Session Variance Calculator

Average expected loss tells you what you'll pay in the long run. Variance tells you what a single session might actually feel like. This calculator computes the percentile band — your typical good session, your typical bad session, and your worst-case session — so you can size your bankroll to survive variance, not just average.

Game

Bet size ($)

Hours

Session percentile band

Each row is one possible session outcome. Negative = you win that much; positive = you lose that much. Median (50th) is your long-run average; 95th is a typical bad night.

5th percentile (good session)+$799
Median (50th)−$40
95th percentile (bad session)−$879
99th percentile (disaster)−$1226

Expected loss $40 · session std dev ±$510 · 320 hands · $8,000 total wagered.

Why average loss is misleading

A 4-hour BJ session at $25 a hand has $40 expected loss. The standard deviation? About $400. So 'expected loss' is buried in the noise — most sessions you'll be up $200 or down $400, both of which feel huge versus the expectation.

The percentiles

Approximate normal-distribution percentiles around expected loss EL with std dev σ:

5th percentile (good session): EL − 1.645σ — better than 95% of sessions
50th percentile (median): EL — half above, half below
95th percentile (bad session): EL + 1.645σ — only 5% of sessions are worse
99th percentile (disaster): EL + 2.326σ — once in 100 sessions or so

Game-specific variance

Blackjack basic strategy: σ ≈ 1.14 per unit bet — moderate variance
Counting at typical spreads: σ ≈ 1.4-1.6 — higher because of bet ramp
Baccarat banker: σ ≈ 0.93 — almost flat
Craps pass+max odds: σ ≈ 3.16 — very swingy because of odds bets
Video poker (JoB 9/6): σ ≈ 4.42 — VP variance is the silent killer
Roulette: σ = 1.0 — wild day-to-day, predictable in aggregate

Bankroll implications

Your bankroll needs to cover the 95th-percentile loss with room to spare. A $5,000 bankroll at $25 BJ play covers ~12 standard deviations — you're never busting from one session, but a 3-bad-session weekend is recoverable. Sized too tight to the average, you bust on the first bad session.

FAQ

Why is variance higher in counting than basic strategy?

Counters bet larger when the count is favorable. Bigger bets mean bigger swings — both directions. The reward (positive edge) requires accepting higher variance.

Why is video poker variance so brutal?

Royal flushes are 1-in-40,000 hands and pay 4000:1. Almost all the long-run EV lives in royals you've barely hit. Day-to-day, you lose. Over millions of hands, you average out.

How do I plan around variance?

Bankroll for the 95th-99th percentile, not the average. Set stop-loss at a level that lets you walk before normal variance turns into a session you can't recover from.

Is craps with full odds high or low variance?

Pass + max odds has σ ≈ 3.16 — very high — because the odds bet is uncapped and pays true odds. Rate the variance, not the house edge alone.

How many sessions should I plan for?

Bankroll for at least 20-30 typical sessions if you're a recreational player. Pros plan for 1000+ rounds before variance starts to look like average.

Last updated 2026-05-06. Spot an error?

Session Variance Calculator

Why average loss is misleading

The percentiles

Game-specific variance

Bankroll implications

FAQ

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