The Poker Tournament Variance Simulator calculates variance for poker tournaments, MTTs and SNGs. Enter your tournament(s), hit *calculate* and let the simulator do its magic. An explanation how this simulator works can be found below.

**Beta Test**: Please note that the new Tournament Variance Calculator is in beta. In case of errors, malfunctions or if you have feature requests, send me a note at *info@primedope.com*.

If nothing works, you can still access the old Tournament Variance Calculator:

## How does the Poker Tournament Variance Calculator work?

Let’s go through an example simulation.

First, you need to enter the poker tournament (or SNG / Sit-and-Go) schedule. Let’s say you’re playing a $215 tournament regularly and want to check what variance you can expect. That’s what the settings can look like:

### Settings

**Players**: Number of players for the tournament. We assumed 100 players (entries) for this tournament.**Structure**: How many places get paid. Standard payout tables are used.**Buy-in and Rake**: In any currency, you fancy (we just use the $ symbol) – buyin must be greater than zero. Buy-In for the example event is $215 and the rake is 7%.**ROI**: In percent, any value is ok. Let’s just assume, we have an ROI of 25% in this tournament.**How many are you going to play?**: How many tournaments should be simulated. For this example, we want to know what results we can expect over the course of 200 events.**Sample size**: How many samples should be simulated – higher numbers yield more accurate results, but also take longer to compute.**Bankroll**: Can be left blank and is only used when calculating the risk of ruin.

Click on *Calculate* and the Poker Variance Calculator does its magic. It simulates whatever tournament schedule you have entered over as many samples as you have entered. In our example, it would simulate 200 tournaments 10,000 times.

### Distribution and Random Samples

The distribution shows the likelihood function for the results. The random samples show 20 random runs plus the best and worst run out of all 10,000 samples. The green areas are the confidence intervals where the results will land with a probability of 70%, 95% and 99.7%.

May I have another question, this time about Confidence Intervals? I’m trying to do it the way as mathematicians say for standard distribution but cannot get results from your output. The green chart looks like normal distribution chart transformed by an angle and I cannot undestand why mean is not in the middle between min and max value for confidence interval

Tool looks really nice. I’m trying to figure out what’s the formula to calculate mathematically SD for one tournament? Each possible solution gives me different values than your app. Can you explain me the mechanism of SD for simple tournament (10$ buy-in, 0% rake, 0% roi, 3 players get payout (50%, 30%, 20%), 100 plays)?

To calculate the standard deviation for this example you first calculate the standard deviation for a single tournament.

In your example the net pay-outs for the tournament are as follows:

First, you need to calculate the expected value μ via this formula:

Next, you calculate the variance σ² via this formula:

The standard deviation σ is the square root of the variance:

This is the standard deviation for one tournament.

To calculate the standard deviation for n multiple identical tournaments X you use this formula:

In your example, this would be

You can find the formulas for example on the Standard Deviation Wikipedia Page

I hope this helps (:

Thank you, it helps. I was unable to go from one tournament to list of tournaments. It looks undestandable now.

One more thing, how is it merged if I insert 2 or 3 different tournaments? Should I calculate μ together and use it for each place in each tournament?

Yes, in this case, it’s all merged together into one random variable.

Why during calculation σ² you use 1% for notWinningProbability? Shouldn’t it be 97%? and σ² = 3800?

Thanks for the great tool.

One question: how do you compute the distribution that leads to the monte Carlo simulation? You must be making some assumption at some point no? For example, a player with 0% Roi might be one who reaches itm 100% of the time and busts straight away, or one who wins 100 BI with probability 1/100. These two players will have vastly different variance.

More generally, different strategies (in particular with respect to icm in FTs) will lead to very different variance patterns. Is there a way to incorporate that in your simulations?

Thanks again

Heya, thanks for the question. For the simulation, I assume that the player reaches each position in the money with equal probability. A player with a higher ROI simply finishes outside the money less often.

I agree that different strategies lead to increased or decreased variance. I’ll look into adding options for playing style for future versions of this tool. It will take me a while, though.

How can the size of rake correlate negatively with risk of ruin, etc.?

In fact, if you put in 100% rake, you are better off than 0%. And I’ve tried multiple rakes and I keep seeing that higher rake improves results – you need lower bankroll to avoid ruin at any % level.

Something is wrong.

There is a simple reason for this. If you increase the rake and don’t also adjust the return on investment, the calculator simply assumes you’re a better player to be able to beat the higher raked tournaments at the same rate.

E.g., you have many more ITM finishes if you manage to beat $50 tournaments that take 20% rake than you have if you beat $50 tournaments that take no rake. And more ITM finishes mean less variance and a lower risk of ruin. But usually, your ROI should decrease with tournaments that charge more rake and thus your variance (and risk of ruin) will also increase.

