Varianza del poker Calcolatrice

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What Is Poker Variance?

In poker, "variance" is shorthand for how much your results swing around your true win rate because of which cards come out. Statistically, the useful number is the standard deviation of your results, measured per session or per 100 hands. Once you know your average and your standard deviation, you can estimate how far your results could reasonably drift over the next 10, 100 or 1,000 sessions, and how many hands it takes before your win rate means much. This page shows how to get those numbers from your own results using the calculator above.

Worked Example: Eight Sessions in Buy-ins

A player records their net result for eight cash-game sessions, in buy-ins (+2.5 means they won two and a half buy-ins). These eight sessions are a sample of all the sessions they will ever play, so use the sample formula.

Data (buy-ins):2.5, −1, 4, −3.5, 1.5, 6, −2, 0.5

  1. Mean. x̄ = 8 / 8 = 1
  2. Deviations and squares. Subtract the mean from each value and square the result:
xᵢxᵢ − x̄(xᵢ − x̄)²
2.51.52.25
−1−24
439
−3.5−4.520.25
1.50.50.25
6525
−2−39
0.5−0.50.25
Sum070
  1. Sum of squares. Σ(xᵢ − x̄)² = 70
  2. Sample variance. s² = 70 / (8 − 1) = 10; sample standard deviation s = √10 = 3.1623

Sample variance s² = 70 / 7 = 10, so the standard deviation is s ≈ 3.162 buy-ins per session against an average of +1 buy-in. A single session tells you very little: the swing is about three times the average result.

Formula

Two formulas do most of the work. The first is ordinary sample standard deviation; the second scales it to a longer stretch of play.

Standard Deviation per Session

s = √[ Σ(xᵢ − x̄)² / (n − 1) ]
  • xᵢResult of session i (in buy-ins, or bb per 100 hands)
  • x̄Your average result per session
  • nNumber of sessions recorded

Spread After k More Sessions

SD of total = s × √k
  • kNumber of future sessions
  • x̄ × kExpected total after k sessions

How to Work Out Your Poker Variance

  1. Record results in a consistent unit.Use buy-ins per session, or big blinds per 100 hands. Do not mix stakes without converting.
  2. Enter them in the calculator (Sample mode).Your recorded sessions are a sample of all the sessions you will play.
  3. Note the mean and standard deviation.The mean is your observed win rate; the standard deviation is your swing per session.
  4. Scale to the horizon you care about.Over k sessions, expect a total of mean × k with a standard deviation of SD × √k.
  5. Read off a range.Roughly 95% of outcomes fall within two of those standard deviations of the expected total.

Using the Numbers

1Expected Range Over the Next 25 Sessions

Data:Mean = +1 buy-in per session, s ≈ 3.162 (from the worked example), k = 25
Solution:Expected total = 1 × 25 = 25 buy-ins. SD of the total = 3.162 × √25 ≈ 15.81 buy-ins.
Answer:About 95% of 25-session stretches end between −6.6 and +56.6 buy-ins (25 ± 2 × 15.81)

2Chance of Being Down After 25 Sessions

Data:Expected +25 buy-ins, SD of total ≈ 15.81 buy-ins
Solution:z = (0 − 25) / 15.81 ≈ −1.58. From the normal distribution, P(Z < −1.58) ≈ 0.057.
Answer:Roughly a 6% chance of being behind after 25 sessions, if +1 buy-in per session is the true win rate

How to Use This Calculator for Poker Results

The calculator works on any list of results:

  1. Export or copy your session results (or results per 100 hands) from your tracker or notes.
  2. Paste them in, one result per line or separated by commas. Use minus signs for losing sessions.
  3. Set the mode to Sample and read the mean (your observed win rate) and standard deviation.
  4. Use the √k rule above to turn the per-session standard deviation into a range for a longer stretch.

What This Tells You

  • Whether a losing stretch is within the normal range for your game or a sign of a real problem.
  • How many sessions you need before your observed win rate is a reliable guide.
  • A realistic basis for bankroll decisions, instead of a gut feeling.

