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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.
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?
I currently am sending my Mental Game Coaching clients over to this website to learn about the true effect of variance in their game. September 56 Comments By Primedope.
Variance in numbers Below the first chart the Variance Calculator compiles a neat list of additional information: This number shows by how much your actual results will differ from the expected results on average.
Probability of loss after X hands: Probability of running at or above observed win rate …: If you entered an observed winrate , this number will show you the probability that you will experience a run at or above this winrate over the amount of hands.
Probability of running below observed win rate …: 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.
For that reason, any and every player needs to take the steps required to ensure that his or her game is on point. Helping you step up to the table and deliver an all-around performance, here are a few ways that you can improve your game.
Think you can play poker blind successfully? Think again, as every successful player looks to carry a poker strategy into battle.
Now, there are countless poker strategies out there, some of which are easy to adopt, while others prove to be a little more complicated.
No matter the strategy you opt for, you need to understand the importance of using it, along with how it can make you a better player.
You can use this simple odds chart for calculating odds and probabilities while playing, helping you to decide which bets to make.
It has basic hand odds given the number of "outs" after the flop or after the turn. Feel free to save this image to your computer for use anytime you need it!
This chart displays some poker odds as well as recommended starting hands for playing poker. These hands generally have the greatest odds of winning any particular hand.
This helpful chart is available for free download, just click the button below. Poker is a hyper-competitive game with real stakes and real cash commonly riding on the line.
This makes having an edge at the tables absolutely crucial, something that a poker odds calculator can easily provide. This information and data will allow you to exert a tighter grip on the action, making your play more effective in the process.
Replaying previous poker hands can be an invaluable learning experience and this free poker odds calculator is perfect for the serious poker player who wants to master the art of winning money at online poker or at the casino tables.
It all depends on how serious you are about wanting to improve your play. Other players might wish to use our free poker odds calculator only when the need arises, such as during a tight game.
Using our pot odds calculator you stand a better chance of analyzing a play correctly and making the right moves to ensure victory.
The pots odds are the ratio of the current pot size when placed up against the odds of a contemplated call. The out card is the card that will essentially complete your hand.
For example, should you be on a potential flush draw, with four hearts already in hand, then there will be nine hearts theoretically left to be claimed to complete the flush.
The Wolfram Mathworld site has detailed odds on all the poker hands to get you clued up. News Nederlandse pokersites Odds Calculator.
So, What is a Poker Odds Calculator? Using a Poker Odds Calculator Effectively Start by selecting your game of choice using the drop-down list in the top left-hand corner.
Next, choose the two cards that your first competitor has. If you have more than one opponent, then you can continue to give out cards in turn as you go along.
Once you have given cards to all the players you want to hand out cards to, you can click into the center to start dealing into the flop. Why Use a Poker Odds Calculator?
Learn as you play Someone that is lacking experience should be looking to learn with every hand, with a poker calculator that becomes much easier.
Work with hypotheticals For all but the most experienced poker players, using an online poker calculator to hone your skills should be a simple decision.
The Best Ways to Improve Your Game Poker has become the game of the people, so competition is picking up no matter where it is you choose to play.
Understand the importance of strategy Think you can play poker blind successfully?