Sample Size Calculator
Determine if your sample size is large enough for statistical significance
Your Experience
Statistical Analysis
Understanding Sample Size & Variance
Why Sample Size Matters
Small sample sizes can show extreme results due to normal variance. You might lose 70% of 100 spins and think the game is rigged, but that's actually within normal statistical variation.
The Law of Large Numbers
As sample size increases, actual results converge toward the expected value. But this requires THOUSANDS or even MILLIONS of trials, not hundreds.
Standard Deviation
For a binary outcome (win/loss), standard deviation = √(n × p × (1-p))
Where n = number of trials, p = probability of success
Results within 2 standard deviations are considered normal (95% confidence interval).
Common Misconceptions
- "I lost 10 in a row - it's rigged!" → Losing streaks happen regularly due to variance
- "I played 50 spins and lost money" → Sample size way too small for any conclusion
- "This slot hasn't paid in 200 spins" → Normal for high variance slots
- "I track results on paper - definitely rigged" → Need thousands of trials, not dozens
How Many Trials Do You Need?
| Game Type | Minimum Trials | Recommended |
|---|---|---|
| Roulette (single number) | 1,000 | 10,000+ |
| Blackjack | 5,000 hands | 50,000+ |
| Slots (low variance) | 10,000 spins | 100,000+ |
| Slots (high variance) | 50,000 spins | 500,000+ |
| Dice/Coin Flip | 1,000 | 10,000+ |
The Bottom Line
Unless you have data from tens of thousands of trials, your experience is likely just normal variance. Licensed and regulated casinos use certified RNGs that are regularly audited. Short-term bad luck doesn't mean the game is rigged - it means you're experiencing normal statistical variation.
Frequently Asked Questions
How many spins or hands do I need for statistically significant results?
For most casino games, you need at least 10,000 trials for statistically meaningful results. For low-variance games like blackjack, 5,000 hands may suffice. For high-variance slots, you may need 50,000 to 100,000 spins before your results reliably reflect the true RTP. Short sessions of 100-500 plays tell you almost nothing about whether a game is fair.
Is 100 spins enough to tell if a slot is rigged?
No, 100 spins is far too small a sample. With a 96% RTP slot, your results after 100 spins could easily range from 60% to 130% return — all within normal statistical variance. You would need at least 10,000 spins, and ideally 100,000+, to draw any meaningful conclusions about whether the game matches its advertised RTP.
What is the law of large numbers and how does it apply to gambling?
The law of large numbers states that as you increase the number of trials, your actual results will converge toward the expected (mathematical) average. In gambling, this means that over thousands of bets, your win rate will approach the game's true probability. However, this requires a very large number of trials — short-term results are dominated by variance, not by the game's true odds.
What does a z-score mean in the context of gambling results?
A z-score measures how many standard deviations your actual results are from the expected results. A z-score between -2 and +2 (covering 95% of outcomes) indicates normal variance. A z-score beyond ±3 (less than 0.3% probability) suggests something unusual may be happening, though it still requires a large enough sample size to be meaningful.
Why do I keep losing even though the RTP is 96%?
A 96% RTP means you lose 4% on average over millions of spins. In the short term, variance dominates — you can easily lose 20-40% of your bankroll in a session of a few hundred spins and that is completely normal. The RTP is a long-term theoretical average, not a guarantee for any individual session. Losing streaks are a natural and expected part of gambling.
How do I calculate the standard deviation for my gambling results?
For simple win/loss outcomes, standard deviation = √(n × p × (1-p)), where n is the number of trials and p is the probability of winning. For example, with 1,000 coin flips (p=0.5), the standard deviation is √(1000 × 0.5 × 0.5) = 15.8. Your actual wins should fall within ±2 standard deviations of the expected value about 95% of the time.