Common Questions Poker Players Answer With This

Downswings

Is losing 15 buy-ins over 25 sessions unusual for my win rate and standard deviation?

Sample size

How many hands until my win rate is trustworthy to within a few bb/100?

Game selection

Comparing the swings of two formats or stakes using your own results.

Bankroll planning

How big a bankroll keeps the chance of going broke acceptably low.

Things to Keep in Mind

These numbers are estimates built on your own history, with the usual caveats:

Your mean is itself uncertain

After 8 sessions, the margin of error on your average is about 2 × 3.162 / √8 ≈ 2.2 buy-ins, more than twice the +1 buy-in average itself. Treat early win rates with suspicion.

Sessions are not all the same length

Results per 100 hands are more comparable than results per session, because session length varies.

The normal approximation is rough

Tournament results in particular are very skewed (many small losses, rare big wins), so ranges based on the normal distribution are less reliable there.

Your game changes

Moving up in stakes or changing style changes both your win rate and your standard deviation. Recalculate from recent results.

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Domande Frecuente: Varianza del poker Calcolatrice

Tutto quello che c'è da sapere sulla varianza.

Cos'è la varianza nel poker?

La varianza nel poker misura la fluttuazione statistica dei risultati. Anche con un tasso di vincita positivo, i risultati a breve termine possono oscillare notevolmente a causa della casualità intrinseca della distribuzione delle carte. Una varianza elevata significa che i risultati si discosteranno in modo significativo dal valore atteso (EV) in brevi periodi. Comprendere la varianza del poker ti aiuta a distinguere tra sfortuna (varianza) e cattivo gioco (EV negativo).

In che modo la varianza influisce sulla mia percentuale di vincita nel poker?

La varianza non modifica la tua percentuale di vincita reale: influisce sui risultati osservati su qualsiasi campione finito. Un giocatore che vince 5 mani bb/100 potrebbe perdere 10 bb/100 o vincere 20 bb/100 a causa della varianza. Maggiore è la varianza del formato di gioco (ad esempio, tornei vs cash games), maggiore sarà il numero di mani necessarie prima che i risultati osservati convergano al tasso di vincita reale.

How many hands do I need before my win rate is reliable?

The 95% margin of error on your win rate is about 1.96 × SD / √(hands / 100), in bb/100. With an SD of 75 bb/100, the margin is ±14.7 bb/100 after 10,000 hands and still ±4.6 bb/100 after 100,000 hands. To be 95% confident that a 5 bb/100 win rate is above zero you need roughly 86,000 hands (1.96 × 75 / 5 = 29.4, and 29.4² × 100 = 86,436).

Quali formati di poker hanno la varianza più alta?

I tornei (MTT) presentano la varianza più elevata perché la maggior parte del montepremi è concentrata nella parte superiore. I Sit & Go hanno una varianza moderata. I cash game (soprattutto full-ring) presentano la varianza più bassa. Nei cash game, stack più profondi e stili di gioco più aggressivi aumentano la varianza. Il PLO (Pot-Limit Omaha) ha una varianza maggiore rispetto all'Hold'em a causa di un esaurimento delle azioni più ravvicinato.

How do I calculate my poker standard deviation?

1. Record your result for each block of 100 hands (or each session). 2. Find the average. 3. Square each block's difference from the average. 4. Add them, divide by the number of blocks minus 1, and take the square root. Figures of roughly 60–100 bb/100 are often quoted for No-Limit Hold'em cash games, but your own number depends on your game and style, so calculate it from your own results.

How likely is a losing stretch for a winning player?

Treat the total over many hands as roughly normally distributed. For a 3 bb/100 win rate and an SD of 80 bb/100, 10,000 hands is 100 blocks of 100: expected result = 3 × 100 = +300 bb, standard deviation = 80 × √100 = 800 bb. The chance of being behind after those 10,000 hands is P(Z < −300 / 800) = P(Z < −0.375) ≈ 35%. Bankroll management exists to survive stretches like this.