Cash Game Variance Calculator: How It Works

A cash game variance calculator estimates the range of possible results (wins or losses) you can expect over a given number of hands or hours, based on your win rate and standard deviation. You enter your average win rate (e.g., big blinds per 100 hands), your standard deviation, and the number of hands or hours you plan to play; the calculator returns a confidence interval, such as “95% of sessions will fall between -50 and +120 big blinds.� This tool is essential for bankroll management, setting expectations, and avoiding tilt when short-term results deviate from your true skill edge.

Formula

The calculator uses the standard normal confidence interval formula:

Expected result (EV) = (win rate per 100 hands) × (number of hands / 100)

Standard deviation of total = (standard deviation per 100 hands) × sqrt(number of hands / 100)

95% confidence interval = EV ± 1.96 × (standard deviation of total)

Variables:

• Win rate (wr) – your average profit per 100 hands, measured in big blinds (bb). This is positive if you are a winning player, negative if losing.
• Standard deviation (sd) – how much your per-100-hands result typically varies from your average. Typical live cash game players have SD around 50–100 bb/100; online players often 70–120 bb/100.
• Number of hands (n) – the total hands you plan to play or have played.
• 1.96 – the z-score for a 95% confidence interval (two-tailed).

The result is expressed in big blinds. To convert to dollars, multiply by your big blind amount (e.g., $2 for a $1/$2 game).

Worked Example

Using the default values: win rate = 5 bb/100, standard deviation = 100 bb/100, hands = 1,000.

1. Expected value: 5 × (1000/100) = 5 × 10 = 50 bb.
2. Standard deviation of total: 100 × sqrt(1000/100) = 100 × sqrt(10) ≈ 100 × 3.1623 = 316.23 bb.
3. Margin of error: 1.96 × 316.23 ≈ 619.81 bb.
4. Lower bound: 50 – 619.81 = -569.81 bb (rounded to -570).
5. Upper bound: 50 + 619.81 = 669.81 bb (rounded to 670).

The calculator shows: EV = 50 bb, lower bound = -570 bb, upper bound = 670 bb. This means that after 1,000 hands, there is a 95% chance your actual result will fall between losing 570 big blinds and winning 670 big blinds. Notice the range is wide – that’s the nature of poker variance.

Why Use a Cash Game Variance Calculator?

Cash game results are noisy. Even a skilled player can have losing weeks or months. A variance calculator helps you:

• Set realistic expectations – know that a 5 bb/100 winner will still have losing sessions 20-30% of the time.
• Manage bankroll – if the 95% interval includes a loss of 100 buy-ins over 10,000 hands, you need a bankroll that can survive that.
• Evaluate performance – compare your actual results to the predicted range. If you fall outside the 95% interval, it may indicate your win rate estimate is off, or you are running unusually hot/cold.
• Avoid tilt – knowing that a -300 bb session is within normal variance can keep you from overreacting.

For example, a player with a 10 bb/100 win rate and 80 bb/100 SD over 5,000 hands has a 95% interval of 500 ± 1.96 × 80 × sqrt(50) = 500 ± 1,108 bb, i.e., -608 to +1,608 bb. That’s a huge spread, but it’s the reality.

How to Choose Your Inputs

Accurate inputs are critical. Here’s what to use:

• Win rate – use your long-term average over at least 50,000 hands if possible. If you don’t have that, use a conservative estimate (e.g., 5 bb/100 for a decent live player). Do not use your last week’s results.
• Standard deviation – most poker tracking software (e.g., PokerTracker, Hold’em Manager) reports this. If you don’t know it, use 100 bb/100 as a default for no-limit hold’em cash games. For limit games, it’s lower, around 15-30 bb/100.
• Number of hands – for live play, estimate hands per hour (about 25-30 for a full ring table) and multiply by hours. For online, you can play 60-100 hands per hour per table.

If you play multiple tables, your combined standard deviation is roughly the square root of the sum of squares of each table’s SD, but for simplicity, many players just use their per-table SD and multiply the number of hands accordingly.

Common Mistakes and Misconceptions

Mistake 1: Using win rate per hour instead of per 100 hands. The formula is built on per-100-hands units. If you enter hourly win rate, you must adjust the SD and hands accordingly. Most tracking software uses per-100, so stick with that.

