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What youre looking for is the standard deviation for the mean. For example the variance for a single fair coin flip is 0.
If you want to know the variance of the sum of 10 coin flips you do 0. The same goes for poker hands. The variance for poker hands in NLH 6max is, say, squared.
To calculate the variance of the sum for 10 thousand hands you have to think how many groups of hands does have? Everything is super misleading.
This means that these tables are significantly underestimating by a factor of about 2 the amount of bankroll needed to only have a 5 percent chance of going broke.
Fortunately, this problem mitigates as the probability of going broke is reduced. Thus the Bankroll Required to Assure a Win tables do contain solid estimates and produce a risk of ruin of approximately 1.
I wrote some of it. It in no way changes the fact that the calculations in that section are no way to compute the bankroll requirement for a desired risk of ruin.
That number gets worse as the risk of ruin is reduced. If we want a 0. The mitigating factor is that both of those numbers are relatively small.
Lots of folks may not care if their risk of ruin is 1. The 0. You chose that as a way to include essentially all of a population as is common in statistics.
Except you are considering the wrong population. We want the population of all random walks that never go broke.
Using the former population for bankroll requirements and risk of ruin is mathematical nonsense. Before that it was well known to the blackjack community, having appeared in papers by George C.
It was surely known in mathematics before that as the general expression is important in financial math, and it can also be obtained from the Weiner process.
There is also an analytical short term ruin formula for risk of ruin in a finite number of hands. The confidence intervals in his graph have nothing to do with risk of ruin.
His graph is showing you a range of results assuming you can play through any drawdowns. IOW, if you lose your at some point, you can still keep playing, as if someone lent you additional funds.
The positive portion of the graph includes the times you lost your bankroll and then recovered to finish positive.
The risk of ruin formula as correctly given by Pokerdope counts these instances as a failure. A risk of ruin formula is not and cannot be based on confidence intervals.
Attempting to use confidence intervals to compute risk of ruin is a well known blunder. Here is a derivation of the risk of ruin formula Pokerdope gave which has been simplified to require nothing more than high school algebra:.
BTW, we developed a similar variance calculator on your site for tournaments which requires a different approach to risk of ruin..
It runs in R which is a platform for statistical computing which free and very easy to install. Here is a link to the script.
Thank you for answering my question. In your example of a 2. The risk of ruin and the necessary bankroll is calculated independently from the confidence interval.
Using the example above with a win rate of 2. Do you have sophisticated guesses for the STD of 6-max five-card Omaha? Maybe something like ?
I noticed that the 20 random graphs in cg variance simulator almost always have one graph that is outside of the 2 std deviation line..
Is this a bug? The range of outcomes is wider. Hello, anyone can explain what observed winrate is? We have winrate and observed winrate, any differences?
Am confused if the BB is big bet or big blind. I would assume it is big bet. The variance calc is complete non sense.
It would be correct if online poker would work with correct and real life daily math, but since it doesnt, any calculation is a fail.
If your ture winrate is 2. Hi Mitch, these is the complete overview of my calculations. Especially since, even though I am a small winner in my games, I am perpetually running below EV and my actual winnings should be much higher than they currently are.
Thank you. Do you assume normal distribution? I always see people on the forums : say it is as likely to run below EV or above EV but this says otherwise.
Help explaining this would be greatly appreciated. Probability of running at or above observed win rate Probability of running below observed win rate You see, those tables were simulated at the distance over mil hands.
So the smaller is your sample the less chance for you will be to ruin. Could anybody explain me.. Also HM2 has 2 different stats for std dev.
One is bb per hands and is as in examples. Another is just std dev. So the difference is like, eg, for midstack nlhe 65 vs 6.
You may put in the description than you use std dev per hands. Any chance you can create a simulator for live players?
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It is mandatory to procure user consent prior to running these cookies on your website. Updated: 8. September 86 Comments By Primedope. Hit "Calculate"!
Hands: 1. Once you have entered the data, hit Calculate and the let the Calculator do its magic. This number will appear as a rather boring straight and black line in the graph.
They basically show, how much variance you should expect to see. Variance in numbers Below the first chart the Variance Calculator compiles a neat list of additional information: EV : win rate entered above Standard deviation : standard deviation entered above Hands : number of hands entered above Expected winnings : estimated winnings over the simulated amount of hands Standard deviation after X hands : This number shows by how much your actual results will differ from the expected results on average.
Meaning: 19 out 20 times your actual winnings will be within this interval. Probability of loss after X hands : probability that you will experience negative winnings meaning: losses over the amount of hands.
Detailed sample with downswings This chart simulates a single run over thousand up to 10 million hands with the winrate and standard deviation entered above.
You can choose how many hands to simulate by moving the slider. Apart from showing a single sample , this graph also shows some insightful information about downswings.
The red area shows for any given point, how much the sample is currently away from its previous peak, meaning it tracks downswings. This chart uses two vertical axes.
While the sample winnings have their scale on the right axis, the downswing tracker has its scale on the left axis.
In this example the simulated player ended up with winnings over 25, big blinds after 2. Downswings in numbers The last section of the Variance Calculator sheds some more light on potential downswings.
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