lose 10+ in a row	0.13%	-$10,230

Expected value per "session":

\text{EV} = (0.9987 \times 10) - (0.0013 \times 10,230) = 9.987 - 13.30 = -$3.31

You lose on average—even with 99.87% "win rate."

Failure Point 4: Time and Opportunity Cost

Metric	Martingale	Flat Betting
Average bet size	Escalating	Constant
Time per session	Long	Flexible
Stress level	High	Low
Same expected loss	Yes	Yes

Simulation Results {#simulation}

10,000 Session Simulation

Settings: $10 base bet, 8 max doubles, European roulette (48.65%)

Metric	Result
Sessions won	9,874 (98.74%)
Sessions lost	126 (1.26%)
Average win	+$42
Average loss	-$2,550
Net result	-$68,946
Net per session	-$6.89

Comparison to Flat Betting

Same total wagered, flat $100 bets:

Metric	Martingale	Flat Betting
Winning sessions	98.74%	~50%
Average session result	-$6.89	-$2.70
Maximum loss	-$2,550	-$100
Variance	Extreme	Low
Same EV?	Yes	Yes

Long-Term Outcome Distribution

Outcome Range	Martingale	Flat Betting
Big win (+$500+)	0.1%	0.5%
Small win (+$1-500)	98.6%	25%
Small loss (-$1-500)	0%	74%
Big loss (-$500+)	1.3%	0.5%

Martingale concentrates losses into rare catastrophic events.

Martingale Variations {#variations}

Reverse Martingale (Paroli)

Rule: Double after wins, reset after loss

Aspect	Standard	Reverse
After loss	Double	Reset to base
After win	Reset to base	Double
Risk profile	Frequent small wins, rare big loss	Frequent small losses, rare big win
EV	Negative	Negative

Grand Martingale

Rule: Double plus one unit after loss

Round	Standard	Grand
1	$10	$10
2	$20	$30
3	$40	$70
4	$80	$150
5	$160	$310

Higher profit per win, faster bankroll depletion.

Modified Martingale

Rule: Stop after N losses

Max Losses	Win Rate	Max Loss	EV Change
3	93.1%	$70	Same
5	98.2%	$310	Same
7	99.5%	$1,270	Same

Limiting losses doesn't change EV—just redistributes risk.

Mini-Martingale

Rule: 1.5x instead of 2x

Round	2x	1.5x
5	$160	$76
10	$5,120	$576

Slower growth, same fundamental problem.

Comparison Table

Variation	Risk Reduction	EV Impact	Practical?
Standard	None	Negative	No
Reverse	Lower variance	Negative	Slightly better
Grand	Worse	More negative	No
Modified	Loss caps	Same negative	No
Mini	Slower growth	Same negative	No

All variations have negative expected value.

Psychological Traps {#psychology}

Trap 1: The "Always Win" Illusion

98%+ of sessions end in profit. This creates false confidence:

Sessions	Likely Profit Sessions	Likely Bust Sessions
10	9-10	0-1
50	49-50	0-1
100	98-99	1-2

After 50 winning sessions, you "know" the system works.

Trap 2: Survivorship Bias

Story	Reality
"I've won $500 with Martingale"	Doesn't mention eventual $2,000+ loss
"My friend uses it successfully"	Small sample, hasn't hit streak yet
"It works if you're disciplined"	Discipline doesn't change math

Trap 3: Gambler's Fallacy Integration

The fallacy: "I've lost 5 in a row, a win is due" The Martingale amplifies this by making you bet more when "certain" of winning.

Reality: Each spin is independent. Previous results don't affect future outcomes.

Trap 4: Sunk Cost Escalation

After 5 losses (- $310), the thought: "I MUST bet$ 320 to recover" This ignores that the $310 is already gone—each bet should be evaluated independently.

Martingale on Different Games {#games}

European Roulette (Even Money)

Metric	Value
Win probability	48.65%
House edge	2.70%
10-loss streak odds	1 in 784
Martingale EV	-2.70% of total wagered

American Roulette (Even Money)

Metric	Value
Win probability	47.37%
House edge	5.26%
10-loss streak odds	1 in 608
Martingale EV	-5.26% of total wagered

Worse game = worse Martingale results

Blackjack

Metric	Value
Win probability	~42.5% (not even money)
House edge	0.5% with basic strategy
Problem	Wins aren't always 1:1

Martingale poorly suited—blackjack has splits, doubles, blackjack payouts.

Baccarat (Banker)

Metric	Value
Win probability	45.86%
House edge	1.06%
Issue	5% commission on wins

Martingale works poorly with commission structures.

The Bottom Line {#conclusion}

What Martingale Actually Does

Claim	Reality
"Guarantees wins"	Guarantees eventual catastrophic loss
"Beats the house"	House edge applies to every bet
"Works with discipline"	Math doesn't care about discipline
"Safe with limits"	Limits just delay the inevitable

Expected Outcome Over Time

\text{Long-Term Result} = -\text{House Edge} \times \text{Total Wagered}

Regardless of betting system. Always. Without exception.

When to Use Martingale

Answer: Never for expected profit

If you want...	Better strategy
Entertainment	Flat betting, accept losses
Best odds	Low house edge games, optimal strategy
Profit	Become the casino

Final Verdict

Martingale is mathematically equivalent to:

Winning $10 frequently
Losing $10,000+ rarely
Net loss over time = house edge

It's a repackaging of the same losing proposition with extra stress and bankroll requirements.

Martingale Simulator - See why it fails
Bankroll Calculator - Understand requirements
Session Simulator - Compare to flat betting

Martingale

Martingale System

Frequently Asked Questions

Evgeny Volkov

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