Probability Basics
What are the chances? Learn how to work out odds for coins, dice and cards, and why “it's due” is one of the most expensive mistakes in the world.
Probability is a fraction
| Event | Probability | As a % |
|---|---|---|
| Coin lands heads | 1/2 | 50% |
| Roll a 6 on a die | 1/6 | ≈ 16.7% |
| Roll an even number | 3/6 = 1/2 | 50% |
| Draw an ace from a deck | 4/52 = 1/13 | ≈ 7.7% |
Probability always sits between 0 (impossible) and 1 (certain). The chance of something not happening is 1 minus the chance it does: not rolling a 6 is 1 − 1/6 = 5/6.
Combining events: “and” and “or”
AND, multiply. For independent events (one doesn't affect the other), multiply the chances.
- 1/2 × 1/2
- 1/4, or 25%
OR, add, as long as both can't happen at once.
- 1/6 + 1/6
- 2/6 = 1/3
“At least one” trick: it's usually easier to work out the chance of none and subtract from 1. Chance of at least one 6 in four rolls = 1 − (5/6)⁴ ≈ 52%.
The gambler's fallacy
A coin lands heads five times in a row. Is tails “due”? No. The coin has no memory. The next flip is still exactly 50/50.
Over thousands of flips, the share of heads drifts towards 50%. That's the law of large numbers. But it happens because the early streak gets swamped by later flips, not because the coin “corrects” itself.
Why casinos win: every game is built so the house has a small edge on each bet. Over millions of bets, that small edge is guaranteed profit.
Roll 10 times and the bars look lopsided. Roll 100,000 and each face lands close to 1/6 ≈ 16.7%.