Why a Good Night Proves Nothing: Variance in Short Sessions
Averages need large samples. An evening's play is a small one, which is why results swing and why streaks mean so little.
Two ideas that get confused
Expected value is what a bet returns on average. Variance is how far individual results scatter around that average. A game can have a small expected loss and still produce large wins and large losses along the way.
The law of large numbers
As the number of bets grows, the average result per bet moves closer to the expected value. The important word is large. A few hundred bets is not enough for the average to settle, so an evening's result is driven mostly by variance.
What streaks are
Toss a fair coin a few hundred times and runs of six or seven heads will appear. Nothing caused them and nothing follows from them. People are quick to see patterns in sequences like this and slow to accept that random sequences are naturally streaky.
Why this matters for money
- A winning session is not evidence of a method that works.
- A losing session does not mean a win is owed.
- The higher the volatility, the larger the bankroll needed to survive ordinary swings, and the more likely a fixed budget is to run out early.
The practical conclusion is unglamorous. Decide the budget in advance, expect the result of any one session to be mostly noise, and do not change the stake because of what the last few rounds did.