Is the coin flip truly 50% random?

Yes. Every toss uses a cryptographically uniform random generator with an exact 50% chance for Heads and 50% for Tails. Each toss is completely independent of past flips.

Can past flips predict future flips?

No. Mathematicians call this the Gambler Fallacy. Even if the coin lands on Heads ten times in a row, the probability that the next flip lands on Heads remains exactly 50%.

How does probability scale with streak length?

Each new consecutive flip multiplies the rarity by 2. A streak of 5 is 1 in 32, a streak of 10 is 1 in 1,024, and a streak of 20 is 1 in 1,048,576.

What are the odds to reach a streak of 10?

The odds to score 10 consecutive correct calls are 1 in 1,024, which equals 0.0976%. A streak of 10 places you in the top tenth of one percent of all players.

Does the game save my progress and best score?

Yes. Your longest streak, total flips, and win count automatically save to your browser local storage and sync to your PlayMemorize profile.

Can MemPi help me study and practice this game?

Yes! Click MemPi in the header or on the game board to summon him. He observes the board, thinks out loud, and can demonstrate moves or guide you through tricky steps.

Pure Luck

Current Streak01 in 1

Best Streak01 in 1

Total Flips050.0% Win Rate

🪙Heads

👑Tails

Pick a side to flip the coin:

Mathematical Probability Distribution

In a fair 50/50 toss, each consecutive correct call doubles the difficulty. No skill, no cheat codes, pure mathematics.

Streak 11 in 2

50.0%

Streak 21 in 4

25.0%

Streak 31 in 8

12.5%

Streak 41 in 16

6.25%

Streak 51 in 32

3.125%

Streak 71 in 128

0.78%

Streak 101 in 1,024

0.098%

Streak 121 in 4,096

0.024%

Streak 151 in 32,768

0.003%

Streak 181 in 262,144

0.00038%

Streak 201 in 1,048,576

0.000095%

About Pure Luck

A pure 50% coin flip game · test your streak against mathematical probability

Pure Luck is a direct experiment in pure mathematical probability and variance.

Every round is a fair, independent 50% coin flip. There are no patterns to memorize, no puzzles to solve, and no reaction timers. Success is governed strictly by the mathematics of independent Bernoulli trials.

The Exponential Ladder of Streaks. Each correct call doubles the statistical rarity of your run. To reach a streak of 5 is a 1 in 32 occurrence (3.125%). To reach a streak of 10 is 1 in 1,024 (less than 0.1%). A streak of 20 requires you to beat odds of 1 in 1,048,576.

Mathematical Probability Distribution. Right below the coin toss, you can explore the exact mathematical probability distribution for consecutive streaks. Each additional win is an independent 50% Bernoulli trial governed by pure mathematics.

Part of the PlayMemorize collection. Fully client-side, privacy-preserving, and playable offline as a Progressive Web App.

Book Recommendation

Language: English

Want to deepen your skills in Pure Luck? Recommended reading: Make It Stick: The Science of Successful Learning by Peter C. Brown, Henry L. Roediger III, Mark A. McDaniel .

Harvard University Press definitive work on retrieval practice, cognitive retention, and turning working memory into permanent recall.

📖 View Book

🎓 Educational Account

Save Your Stats & Worksheets for Pure Luck

Lock in your percentile rankings, practice sheets, and daily streak progress. 100% free with 1-click biometric passkeys.

New game videos on YouTube

YouTube channel

FAQ

Is the coin flip truly 50% random?

Yes. Every toss uses a cryptographically uniform random generator with an exact 50% chance for Heads and 50% for Tails. Each toss is completely independent of past flips.
Can past flips predict future flips?

No. Mathematicians call this the Gambler Fallacy. Even if the coin lands on Heads ten times in a row, the probability that the next flip lands on Heads remains exactly 50%.
How does probability scale with streak length?

Each new consecutive flip multiplies the rarity by 2. A streak of 5 is 1 in 32, a streak of 10 is 1 in 1,024, and a streak of 20 is 1 in 1,048,576.
What are the odds to reach a streak of 10?

The odds to score 10 consecutive correct calls are 1 in 1,024, which equals 0.0976%. A streak of 10 places you in the top tenth of one percent of all players.
Does the game save my progress and best score?

Yes. Your longest streak, total flips, and win count automatically save to your browser local storage and sync to your PlayMemorize profile.
Can MemPi help me study and practice this game?

Yes! Click MemPi in the header or on the game board to summon him. He observes the board, thinks out loud, and can demonstrate moves or guide you through tricky steps.