Hope that helps 🙂

could we simulate MTT with overlay ?

why when i type 1,65 or 1.65 (with the point) it din´t read the info?. i mean whwn i write 2 or 3 etc, numbers without decimal number it calculates with no problem. but when i type numbers like 1.65 1.10 it dosen´t. thanks ¡¡

Need to fix… When you enter a new tournament your bankroll/sims run reset and need reedited [still useful anyways though]

Would really prefer to enter rake as a $ amount and/or have the option of choosing the $ amount or percent.

OMG I really hate this new version give us old one

The new version is awful! Much more difficult to use. We have to calculate the percentage of fee, some SNG formats are impossible to calculate (45 man MTTs, with 7 payouts. Why did you remove 7, but allow 6 and 8???) The graphs look worse and we can no longer see info on each point of the line. The old version was pretty much perfect. Very disappointing and non-sensical change.

I do sincerely thank you for making a tool that has helped me a lot over the past few years tho!

Why did you fuck things up so bad? Like, what was wrong with the old one? This one is awful. What a fucking train wreck.

Hello, Is there any way to edit the payout structure? I am interested in satellite tourney variance. So 10 players recieving 10% of prize pool for instance. Is this possible? Thank you for the website/tool 🙂

Thanks for working on this. Other comments are pointlessly dickish, your stuff is great

Tbf, I prefer the stats and distribution of the old version.

This new verson is shit

I’m having trouble figuring out bankroll management and variance calculating for Rebuys + Add-ons tournaments. Any suggestions?

Hello, i am looking for the data table of the histogram of the distribution or all tournaient please.

For sng 45 man, the itm is 7 players, but on selection “places paid”, have 8 or 6 players for itm. It is a report to add 7 players paid.

But if i wanna simulate 45 man, it is better put 6 or 8 in places paid?

This new verson is shit. Use the old

link old calculator plz

hello,

I am wondering what does “confidence interval ” mean and how is it calculated?

“Confidence Interval” is a statistical term. A 70% confidence interval for example means that 7 out of 10 samples are within this interval.

The confidence intervals in the chart are calculated for a random variable that is normally distributed with the mean and standard deviation of the accumulated tournament results. (It’s important to note that accumulated tournament results are only approximately normally distributed when the number of tournaments is really large. For smaller numbers the tournament results can be quite “spiky”.

The simulated confidence intervals (in the table below the chart) are more interesting because those numbers are taken directly from the simulation and are not approximated. Let’s say you simulate 1,000 tournaments and the 70% interval is $500 – $2,000. This means that your winnings will be between $500 and $2,000 70% of the time. To be more precise: 15% of the time your winnings will be below $500, 15% of the time your winnings will be above $2,000. The same goes for the 95% and 99.7% intervals.

I like being able to see the distribution so am still using the legacy version

Fair point, will look into that.

Also side note, your website is amazing thank you for providing these free tools

this new verson is shit.. I too use the legacy.

Where is the probability of loss? It used to show that info. If I play 400 tournaments with 700 players and a 20% ROI, paying top 20% of the field, how many times will I be losing at the end of the 400 mtts?

Oh, you’re right, I didn’t include that stat. Will do so in a bit.

Thank you!

Were you able to do it? Still cant find it

It should be there now. 🙂

Many thanks!

It would be interesting to know what’s the probability of a certain observed ROI%. For instance, with a 20% theoretical ROI, what’s the probability of having just 10% ROI after 1000 tournaments of a particular structure?

Thank you

Best regards,

Diogo Morais

Thank you for this tool! So great!

Thanks a lot for the new tool, its awesome!

Do you have any suggestion on how can I calculate my risk of ruin if I’m willing to move down stakes depending on how many buy-ins I’m down?

I’m trying to figure out the threshold (optimal number of buyins I’m UP or DOWN to move up or down in stakes). Thx.

Hi Daniel, thanks for your kind words.

Unfortunately this question is impossible to answer with my current tournament variance tool.

Purely theoretically speaking, it’s impossible to go bankrupt if you always move down in stakes after falling below a certain threshold (e.g. when you move down whenever you have less than, say, 50 buy-ins). But this information isn’t really helpful.

It sounds like, you’re looking for some sort of Kelly Criterion for tournaments. That’s an intriguing question. Maybe I’ll have time to look into that at some point in the future.

Thanks a lot. Yes I’ve heard about the Kelly Criterion but never realized how to apply for Poker Bankroll.

The risk of ruin/bankroll part doesn’t seem to be correct? Why would it suggest lower bankroll requirement the higher your risk of ruin is? Shouldn’t that be the opposite? Higher risk of ruin, thus bigger bankroll requirement?

