Probability Basics
Odds, percentages, and implied probability fundamentals.
Probability is the language of gambling. Every bet, every game, every outcome can be expressed as a probability. Understanding the basics helps you evaluate whether a bet is fair, good, or terrible.
Expressing Probability
Probability can be written three ways:
| Format | Example | Meaning |
|---|---|---|
| Percentage | 25% | 25 out of 100 times |
| Decimal | 0.25 | Same as 25% |
| Fraction | 1/4 | 1 win for every 4 attempts |
1/4 = 0.25 = 25%. All mean the same thing.
Independent vs. Dependent Events
Independent Events
Previous outcomes don't affect future probabilities.
- Coin flips – each flip is 50/50 regardless of history
- Roulette spins – past numbers don't influence future spins
- Slot machine spins – RNG resets each spin
Good to Know
Dependent Events
Previous outcomes DO affect future probabilities.
- Blackjack – cards dealt affect remaining deck composition
- Poker – seeing cards changes your opponent's possible holdings
Strategy Insight
Implied Probability
In sports betting, odds imply the probability the sportsbook assigns to an outcome:
A -150 favorite implies a 60% chance of winning.
A +200 underdog implies a 33.3% chance of winning.
The Law of Large Numbers
As you make more bets, your results converge toward expected probability:
- Flip a coin 10 times → might get 7 heads (70%)
- Flip a coin 100 times → probably around 45-55 heads
- Flip a coin 10,000 times → almost certainly 48-52% heads
Warning
Common Probability Misconceptions
"It's due!"
Past results don't influence independent events. Black isn't more likely after 5 reds.
"Hot streaks are real"
In games of pure chance, streaks are just variance, not momentum.
"Near misses mean I'm close"
In slots and roulette, a near miss is just another loss. It has no predictive value.
Practical Applications
Use probability thinking to:
- Compare games – Higher probability of winning doesn't always mean better value (payouts matter too)
- Evaluate sports bets – Is the implied probability lower than your estimated true probability?
- Set expectations – Know that a 90% favorite still loses 1 in 10 times
Key Takeaways
- 1Probability can be expressed as percentages, decimals, or fractions
- 2Most casino games use independent events—past results don't affect future odds
- 3Implied probability shows what sportsbooks think is the true likelihood
- 4The Law of Large Numbers means short-term variance evens out long-term
- 5Avoid common fallacies: due wins, hot streaks, and near-miss thinking