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The second table shows how long downswings last on average. Meaning, by this definition a downswing is not over until the player has fully recovered its losses.
In general these simulations underestimate the extent of downswings, but the numbers should still give you a decent idea of the vastness of downswings you should expect.
Should you have any questions, encounter any errors or have ideas for improvements, please let me know.
Winnings are measured in big blinds. That means you have won big blinds over 10, hands. This is equal to 2. Everything is super misleading.
It has been pointed out to me by Bruce Zastera, one of the most knowledgeable posters on our forums at http: 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. 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.
BR is the required bankroll, R is the risk of ruin, Var is the variance which is the standard deviation squared, and WR is the winrate. 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? 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.
Do you assume normal distribution? I always see people on the forums: 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.. If I see this: Also HM2 has 2 different stats for std dev.
As you can see from this graph the rate at which this player wins money is far from linear. Sure, his stats may show a winrate of 1.
If we plot this expected winrate on the graph, we get to see how much variance is taking place compared to what this player expects to be winning in a perfect world.
Over a long enough period of time his actual results will meet up with his expected results, but in the short term the amount that he wins or loses in the hands of our good friend variance.
As we know there is an element of skill involved in poker, but there is also a lot of luck. To get a really good idea of how much your winnings can vary over a set number of hands, try using this poker variance simulator.
Just enter your winrate and standard deviation which can be found in PokerTracker or Holdem Manager and see how differently the outcomes can be.
You may be surprised at the size of the possible swings and just how different your results can be over large sample sizes.
It's a real eye opener if you think your recent 5 buy-in downswing was bad. More information on standard deviation and variance can be found in the Holdem Manager guide video starting at 6: You might be playing out-of-your-skin poker but still lose money, which makes it frustratingly difficult to analyse what you might be doing right and what you might be doing wrong.
You have to trust that you are making good plays and feel genuinely comfortable about how you are playing, regardless of what current results attempt to indicate.
Confidence in your ability at the poker table is a very important quality to posses during a downswing.
However, you have to get used to it if you want to win money from poker over the long run. We all encounter bad doses of variance, but not all players can handle it.
If these bad players never won any money, half of them would just quit playing. Be thankful that bad beats exist so that these bad players can slowly but surely hand their money to you.
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