Coin Flip

Flip a virtual coin online with real-time Bernoulli probability tracking, streak counters, multi-flip simulation, and cumulative distribution statistics.

Virtual Coin Toss

🪙Heads
Multi-Flip Simulation Batches
Current Outcome
Heads
50/50 Fair Trial

Total Flips

5

Heads Count

3 (60.0%)

Tails Count

2 (40.0%)

Current Streak

1x Heads

Heads (60.0%)Tails (40.0%)
Recent Flips Trail (5 recorded)
HTHHT

Independence of Trials

Every coin toss is independent of preceding outcomes. A streak of 5 Heads never alters the 50/50 probability on the 6th flip.

Bernoulli Trials & Binary Coin Flip Probability

A fair coin toss represents the foundational model of a Bernoulli trial — a random experiment with exactly two mutually exclusive outcomes: Heads ($X=1$) and Tails ($X=0$), each with probability $p = 0.5$.

1. Single Flip Bernoulli Probability
P(Heads)=p = 0.50 (50%),P(Tails)=1 − p = 0.50 (50%)
2. Binomial Distribution Formula (k Heads in n Flips)
P(K = k)=
n!k! × (n − k)!
×pᵏ × (1 − p)ⁿ⁻ᵏ
Step-by-Step Probability Breakdown (Probability of Exactly 3 Heads in 5 Flips)
Step 1: Calculate Combinations C(5, 3)
C(5, 3) = 5! / (3! × 2!) = (120) / (6 × 2) = 10 distinct combinations
Step 2: Calculate Probability per Path
(0.5)³ × (0.5)² = (0.5)⁵ = 0.03125 (1/32)
Step 3: Total Binomial Probability
P(3 Heads in 5 Flips)=10 × 0.03125=0.3125 (31.25%)

Coin Streak Probability Reference

Streak Length (Consecutive)Formula (0.5ⁿ)Decimal ProbabilityOdds (1 in X)
2 Consecutive Heads(0.5)²25.0%1 in 4
5 Consecutive Heads(0.5)⁵3.125%1 in 32
10 Consecutive Heads(0.5)¹⁰0.0977%1 in 1,024

Frequently Asked Questions

Is this digital coin flip truly fair and unbiased?
Yes. The outcome is generated by evaluating Math.random() < 0.5, ensuring exactly equal 50.0% theoretical probability for Heads and Tails on every single trial.
What is the Gambler's Fallacy?
The Gambler's Fallacy is the mistaken belief that a streak of one outcome (e.g., 5 heads in a row) makes the opposite outcome 'due'. Each coin flip is a completely independent Bernoulli trial with an unchanged 50% probability.
What is the Law of Large Numbers in coin tossing?
As the number of coin flips approaches infinity, the relative frequency of heads approaches its theoretical probability of 0.50 (50%).
What are the odds of getting 5 heads in a row?
The probability of 5 consecutive heads is (0.5)^5 = 1/32 ≈ 3.125% (or 1 in 32 attempts).

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