Variance
After being part of some interesting threads where players feel that a number of positive results are due to variance, I'm curious to know what players feel is the number of hours that needs to be played before it would be considered outside the boundaries of variance. 200? 500? 1,000? Let's assume that a player is consistently playing at the same steaks and buying in for the same amount every time.
If this question has already been asked many times, then feel free to point me in the direction of the post. Thanks!
4 Replies
personally i'd argue it might be impossible in a single person's lifetime of only live cards to fully realize with high confidence the upper and lower boundaries of statistical deviation outside of playing an absurd amount of hours that may even approach impossible.
strictly speaking, there was a time you could play multiple lifetime's of live poker inside of a year MT'ing online.
I think the difference though of achieving certainty and demonstration of results within a set period is offset largely by the skill differential live cards generally offers in comparison to online player pools, so things like "certainty" based on data accumulated are obfuscated by an individuals ability to exceed their opponent's ability by large enough margins to make up what would normally be a distribution of numbers alone based on necessary inputs.
that said - search poker dope variance calculator
and just run the sim results a few times and you'll see even if you input same key indicators at the outset, potential "runs" within some tolerance range will still vary wildly.
It wouldn't be unusual to see an online HU grudge matche set at 50,000 hands. That should tell you something.
That said, a player with no baseline who wins five BB/hour over 500 hours is much, much more likely to be a winning player than someone with no baseline who loses 5 BB/hour over the same period in the same game.
This is highly dependent on your definition of 'out of the bounds of variance', since you can literally apply mathematics to the data and come back with the results. Is 90% good enough for you? 95%? 99%? You may find that you need more data that you're going to get in order to return a result that satisfies your curiosity.
The factor that determines how quickly you get to your desired confidence interval, is the extremity of your winrate. If you crush at 20bb / hour and continue to do so - or lose at 20bb hour - then you will get your confidence interval much more rapidly than someone who sits around +2bb per hour.
The spanner in the works is that games conditions and your own skills can vary widely over the type of time it takes to get meaningful results from live poker. It might take a year or more to obtain as many hands live as it does in a couple of weeks online.
Cliffs: Depends heavily on your Standard Deviation. The general formula to determine the variance between your "actual winrate"* vs your observed is:
2*(standard deviation per hour in BBs)/square root of hours played, so the lower your SD, the fewer hours needed to get decent bounds on your actual winrate/lossrate.
For more discussion, see the winrates thread and search on the phrase "95% confidence interval"