Mistake 2: Interpreting the 95% interval as a guarantee. There is a 5% chance your result falls outside the interval. That’s not negligible – over many sessions, you will see “outlier� results.

Mistake 3: Ignoring the effect of sample size. The interval widens with the square root of the number of hands, not linearly. Doubling your hands only widens the interval by about 41%, not 100%. So short-term results are extremely noisy.

Misconception: “I’m a winning player, so I should never have losing months.� Even a 10 bb/100 winner with 100 bb/100 SD has about a 20% chance of losing over 1,000 hands. Over 10,000 hands, that drops to about 5%, but it’s still possible.

Limits of the Formula

This calculator assumes your win rate and standard deviation are constant and that your results are normally distributed. In reality:

• Your true win rate changes as you improve, as opponents change, and as game conditions vary.
• Poker results have “fat tailsâ€� – extreme results happen more often than a normal distribution predicts, especially in games with big pots and all-ins.
• The formula ignores the effect of rake, which reduces your win rate but does not change variance much.

Also, the calculator gives you a range for total profit/loss, not for the maximum drawdown (the worst point during the session). If you are concerned about bankroll survival, you need a risk-of-ruin calculator, which uses different math.

Comparing to Tournament Variance

Cash game variance is different from tournament variance. In tournaments, you can bust out and lose your buy-in, but you can also win large prizes. The standard deviation for tournaments is much higher relative to win rate, often 1.5-2.5 times your buy-in per tournament. Cash game SD per 100 hands is typically 50-120 bb, which is about 0.5-1.2 buy-ins (if a buy-in is 100 bb). So tournaments require a larger bankroll relative to your average win. A cash game variance calculator is not suitable for tournaments; you need a tournament-specific tool that uses the prize structure and your ITM (in-the-money) rate.

Frequently Asked Questions

What is a good win rate in cash games?

For no-limit hold’em cash games, a win rate of 5-10 bb/100 is considered solid for a professional or strong amateur. Anything above 10 bb/100 is exceptional and rarely sustainable over large samples. Live players often measure in bb/hour; 10 bb/hour is a common target, but that translates to roughly 40 bb/100 at 25 hands per hour.

How many hands do I need to know my true win rate?

To get a reasonably accurate estimate (within ±2 bb/100 with 95% confidence), you need about 100,000 hands if your SD is 100 bb/100. With 50,000 hands, the margin of error is about ±2.8 bb/100. Many players use 50,000 hands as a minimum, but even then, the confidence interval is wide.

What is standard deviation in poker?

Standard deviation measures how much your results vary from your average. In poker, it’s typically expressed per 100 hands (bb/100). A higher SD means more variance – bigger swings in both directions. For no-limit hold’em cash games, 80-100 bb/100 is common. For limit games, it’s much lower, around 15-30 bb/100.

Can this calculator tell me if I’m a winning player?

No. It only shows the range of possible results given your inputs. If your actual result over a sample falls outside the 95% interval, it suggests your win rate estimate might be wrong, but it doesn’t prove it. To determine if you are a winning player, you need to test whether your win rate is statistically significantly above zero, which requires a different calculation.

Should I use bb/100 or bb/hour?

Use bb/100 for consistency, especially if you play online or multi-table. If you play live, you can convert your hourly rate to per-100 by estimating hands per hour (typically 25-30 for a full ring). The calculator works with per-100, so stick with that.

What is the difference between variance and standard deviation?

Variance is the square of the standard deviation. Standard deviation is more intuitive because it’s in the same units as the data (big blinds). In poker, we usually talk about standard deviation per 100 hands. The formula uses standard deviation directly, not variance.

Related

• Beta Binomial Distribution Calculator & Guide
• Binomial Distribution Calculator: How It Works
• Batting Average Calculator: Formula & How to Use

in wr | Win rate (bb/100) | bb/100 | 5 | 0
in sd | Std dev (bb/100) | bb/100 | 100 | 0
in n | Hands played | hands | 1000 | 0
out lower | Lower bound (95%) | bb | wr * n/100 - 1.96 * sd * sqrt(n/100) | 0
out upper | Upper bound (95%) | bb | wr * n/100 + 1.96 * sd * sqrt(n/100) | 0
out ev | Expected value | bb | wr * n/100 | 0