Odds & Probability Tools

Professional calculators for odds, probabilities, and expected values

✓ Mathematical Accuracy

✓ Multiple Formats

✓ Instant Results

Odds & Probability Calculators

Popular

Odds Calculator

Beginner

Convert between different odds formats and calculate payouts

Features:

Decimal/Fractional/American

Payout Calculator

Implied Probability

Multiple Formats

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Probability Calculator

Intermediate

Calculate probabilities for various casino game scenarios

Features:

Single/Multiple Events

Conditional Probability

Combinations

Permutations

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House Edge Calculator

Intermediate

Calculate the house edge for any casino game or bet

Features:

Game Analysis

Bet Comparison

Long-term Expectations

EV Calculations

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RTP Calculator

Advanced

Calculate Return to Player percentages for slots and games

Features:

Slot Analysis

Paytable Evaluation

Variance Calculation

Hit Frequency

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Expected Value Calculator

Intermediate

Calculate expected value for any gambling scenario

Features:

Multiple Outcomes

Weighted Averages

Risk Assessment

Decision Analysis

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Variance Calculator

Advanced

Calculate variance and standard deviation for gambling outcomes

Features:

Statistical Analysis

Risk Metrics

Confidence Intervals

Distribution Analysis

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Casino Game Odds Comparison

Blackjack

Skill-Based

House Edge

0.28% - 2%

RTP

98% - 99.72%

Best Bet

Basic Strategy

Worst Bet

Insurance (7.4% house edge)

House edge varies significantly with rules and player skill

European Roulette

House Edge

2.70%

RTP

97.30%

Best Bet

Any single number or outside bet

Worst Bet

All bets have same house edge

All bets except neighbors have identical house edge

American Roulette

House Edge

5.26%

RTP

94.74%

Best Bet

Any bet except five-number

Worst Bet

Five-number bet (7.89% house edge)

Double zero significantly increases house edge

Baccarat

House Edge

1.06% - 14.4%

RTP

85.6% - 98.94%

Best Bet

Banker bet (1.06%)

Worst Bet

Tie bet (14.4%)

Banker bet has lowest house edge despite commission

Craps

House Edge

0.60% - 16.67%

RTP

83.33% - 99.40%

Best Bet

Pass/Don't Pass (1.36%/1.40%)

Worst Bet

Any 7 (16.67%)

Wide range of house edges depending on bet type

Video Poker

Skill-Based

House Edge

-0.76% - 5%

RTP

95% - 100.76%

Best Bet

Jacks or Better (optimal play)

Worst Bet

Side bets and poor strategy

Can have positive RTP with perfect play

Understanding Odds Formats

Decimal Odds

Most common in Europe and Australia

Example:

2.50

Calculation:

Payout = Stake × Decimal Odds

Profit Formula:

Profit = (Stake × Decimal Odds) - Stake

Implied Probability:

Probability = 1 / Decimal Odds

Fractional Odds

Traditional UK format

Example:

3/2 or 6/4

Calculation:

Payout = Stake × (Numerator/Denominator) + Stake

Profit Formula:

Profit = Stake × (Numerator/Denominator)

Implied Probability:

Probability = Denominator / (Numerator + Denominator)

American Odds

Used primarily in the United States

Example:

+150 or -200

Calculation:

Positive: Profit = (Stake × Odds) / 100

Profit Formula:

Negative: Profit = Stake / (Odds / 100)

Implied Probability:

Positive: 100 / (Odds + 100) | Negative: Odds / (Odds + 100)

Probability Fundamentals

Independent Events

Events where one outcome doesn't affect another

Example:

Each roulette spin is independent of previous spins

Formula:

P(A and B) = P(A) × P(B)

Why It Matters:

Critical for understanding casino games

Mutually Exclusive

Events that cannot happen at the same time

Example:

A roulette ball cannot land on both red and black

Formula:

P(A or B) = P(A) + P(B)

Why It Matters:

Important for calculating total probabilities

Conditional Probability

Probability of event A given that event B has occurred

Example:

Probability of blackjack given first card is an Ace

Formula:

P(A|B) = P(A and B) / P(B)

Why It Matters:

Key for card counting and dependent events

Expected Value

Average outcome of an event over many trials

Example:

Average profit/loss per bet in the long run

Formula:

EV = Σ(Probability × Outcome)

Why It Matters:

Essential for evaluating any gambling decision

Common Probability Mistakes

Gambler's Fallacy

High - leads to poor betting decisions

What People Think:

Believing past results affect future independent events

Example:

Thinking red is 'due' after several black numbers in roulette

Reality:

Each spin is independent with same probabilities

Confusing Odds and Probability

Medium - causes calculation errors

What People Think:

Using odds and probability interchangeably

Example:

Saying '50/50 odds' instead of '50% probability'

Reality:

Odds are ratios, probability is percentage or fraction

Ignoring House Edge

High - fundamental misunderstanding of gambling

What People Think:

Focusing only on short-term wins and losses

Example:

Not considering long-term mathematical disadvantage

Reality:

House edge determines long-term expectations

Overestimating Skill Impact

High - leads to unrealistic expectations

What People Think:

Believing skill can overcome house edge in luck-based games

Example:

Thinking you can predict slot machine outcomes

Reality:

Only certain games allow skill to reduce house edge

Key Mathematical Concepts

Law of Large Numbers

As the number of trials increases, actual results approach theoretical probabilities. This is why casinos always win in the long run.

Example: A coin might land heads 7 times out of 10 flips, but over 10,000 flips it will approach 50% heads.

Standard Deviation

Measures how spread out results are from the average. Higher standard deviation means more volatile results and bigger swings.

Example: Slots have high standard deviation (big wins/losses), while blackjack has lower standard deviation.

📊 Remember: Mathematics Doesn't Lie

Casino games are designed using rigorous mathematics to ensure the house always has an edge. Understanding these concepts helps you make informed decisions, but cannot change the fundamental mathematical reality that the house edge will prevail over time.