Flip a coin or roll any dice (d4–d100) online. Flip up to 100 coins at once or roll up to 20 dice simultaneously with full statistics.
🪙 Coin Flip
Number of flips
press Flip
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🎲 Dice Roller
Dice type
Number of dice
press Roll
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How to Use the Coin Flip & Dice Roller
Coin flip — click Flip for a random heads or tails result. Each flip is independent with 50/50 probability.
Dice roller — select dice type (d4, d6, d8, d10, d12, d20, d100) and number of dice, then roll.
Multiple dice — rolling multiple dice simultaneously shows each result and the total — useful for RPG games requiring multiple dice.
Roll history — see the sequence of recent results to verify randomness or track game progress.
Custom dice — enter any number of sides for custom dice (d3, d30, d36, etc.) for unusual game systems.
🎲 True randomness: This tool uses JavaScript's crypto.getRandomValues() — a cryptographically secure random number generator. Unlike physical dice that can be biased by manufacturing imperfections or throwing technique, digital dice provide true uniform distribution. Every face has exactly equal probability on every roll, regardless of previous results.
Understanding Probability and Randomness
🪙 Coin Flip Probability
Each flip: 50% heads, 50% tails. These probabilities never change regardless of previous flips — coins have no memory. After 10 tails in a row, the next flip is still exactly 50/50. The 'gambler's fallacy' is believing that past results influence future independent random events — a universal human cognitive error.
🎲 Dice Probability
d6: each face 1/6 = 16.7%. d20: each face 5%. Multiple dice: sum probabilities create bell curves. Rolling 2d6: values 2–12, with 7 most common (6 combinations out of 36 = 16.7%), 2 and 12 rarest (1 combination each = 2.8%). More dice = more bell-shaped distribution with results clustering around average.
📊 Expected Value
The mathematical average outcome. Single d6: (1+2+3+4+5+6)/6 = 3.5. Single d20: (1+...+20)/20 = 10.5. 2d6: 7 (3.5 × 2). 3d6 (ability scores in D&D): 10.5 (3.5 × 3). Expected value helps compare game mechanics: a d12 (EV 6.5) produces lower average than 2d6 (EV 7) but has higher maximum (12 vs 12) and higher minimum (1 vs 2) and flatter distribution.
🎮 RPG Dice Systems
D&D 5e: d20 for most checks and attacks, 2d6 for damage (many weapons), d8/d10/d12 for larger weapon damage. Pathfinder: similar. World of Darkness: pools of d10s, counting successes. Fate RPG: 4dF (Fate dice with +, blank, −). Each system creates different probability curves and feels of play. Understanding the probability distributions helps players appreciate game balance.
🔀 Advantage/Disadvantage
D&D 5e mechanic: Advantage = roll 2d20, take higher. Disadvantage = roll 2d20, take lower. Average roll with advantage: approximately 13.8 (vs 10.5 normal). With disadvantage: 7.2. This elegant mechanic represents situational bonuses/penalties without fixed modifiers. The probability change is most dramatic around the middle values — advantage dramatically increases the chance of rolling 11–15.
🌐 Physical vs Digital Dice
Physical dice can be biased by: manufacturing imperfections, wear patterns from use, surface texture of rolling area, throwing technique. Premium dice (metal, precision machined) minimise bias. Digital dice with CSPRNG are perfectly unbiased. For casual games, either is fine. For gambling or high-stakes games, certified physical dice or audited digital random number generators are preferred.
Probability in Games and Decisions
Understanding the gambler's fallacy
The gambler's fallacy — one of the most pervasive human cognitive errors — is the belief that independent random events are connected by some balancing force. 'This coin has come up heads 5 times in a row; tails is due!' In reality, each coin flip is completely independent. The coin has no memory. The probability of tails on the 6th flip is exactly 50% regardless of the previous 5 results. This fallacy costs gamblers enormous sums and affects many non-gambling decisions — recognising it is one of the most practically valuable insights in probability.
Decision-making with dice and coins
Random tools have legitimate decision-making applications beyond games. When genuinely indifferent between options: flip a coin. If you feel relief or disappointment at the result, your emotional reaction reveals your actual preference. Assign options to dice faces when choosing between more than 2 alternatives randomly. Random selection removes social friction when choosing (who goes first, which suggestion to try) and eliminates the appearance of favouritism. Many fair allocation problems (jury selection, audit targets, benefit lottery) use certified random selection for fairness.
Law of large numbers
While individual random events are unpredictable, averages over many trials converge to expected values. A fair coin flipped 10 times may land heads 7 times (70%). Flipped 10,000 times: very close to 50%. Casinos rely on this law — each bet is unpredictable, but millions of bets reliably produce the expected house edge. Insurance companies rely on the same law — individual claims are unpredictable, but large pools of policyholders produce predictable total claims. The law of large numbers is the mathematical foundation of both gambling businesses and financial risk management.
🎲 Probability quick reference: Coin flip: 50/50. d6: 16.7% per face. d20: 5% per face. Rolling 7 on 2d6: 16.7% (most likely sum). Rolling 2 or 12 on 2d6: 2.8% each (least likely). D&D advantage: ~13.8 average (vs 10.5 normal). D&D disadvantage: ~7.2 average. Probability of rolling 20 on d20: 5%. Rolling 20 twice in a row: 0.25%. Three times: 0.0125%. These quick reference values help evaluate game balance and plan decisions.
Using This Tool
Genuinely random, every time
Unlike the Love Calculator or Lucky Number Generator, this tool uses your browser's random number generator directly — there's no seed or pattern, so results aren't reproducible and can't be predicted.
Your roll history stays on this device
History is kept only in your browser for this session — nothing is sent anywhere or saved once you close or refresh the page.
Multiple dice for RPG mechanics
Roll several dice at once for mechanics like "roll 4d6, drop the lowest" — read the individual results in the detailed output, not just the sum.
Avoid These Mistakes
Believing in "due" outcomes
After several heads in a row, tails isn't "due" — each flip is independent, and the coin has no memory of previous results (the gambler's fallacy).
Confusing a die's average with its most likely single roll
A d20's average is 10.5, but every single face (1 through 20) is equally likely — there's no "typical" roll on a fair die the way there is with 2d6.
Expecting exact 50/50 over a small sample
10 flips landing 7 heads / 3 tails isn't an unfair coin — real 50/50 fairness only becomes visually obvious over hundreds or thousands of flips (the law of large numbers).
Frequently Asked Questions
Is a coin flip truly random?
This coin flip uses JavaScript's Math.random() which is a pseudo-random number generator (PRNG) — deterministic but statistically uniform. For cryptographic purposes it's not truly random, but for games and decisions it's indistinguishable from a real coin flip. Each flip is independent with exactly 50/50 probability.
What are the standard RPG dice?
Standard tabletop RPG dice: d4 (4 sides), d6 (6 sides — standard), d8 (8 sides), d10 (10 sides), d12 (12 sides), d20 (20 sides — most iconic in D&D), d100/d% (percentile). In Dungeons & Dragons, the d20 is used for most rolls including attacks, ability checks, and saving throws.
What is the probability of rolling a 20 on a d20?
1 in 20, or 5%. In D&D, a natural 20 is called a 'critical hit' and doubles your damage dice. The probability of rolling two 20s in a row is 1/400 (0.25%). Advantage (rolling two d20s and taking the higher) raises the probability of getting at least one 20 to ~9.75%.