No, it makes perfect sense that way. The risk of ruin is the probability of losing your entire bankroll. Thus, the bigger your bankroll is, the lower your risk of ruin is. Conversely, if you can live with a higher risk of ruin you have a lower bankroll requirement.

Is it possible to have adaptive Bankroll in the risk of ruin calculation? E.g. you want to run a simulation for different game types roughly 6k game sample and set a bankroll to like $4,000. But since the sample is 6k games, obviously with a positive ROI the bankroll should grow along the way with sample. Nobody really puts 100% of their profit into growing their bankroll, but have maybe an option to add X% of profit into bankroll after certain interval/games etc. And then have risk of ruin calculated taking that into account? Because nobody really uses a static bankroll all the time right?

Sim fails if >~350 ROI is entered

damn you must be pro

Yes, it does fail. It works only with ROIs that are theoretically attainable for the given payout structure.

While i think the new update is good, with more useful info, i believe you should somehow get back the interactive graphs, where you can see stuff while your mouse is on the graphs. Thanks for this amazing tool btw.

Thank you. I’ll look into interactive graphs.

Are you serious???? You’ve made this tool suck balls.

You’ll need to be more specific. Also, the old tool is still available: https://www.primedope.com/tournament-variance-calculator-legacy-version/

Hi, can I use this calculator to calculate variance based on ABI mean and AFS mean?

Help me out, what are

ABIandAFS?ABI- Average Buy-In

AFS – average number of players in a tournament

Yes, this should work without any problem. But you can also combine multiple types of tournaments in one simulation – e.g. $5 tournaments with 2,000 players and $100 tournaments with 100 players.

Hi!

First, let me congratulate you by this awesome tool, it really has changed all my tournament grid. Right now I’m rethinking about some strategies and a doubt pops up, my plan is to find some metric to guide me to figure out how much risk I can take on scaling stakes. I thought “standard deviation” would be a good metric to achieve this goal, but I hadn’t understood how the logic of it works. I ran this sim:

But with different ROIs: 10% and 40%. The result was:

My question is, shouldn’t standard deviation be lower on ROI 40% scenario? Because as this player is way more skilled, I expect it to have a way lower variance but got surprised to see that it was even higher. Can you explain it to me? Oh, and the standard deviation is the same as “variance” in poker vocabulary?

Hi Leonardo, thanks for your kind words! 🙂

Regarding, your question, I assume you mean 1,400 players and not 400.

And no, it makes perfect sense for the variance to be higher with a higher ROI. Higher ROI means hitting top payouts more frequently and this adds to the variance.

It’s maybe easier to understand when you look at the

(i.e. the range 95% of the samples end up in). For the example you gave above, this interval is:95% confidence interval10% ROI: -$1,437 .. $3,012 (a difference of $4,449)40% ROI: -$923 .. $4,116 (a difference of $5,039)The interval for 40% ROI is wider than the interval for 10% ROI (5,039 vs. 4,449). But that’s mainly because more samples have very high outcomes.

Another way to look at it would be to consider a player who has an ROI of -100% (i.e. someone who never finishes in the money). This player will have a variance of 0. But his EV (in the example above) will simply be -$2,750.

And regarding your other question – actually the standard deviation is the square root of the variance mathematically speaking. But poker players virtually always mean standard deviation, probability of loss or confidence intervals when speaking about the concept of variance and poker.

interesting! very nice reply.

What leaves me thinking we should have a sortino ratio for poker, where just downside variance would count to really differentiate SDs by ROI.

Yh compare tourneys not working, plz fix 🙂

Fixed it. Unfortunately the entire code base for this tool looks a bit like spaghetti code. So, more fixes might take some time.

The “compare tournaments” button doesn’t work anymore?

any chance of adding, for tournaments, the biggest loss in buyins, AT ANY POINT, for each sim in the report. would be very useful for judging how big a bankroll would be needed

Sounds like a good idea. Will be added in soonish(tm).

awesome. thank you

hey can you please share the formula that was used to create the graphs?

It’s not a formula. The calculator is running a Monte Carlo Simulation to create the graphs and stats.

Hi,

First, thx for this, it’s really great !

Would it be possible to had a bankroll advice for less than 5% ruin, like in cash game mode ? Or maybe the “95% confidence interval (simulated)” gives this info, i’m not sure…

Wish you my best 🙂

Hi Kharn, thanks for your idea. Can do.

I’ll try to add this within the next days!

it would be awesome if you could add that! thx

I’m currently working on a complete redo of this tool. It will take a bit longer, but should be finished within the next weeks.

wow, thanks a lot for that!!!

