Poker
Coin-flip duel
Two players, different chances of winning, and hundreds of rounds — a clear visualization of the advantage.
Set the bias, the number of throws and rounds, then start the simulation. The results will appear here without reloading the page.
A streak is consecutive rounds won. A draw or an opponent's victory interrupts it. The longest streaks are grouped in the "24+" bucket.
| Round | Player 1 | Player 2 | Winner | Edge |
|---|---|---|---|---|
| Run the simulation — the last 15 rounds will appear here. | ||||
This is an educational simulator of probability theory and poker variance. It is not gambling: bets are not accepted, no prize fund is formed, winnings are not paid out, and results have no monetary value. Legal information
Coin duel: how probability turns into outcome
"Duel on a Coin" is the oldest site simulator. Two players agree that the first one has a slightly higher chance of winning each toss, and they flip the coin many times. The task is to see how a small advantage behaves over the long run: where luck ends and mathematics begins.
What happens in one round
A series of independent tosses is performed in a round. The player with more 'heads' wins; if the numbers are the same — it's a tie. The difference between 'heads' and 'tails' is the round advantage: 6:4 is an advantage of 2, 7:3 is an advantage of 4.
The more throws in a round, the less frequent ties occur and the more consistently the player with the advantage wins. With a single throw, the round is just that one throw, so the proportion of wins almost matches the given advantage.
Why a 55% edge does not guarantee a win
An advantage of 55% means that, on average, player 1 gets 55 "heads" out of 100. But in a particular round, he may get 48, 52, or 61 — this variance. Randomness does not have to coincide with expectation in the short term: this is why a player with an advantage sometimes loses several rounds in a row.
The simulator also shows the reverse side: over the long distance, the advantage almost always manifests, while a 'losing streak' can be longer than it intuitively seems.
How to read the results
- Win rate — how many rounds each player won out of the total number.
- Average edge — how large the rounds were won on average.
- Maximum series — the longest winning streak in a row.
- Distribution of series — how many times series of each length occurred.
- Accumulated victories — a graph showing how the gap grew.
Compare the scenarios: 55% on 10 throws and 55% on 1000 throws — these are two different games in terms of result stability.