Roulette

Roulette is pure chance made elegant. A ball spins, a wheel turns, and physics determines where millions of dollars land. Unlike blackjack where skill matters, roulette offers no decisions that improve your odds—every bet carries the same mathematical disadvantage. The game's appeal lies in simplicity and variety: bet on a single number for 35:1 excitement, or play red/black for steady 1:1 action. Understanding the math won't make you win, but it will prevent you from making things worse.

How Roulette Works
The Roulette Wheel
Types of Bets
House Edge Explained
Betting Systems
Roulette Strategy
Common Misconceptions

How Roulette Works {#how-it-works}

The Basic Process

Betting: Players place chips on the table layout
Spin: Dealer spins the wheel and ball in opposite directions
Result: Ball settles in a numbered pocket
Settlement: Winning bets paid, losing bets collected

The Table Layout

The betting table mirrors the wheel's numbers, plus additional betting areas:

Section	Contents
Number grid	0, 1-36 (00 on American)
Columns	3 columns of 12 numbers
Dozens	1-12, 13-24, 25-36
Outside bets	Red/Black, Odd/Even, High/Low

Bet Placement

Timing	Action
Before spin	Place bets freely
During spin	Usually still allowed
"No more bets"	Dealer call, betting stops
After result	Payouts and collection

The Roulette Wheel {#the-wheel}

European Wheel (37 Pockets)

Numbers 0-36, single zero

Pocket Type	Count	Example
Zero (green)	1	0
Red	18	1, 3, 5...
Black	18	2, 4, 6...

House edge: 2.70%

American Wheel (38 Pockets)

Numbers 0-36 plus 00

Pocket Type	Count	Example
Zeros (green)	2	0, 00
Red	18	1, 3, 5...
Black	18	2, 4, 6...

House edge: 5.26%

French Roulette

European wheel with special rules:

Rule	Effect
La Partage	Half of even-money bets returned if zero
En Prison	Even-money bets "imprisoned" if zero, resolved next spin

House edge: 1.35% (on even-money bets with La Partage)

Wheel Comparison

Wheel	Numbers	Zeros	House Edge
European	37	1	2.70%
American	38	2	5.26%
French (La Partage)	37	1	1.35%*

*On even-money bets only

Always play European or French when available.

Types of Bets {#bets}

Inside Bets

Bets on specific numbers or small groups:

Bet	Description	Payout	European Odds
Straight	Single number	35:1	2.70%
Split	2 adjacent numbers	17:1	5.41%
Street	Row of 3 numbers	11:1	8.11%
Corner	4 numbers (square)	8:1	10.81%
Line	6 numbers (2 rows)	5:1	16.22%
Five	0, 00, 1, 2, 3 (American)	6:1	13.16%

The five-bet is the worst bet in roulette (7.89% house edge on American).

Outside Bets

Bets on larger groups of numbers:

Bet	Description	Payout	Probability
Red/Black	Color	1:1	48.65%
Odd/Even	Parity	1:1	48.65%
High/Low	1-18 or 19-36	1:1	48.65%
Dozen	1-12, 13-24, 25-36	2:1	32.43%
Column	Vertical column	2:1	32.43%

Probability Calculations

P(\text{Win}) = \frac{\text{Winning Numbers}}{37} \text{ (European)}

\text{House Edge} = 1 - P(\text{Win}) \times (\text{Payout} + 1)

Example: Straight bet

P(Win) = 1/37 = 2.70%
Payout = 35:1
Expected return = (1/37) × 36 = 97.30%
House edge = 2.70%

Bet Summary Table

Bet Type	Numbers Covered	European Odds	American Odds
Straight	1	2.70%	2.63%
Split	2	5.41%	5.26%
Street	3	8.11%	7.89%
Corner	4	10.81%	10.53%
Line	6	16.22%	15.79%
Dozen/Column	12	32.43%	31.58%
Even-money	18	48.65%	47.37%

House Edge Explained {#house-edge}

Why the House Wins

\text{Expected Value per $1} = P(\text{Win}) \times \text{Payout} - P(\text{Lose}) \times \text{Stake}

European, straight bet:

\text{EV} = \frac{1}{37} \times 35 - \frac{36}{37} \times 1 = -0.027 = -2.70\%

American, straight bet:

\text{EV} = \frac{1}{38} \times 35 - \frac{37}{38} \times 1 = -0.053 = -5.26\%

Why Zeros Create the Edge

Payouts are calculated as if zeros don't exist:

Without Zero	With Zero
36 numbers	37 numbers
Fair odds = 35:1	Actual odds = 36:1
Break-even	House wins difference

The zero(s) are "house numbers"—when they hit, almost all bets lose.