Any update on the progress? thx!

Hi Daniel, holidays and work kept me a bit more busy than expected. ETA for this is now not before September.

is the new version already avaiable?

Perfect!

comment faire pour avoir l’application en français ?,merci

ai putea sa folosesti translate sau sa inveti putina engleze rahatel mic

I built a web based hand range calculator: handcombos.com

this tool is crap

you just suck and dont know what its for

qu est ce que tu racontes, sur quoi tu te base pour dire que c est de la merde ? Je trouve au contraire que c est tres fiable.

thanks for the reply that i did not get

i do not understand with the number and the sample size? how many tournaments should be simulated and how many samples should be simulated? i do not understand what the difference is

Its fuckin obvious mate.

Assuming you play 20 tourneys a day 5 days a week = 4800 a year

How many you are going to play = 4800

Sample size is samples of those 4800.

So if you make 10 samples, that is 10 “snapshots” of the 4800 mtt’s a year

Ideally you want to run as many samples as possible for the most accurate results

Guys,

Can you help me with the answers to the following questions; since I don’t seem to get is;

-How do I determine my ROI for $2.50 sit and go’s where $0.5 is fee; with 9 handed tables within a field of 180 players; where the pay-outs are spread over 29 players

-What is the difference between the number and the number. I assume that the number is how much I plan to play of this format; and that the samplesize is the times I run a simulation based on this n-amounts of times I want to play? So if I plan to 50 sit and go’s; with a sample size of 1000; then the tool calculates its varians distribution based on a simulation where I play 50 games for 1000 times ? ? ?

– What are skurt and kurtosis

THANKS

– Its hard to determine your ROI as it is dynamic. If you have a tracker and tracked how many 180 sng of 2.5 you played, you can get a raw estimate of your ROI.

– The number is indeed the number of SNG’s from this tournament you want to play. Samplesize is how many times you want to let the computer play that amount of SNG’s, if you only let it play once then you don’t know wether the computer his result comes through hot run, or bad run or just standard run. Thats why u want the computer to go through the process of playing that conserning number of tournaments a lot of times (take sample size as high as possible for stable results). Because then, you include the times in which we ran bad, ran good, ran standard, and this we average to become an avarage profit 🙂

– In simple words skew and kurtosis are statistical properties that discribe how a distribution differs from a standard normal one. I think in this application, you need to look at it as an indicator for reliable results in all other estimates. If both are 0 (which is the case for standard normal distribution) you can rely better on the results then if they where different from 0. You want to assume a stardard normal distribution (aka skew and kurtosis = both 0), because you want to have your errors/variance balanced (= as much as good runs as bad runs). Obviously, this will be the case when the number of tournaments and/or the sample size gets higher and higher.

I’ll consider this for next time. Thanks.

It will be cool to know, what is the probabillity of worst run?

Hi,

would it be possible to include spin and go ? With the probabilities of jackpot i would be interested to see simulations.

Thx

Which satellite do I have to select, to run a Hyper 6max with two tickets? I don’t really understand the satellite distribution.

Thank you

Hello,

First of all very interesting and useful tool…

I have 1 question though.When it comes to calculating variance and SD in a non-winner take take all tournaments(like 6man or 9man SNGs),what formula or algorithm do you use to actually calculate SD for those?I mean when it comes to those formats with a set payoff structure(65-35,and 50-30-20)I would assume that in order to calculate variance and SD for these formats you have to know what % of the time should a player finish in each place when he is ITM and also how often does he not finish ITM.But since the only ”money regarded parameters ‘ here are a player’s ROI,a preset optional pay off structure and buy in size,how do you actually determine what % of the time a player finishes in each of the above stated positions based only on these three parameters,since ROI and ITM finish % s are not proportionate mathematical sizes(i.e.if someone has higher ITM % finishes than other does not mean that he is more profitable player, and also if two players have the same ITM % does not mean hat they have the same ROI) and can you give me a brief example?

Very useful, thank you. Consider adding a dead/added money option to calculate outcomes of loyalty freerolls, guarantees with overlays etc.

Please add a possibility to add Twister SNGs and Spin & Go, where only 3 players, and 1 buyin out of 3 payed goes off to the Jackpot.

Hello, can you add TURBO double or nothing?:)

could you please post the calculation for 18% MTT ( non satellite pay out structure)? this only goes up to 10-11% which isnt really reflecting what the variance would be on a say a schedule of sunday majors on Stars

I use your calculator mostly for sit n gos with 6 entrants where first pays 65% of the prizepool and 2nd pays 35%. I don’t think the pay outs for two players paid out of 6 total entrants are the correct 65/35 that I need. Could you verify that?