You played perfect blackjack strategy and still lost $500. Your friend played terribly and won $1,000. What happened? Variance. Understanding this concept is essential for anyone who gambles regularly.
What Is Variance?
Variance measures how much actual results differ from expected results.
In gambling terms:
- Expected value tells you what should happen on average
- Variance tells you how much results swing around that average
Example: A coin flip has 50/50 odds. Expected: 50 heads in 100 flips. But any specific 100 flips might give you 45 heads, or 55, or even 40 or 60. That swing is variance.
Variance vs. House Edge
These are different concepts:
House edge: The casino's long-term mathematical advantage. Fixed and predictable.
Variance: How widely results scatter around expectations. Creates unpredictability.
| Game | House Edge | Variance |
|---|---|---|
| Blackjack | ~0.5% | Low |
| Baccarat | ~1.1% | Low |
| Craps (pass line) | ~1.4% | Low |
| Roulette | 2.7-5.3% | Medium |
| Video Poker | 0.5-5% | Medium-High |
| Slots | 5-15% | Very High |
A game can have low house edge but high variance, or vice versa.
Why Variance Matters
Short-Term Swings
Over a few hours, variance dominates outcomes:
100 hands of blackjack (0.5% house edge):
- Expected loss: ~$5 (on $1,000 wagered)
- Actual result: Could be +$200 or -$300
Variance can completely override expected value in short sessions.
Winning Despite Negative EV
Many gamblers have winning sessions because variance allows short-term wins even with negative expected value.
This is why gambling is addictive: You can win despite the math being against you, creating the illusion that you're "good" at it or that luck favors you.
Losing Despite Positive EV
Even advantage players with +EV situations lose frequently. A card counter with 1% edge can easily lose 10 sessions in a row through variance.
Measuring Variance: Standard Deviation
Standard deviation (SD) quantifies variance:
Low SD: Results cluster near expected value High SD: Results scatter widely from expected value
One Standard Deviation
About 68% of results fall within one SD of expected value.
Example:
- Expected result: -$50
- Standard deviation: $100
- 68% of sessions: -$150 to +$50
Two Standard Deviations
About 95% of results fall within two SDs.
Same example:
- 95% of sessions: -$250 to +$150
Three Standard Deviations
About 99.7% of results fall within three SDs.
Same example:
- 99.7% of sessions: -$350 to +$250
That remaining 0.3%? You might lose (or win) even more.
Variance by Game
Low Variance Games
Blackjack:
- Frequent small wins and losses
- Rarely huge swings in single session
- Long-term results converge to expected value faster
Baccarat:
- Nearly even money bets
- Sessions rarely deviate dramatically
- Consistent grinding feel
Craps (pass/don't pass):
- Similar to baccarat
- Moderate swings possible with odds bets
Medium Variance Games
Roulette:
- Single number bets are high variance
- Outside bets (red/black) are lower variance
- Mixed betting creates medium variance
Video Poker:
- Base game is medium variance
- Royal flush hunting increases variance
- Full-pay machines are lower variance
High Variance Games
Slots:
- Long periods without significant wins
- Occasional big hits
- Extremely wide result distribution
- Sessions commonly swing +/- 50%+ of buy-in
Progressive jackpots:
- Near-zero probability events
- Life-changing if hit
- Virtually guaranteed loss if not
Understanding What This Means
Low variance: More predictable sessions. Easier to budget. Less exciting. Better for extended play.
High variance: Wild swings. Harder to plan. More exciting. Risk of fast bust-out or big win.
Variance and Bankroll
The Relationship
Higher variance requires larger bankroll to survive:
Low variance (blackjack):
- 20-30 betting units for a session
- Rarely lose entire session bankroll
- Results feel more "fair"
High variance (slots):
- 100+ spins worth of bankroll advisable
- Easy to lose entire session bankroll
- Big wins or busts common
Risk of Ruin
Risk of ruin is the probability of losing your entire bankroll before reaching your goal.
Same expected loss, different variance:
- Low variance: 5% risk of ruin with 100 units
- High variance: 30% risk of ruin with 100 units
Variance kills bankrolls faster than house edge in short term.
Variance Over Time
The Long Run
Over thousands of bets, variance matters less and expected value dominates.
Short term: Variance dominates. Winners and losers emerge randomly.
Long term: House edge takes over. Most players lose their expected percentage.
How Long Is Long?
Depends on game variance:
| Game | Hands to "Long Run" |
|---|---|
| Blackjack | 10,000+ |
| Video Poker | 100,000+ |
| Slots | 1,000,000+ |
Most recreational players never play enough for true long-run to emerge.
The Gambler's Paradox
Understanding variance creates a paradox:
- Short-term wins are possible (variance)
- Long-term loss is likely (house edge)
- Most gambling is short-term
- So winning feels achievable
This mathematical truth is why casinos remain profitable while players have frequent winning sessions.
Managing Variance
Accept Reality
Variance is not luck—it's math. Good decisions can lead to losses. Bad decisions can lead to wins. Neither changes what was "correct."
Size Your Bankroll
Match bankroll to game variance:
- High variance = larger bankroll buffer
- Low variance = smaller bankroll sufficient
- Never bet more than you can afford to lose
Set Session Limits
Variance swings both ways. Set:
- Loss limits (walk away down $X)
- Win goals (protect profits at +$X)
- Time limits (play only X hours)
Choose Appropriate Games
If you hate losing your session bankroll:
- Play lower variance games
- Accept smaller potential wins
- Enjoy longer playing time
If you want excitement and big swings:
- Accept high variance
- Budget for more losing sessions
- Enjoy the thrill of potential big wins
Don't Chase
Variance-driven losses are not "mistakes" to be recovered. Chasing losses assumes you're owed positive variance—you're not.
Variance and Psychology
Why Losses Feel Worse
Psychological research shows we feel losses more intensely than gains (loss aversion). A $100 loss hurts more than a $100 win pleases.
High variance amplifies this:
- Bigger swings = more emotional impact
- Losing streaks feel personal
- Winning streaks feel earned
Gambler's Fallacy Revisited
Variance doesn't "balance out" in ways we expect:
Wrong: "I've lost 10 hands, so I'm due to win."
Right: Each bet is independent. Previous variance doesn't predict future variance.
Overconfidence from Winning
Winning despite negative EV creates dangerous overconfidence:
- "My strategy works!"
- "I'm good at this!"
- "I can beat the casino!"
Variance-driven wins don't indicate skill.
Practical Takeaways
For Session Planning
- Calculate how many bets your bankroll covers
- Choose games matching your variance tolerance
- Set firm stop-losses before playing
- Don't increase bets to recover losses
For Emotional Management
- Accept that losses happen with correct play
- Don't attribute wins to skill (in negative EV games)
- Focus on decisions, not outcomes
- Take breaks during losing streaks
For Long-Term Perspective
- The house edge wins eventually
- Short sessions are mostly variance
- Consistent losses indicate expected value, not bad luck
- Entertainment value is the realistic "return"
The Bottom Line
Variance is why gambling feels unpredictable in the short term but predictable in the long term.
Short-term: Anything can happen. Winners and losers emerge randomly.
Long-term: House edge grinds everyone down. The casino always wins eventually.
Understanding variance helps you:
- Size bankrolls appropriately
- Choose games matching your preferences
- Make emotional peace with results
- Recognize that outcomes don't always reflect decision quality
You can't control variance. You can control how you respond to it.