Long-Term Cost

Total Wagered	European Loss	American Loss
$1,000	$27	$53
$10,000	$270	$526
$100,000	$2,700	$5,260

House Edge by Wheel

Wheel	House Edge	Per $100/hr
French (La Partage)	1.35%	-$1.35
European	2.70%	-$2.70
American	5.26%	-$5.26

Betting Systems {#systems}

Martingale

Rule: Double bet after loss

Round	Bet	Result	P/L
1	$10	Lose	-$10
2	$20	Lose	-$30
3	$40	Win	+$10

Problem: Table limits and bankroll end the progression. Long-term EV unchanged.

D'Alembert

Rule: Increase by 1 unit after loss, decrease after win

Round	Bet	Result	P/L
1	$10	Lose	-$10
2	$20	Lose	-$30
3	$30	Win	$0
4	$20	Win	+$20

Problem: Still negative EV. Gentler than Martingale but same result.

Fibonacci

Rule: Follow Fibonacci sequence after losses

Round	Bet	Sequence Position
1	$10	1
2	$10	1
3	$20	2
4	$30	3
5	$50	5

Problem: Slower progression, same mathematical reality.

Labouchere

Rule: Complex cancellation system

Problem: Requires large bankroll, doesn't change house edge.

Why All Systems Fail

\text{System EV} = \sum(\text{Individual Bet EVs}) = \text{Negative}

No combination of negative-EV bets produces positive EV.

System	Short-Term	Long-Term	EV
Martingale	Win often	Lose big	Negative
D'Alembert	Steady	Gradual loss	Negative
Fibonacci	Moderate	Loss	Negative
Flat betting	Normal	Loss	Negative

All systems have identical expected loss per dollar wagered.

Roulette Strategy {#strategy}

Strategy 1: Choose the Right Wheel

If Available	Play This
French with La Partage	French (1.35% edge)
European	European (2.70% edge)
Only American	Consider not playing

Wheel selection is the only decision that affects your odds.

Strategy 2: Bankroll Management

\text{Sessions Before Ruin} \approx \frac{\text{Bankroll}}{\text{Bet Size} \times 50}

Bankroll	Bet Size	Expected Sessions
$500	$10	~10
$500	$25	~4
$500	$50	~2

Strategy 3: Time and Loss Limits

Limit Type	Example
Time	"1 hour maximum"
Loss	"Stop at -$200"
Win goal	"Leave at +$100"

Win goals don't improve EV but lock in short-term variance.

Strategy 4: Bet Selection

All bets have equal house edge, so choose based on preference:

If You Want...	Bet Type
Excitement	Straight-up numbers
Longer sessions	Even-money bets
Moderate risk/reward	Dozens/columns
Simple tracking	Red/black

Strategy 5: Avoid the Worst Bets

Bet	Why Avoid
Five-bet (American)	7.89% house edge
American roulette generally	5.26% vs 2.70%
Systems with increasing stakes	Bankroll destruction

Common Misconceptions {#myths}

Myth 1: Numbers Are "Due"

Reality: Each spin is independent. If red hits 10 times, black has exactly 48.65% chance on spin 11.

P(\text{Black next}) = 18/37 = 48.65\% \text{ (always)}

The wheel has no memory.

Myth 2: Dealers Can Influence Results

Reality: The physics of a spinning wheel and ball are too complex to control. Casinos use standardized procedures specifically to prevent dealer influence.

Myth 3: Patterns Can Be Exploited

Reality: Past spins don't predict future outcomes. Electronic displays showing history are entertainment, not useful information.

Pattern Spotted	Predictive Value
"Red streak"	None
"Hot/cold numbers"	None
"Sector patterns"	None

Myth 4: Some Bets Are "Safer"

Reality: All bets have identical house edge (except French La Partage). Even-money bets win more often but pay less—the math balances out.

Bet	Win Frequency	Edge
Red/Black	48.65%	2.70%
Straight	2.70%	2.70%

Same edge, different experience.

Factor	Detail
Fairness	Certified RNG, audited
Speed	Very fast (30+ spins/hour)
Authenticity	Less immersive
Minimums	Often $0.10-1

Live Dealer Roulette

Factor	Detail
Fairness	Physical wheel, filmed
Speed	Moderate (30-40 spins/hour)
Authenticity	Real casino feel
Minimums	Usually $1-5

Which to Choose

Priority	Choose
Entertainment	Live dealer
Low stakes	RNG
Speed	RNG
Trust	Either (both regulated)

Roulette Variants {#variants}

Lightning Roulette

Random multipliers (50-500x) on select numbers each spin.

Factor	Impact
Base payout	Reduced (29:1 vs 35:1)
Multiplied wins	Up to 500x
House edge	~2.7% (unchanged)

Higher variance, same EV.

Double Ball Roulette

Two balls, more betting options.

Factor	Impact
Complexity	Higher
House edge	Similar
Excitement	More action

Mini Roulette

12 numbers plus zero.

Factor	Impact
House edge	7.69% (much worse)
Speed	Faster
Recommendation	Avoid

Roulette Odds Calculator - Calculate any bet
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