One of the most common questions in probability, gambling, and gaming is: “If something has a 1% chance of happening, and I try 100 times, am I guaranteed to succeed?”
The intuitive answer is “Yes,” but the mathematical answer is “No, you only have a 63.2% chance.”
This is known as the Cumulative Probability of “At Least One Success.” Whether you are a slot player chasing a bonus round, a gamer farming a rare drop, or a bettor looking for one win in a series of longshots, our calculator reveals the harsh reality of variance and helps you plan your attempts accurately.
Chance After N Attempts
BinomialHow to Use the Calculator
This tool uses the Binomial Distribution formula to calculate your chances. Here is how to configure it:
- Choose Your Input Mode:
- Odds (1 in X): Best for slots or loot drops (e.g., “1 in 100” chance).
- Percentage (%): Best for sports betting or general stats (e.g., “5%” win probability).
- Enter Single Event Probability: Input the chance of success for a single trial.
- Enter Number of Attempts (N): How many spins, rolls, or bets are you planning to make?
- Analyze the Milestones: The calculator doesn’t just give you the final percentage; it tells you exactly how many tries you need to be 50%, 90%, or 99% confident of hitting your target.
Related Tools: If you are analyzing a sequence of wins/losses that have already happened, use our Streak Calculator. To check if your recent session results were statistically normal, try the Slot RTP Estimator.
Real-World Examples: The “63% Rule” Explained
Why isn’t 100 attempts at 1% a guarantee? Because with every failed attempt, the total probability of “failure” compounds.
Example 1: The Slot Machine Bonus
You are playing a slot where the Bonus Round triggers, on average, once every 100 spins (1% probability).
- You play 100 spins.
- Intuition says: 100% chance to hit.
- Math says: 63.4% chance to hit.
- Reality: Roughly 1 in 3 players will play 100 spins and get zero bonuses. This is often called the “Gambler’s Ruin.”
Example 2: The Rare Loot Drop (Gaming)
You are farming an item in an MMO with a drop rate of 1 in 1000 (0.1%). You decide to kill the boss 2,000 times.
- The Calculator Results: After 2,000 attempts, your chance of getting at least one drop is 86.4%.
- Verdict: Even with double the “required” attempts, there is still a 13.6% chance you walk away empty-handed.
Example 3: Roulette Betting
You want to see the number “7” appear on a European Roulette wheel (1 in 37 chance). You spin the wheel 37 times.
- Result: You have a 63.7% chance of seeing the number 7 at least once. To be 99% sure you will see a 7, you would need to spin the wheel 168 times.
Frequently Asked Questions (FAQ)
What is the formula for “At Least One Success”?
The easiest way to calculate this is to calculate the probability of failing every single time, and subtracting that from 1. The formula is:
P(Success) = 1 – (1 – p)^n
Where p is the probability of a single event, and n is the number of attempts.
Does the machine know I played N times?
No. This calculator assumes Independent Events (like slots or dice). The machine has no memory. If you missed 99 times, the chance of hitting on the 100th time is exactly the same as the first time. The calculator shows the cumulative probability of the entire session, not the specific odds of the next spin.
Why does the probability never reach 100%?
Mathematically, you can never be 100% certain of a random event outcome. Even if you try a million times, there is a microscopically small chance that you fail every time. However, you can reach 99.999% certainty, which is a “virtual” guarantee.