Chapter 9: Variance and Management

This Is What Variance Really Is

25 patterns of a winning player at 3bb/100 playing 100,000 hands

What you can read from it

• The red line is the expected value (+3000BB)
• The grey lines are all trials of the same skill
• Even after 100,000 hands, 16% are negative

Drawdowns

• The median of the largest drop is about 2100BB
• About 6100BB in the worst case
• Everyone has the same skill

Simulation: a win rate of 3bb/100 and a standard deviation of 90bb/100, 100,000 hands × 25 times. Even with the same skill, results scatter this much.

Risk of Ruin

Formula: exp( −2 × win rate × bankroll ÷ standard deviation² )

Probability of going broke (%) (standard deviation 90bb/100, calculated from the approximate formula)

• Win rate 1bb/100
• Win rate 3bb/100
• Win rate 5bb/100

Bankroll (BB)	Win rate 1bb/100	Win rate 3bb/100	Win rate 5bb/100
500	88.4%	69%	53.9%
1000	78.1%	47.7%	29.1%
2000	61%	22.7%	8.5%
3000	47.7%	10.8%	2.5%
5000	29.1%	2.5%	0.2%
10000	8.5%	0.1%	0%

What this formula says

• The higher the win rate, the harder it is to go broke
• The larger the variance, the easier it is to go broke
• Bankroll works exponentially

Examples of how to read it

• Even at 3bb/100, 47.7% go broke with 1000BB
• 10.8% with 3000BB, 2.5% with 5000BB
• Even with positive EV, you go broke if your bankroll is not enough

This is an approximation by a continuous model. In reality it varies with shot taking, stop-losses and withdrawals.

Check with the calculator (Risk of ruin)

Bankroll Standards

Realistic estimates, worked backward from the calculation above

Situation	Bankroll needed	Probability of going broke (est.)
Minimum (high risk tolerance)	1500 – 2000BB	22.7 – 32.9%
Standard (if not a professional)	3000BB	10.8%
Safe (if it pays your living costs)	5000BB or more	2.5% or less
Tournaments (variance on another level)	100 buy-ins or more	－

Shot-taking

• Rules for when you try a higher stake
• Example: prepare a bankroll of 10 buy-ins for the new stake
• Go back down immediately if you lose 5 buy-ins

Stop-loss

• Decide in advance the most you will lose in one session
• Example: stop at 3 buy-ins
• The reason is not the bankroll, but to prevent your judgment from slipping

Keep your living expenses and your bankroll physically in separate accounts. The moment they mix, your decisions will always be distorted.

Managing Tilt

Variance cannot be avoided, but you can choose your reaction

Common triggers

• Bad beats (losses where you were ahead in EV)
• Anger at your own mistakes
• Trying to win back losses (chasing losses)
• Fatigue and lack of sleep

What is happening

• Your range widens and you can no longer fold
• Bluffs increase and thin value decreases
• You want to raise the stakes

Countermeasures (decided in advance)

• Set a stop-loss as a number
• Before a session, decide “today’s goal is the quality of decisions”
• If you are unsure in three hands in a row, take a 5-minute break
• Judge a session by your decisions, not by results

Handling it afterward

• Review the hands where you tilted on the next day
• Reflecting on the spot distorts things further

Treat tilt not as a personality problem but as a problem of designing rules in advance.

Game Selection

Which table you play at carries as much weight as skill

Table average VPIP	The higher the better. 35% or more is excellent
How many limps	Tables with many limps tend to be weak
How to choose a seat	Sit to the left of (behind) weak opponents
Where strong opponents sit	Ideally, strong opponents sit to your right (in front of you)
Rake	It affects your win rate directly. Check whether there is a cap
Effective stack	The deeper, the more easily skill differences show
Your own condition	On days you are tired, not playing is also a choice

Even with the same skill, your win rate changes by several bb/100 with table selection. This is part of strategy.