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.

## 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 the Sunday Million regularly and want to check what variance you can expect. That’s how the settings can look like:

### Settings

**Players**: Number of players for the tournament. We assumed 5,750 players (entries) for the Sunday Million.**Structure**: How many places get paid. Standard payout tables are used. You can also choose satellite structures.**Buyin and Fee**: In any currency you fancy – buyin must be greater than zero. Buy-In for the Sunday Million is $215, but for this calculator we split up the real buy-In ($200) and the fee ($15).**ROI**: In percent, any value greater than -100% is ok. Let’s just assume, we have an ROI of 50% in the Sunday Million.**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 one year. That’s roughly 50 weeks and 50 Sunday Millions.**Sample size**: How many samples should be simulated – higher numbers yield more accurate results, but also take longer to compute.

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 50 Sunday Millions 10,000 times.

### Distribution

This distribution shows the cumulative likelihood function for the results. In this example it shows you that about 70% of all samples had a negative result and only the top 5 percent of the samples showed significant winnings.

By clicking the the *“N”-Button* inside the diagram you can compare the distribution to how a normal distribution (with the same expected value and standard deviation as the original distribution) would look like.

Poker cash game results are, if played over a couple of thousand hands, normally distributed. Playing only a few (50 in this example) tournaments yields quite different results:

### 20 sample tournament runs

The next graph shows 20 sample runs from the simulation as well as the best and worst run over all samples. In this example, in at least one sample we managed two first places (not that unlikely over 10,000 samples) and most other samples show much lower winnings.

### Poker MTT Variance Statistics

Lastly the Tournament Variance Simulator shows some interesting statistics, like your probability of loss, your 70, 95 and 99.7 confidence intervals as well as the statistical standard deviation, skew and kurtosis.

In our example, 50 Sunday Millions, the probability of loss is a whopping 71% despite having an ROI of 50%. Obviously, since poker tournaments are so top-heavy it needs a lot more than just 50 tournaments to turn this ROI into a secure income.

All those numbers are derived by Montecarlo simulation, thus they are not completely accurate. But going with a decent sample size (1,000 or more) they are correct within a 2%-margin of error.

### More options

You can enter up to 10 different tournaments, MTTs, SNGs or sit-and-gos and the Tournament Variance Simulator will simulate the whole schedule. By clicking on *“Compare tournaments”* you can compare the distributions of the different tourneys you entered.

Should you have any questions, remarks or feedback, please leave a comment!

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.

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.

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?

I find this tool most useful but is there a way to add “winning and losing streaks” into the equation? I’m playing Jackpot games on I-Poker at an 18% ROI over a 500 sample and I know my graph is towards the top end of your calculations. Even with such a high ROI my biggest streak is 2 wins and 8 losses and I’d just like to know over what sample I’d have a chance at winning a jackpot.

Many thanks for a great tool.

Could you add calculation of profits with cuts, commonly used in stacking now? You just need in each profitable sample to subtract cuts. It would be good to have all these statistics not only from a player’s point of view, but from a backer’s point of view too. All backers will really appreciate it.

Thanks for the feedback.

That’s a feature I might (most likely will) add in the future. Right now the first diagram already shows you the probability of winning less than amount Y. You can hover over the graph to see the values. But this only shows downswings which occur at least .5% of the time.

Very nice tool, when I went on a 125 buy-in downswing over about 1,000 to 1,500 tourns with an approx 15% ROI on Bovada I became suspicious that it was rigged in some way so I started writing my own simulation program…before I could finish it I pulled out of the downswing and abandoned it. Your program that you created is largely what I was trying to do. It shows 1 sample out of 1,000 to be that of a losing player, and I’ll bet that one player didn’t lose 125 buy ins also! How would I figure out what the probability of going on an x buy-in downswing over y sample would be? Do you have plans to add this feature? You made an excellent program!

This will be difficult. The calculator translates the ROI to ITM and assumes, your finishing positions will be evenly distributed.

For example, say you’re playing a $10 tourney (no fee) and 3 places get paid. If you assume an ROI of 20%, the calculator translates this to an ITM rate of 36% where you will finish on positions 1, 2 or 3 with a probability of 12% and will finish on positions 4 – 10 with a probability of ~9.14%.

I think you are the only only who understand and knows how to use this tool.

Great Tool.

Please, add % ITM parameter