Quote:
Originally Posted by burden2
Maybe my true ROI is 9 at the worst. But with a 300 game sample I don't think it's truly 6 which is what it is at stars. For all you probablity masters what is the chance, with a 300 game sample, that my true roi is 6 or less given that it is currently 17?
Actually this isn't possible to calculate without some assumptions about the underlying distribution of win rates, and then an application of Bayes' theorem. It's quite technical so I will give a more simplified example.
Suppose we flip a coin 100 times and score +1 for head and -1 for tails. Your observed result is, lets say, +10, or +0.1 units per trial. You then ask what the chances are you win more than 0.05 units per trial 'longterm'. If we assume the coin is fair then the chance is zero. If we assume the coin came from a sample of two coins, one of which is fair and one of which is rigged to come heads 60% of the time, then our observed score is equally likely to have come from either coin, so the cahnce is 0.5. If we assume that the coin could be biased anywhere between always heads and always tails and constuct a uniform distribution of coins we get a different answer.
Actually that simplified example wasn't that great, so lets try a poker example. Suppose you are one of a set of players, 80% of whom lose 1bb/100 playing poker, 10% of whom break even, and 10% of whom win 1bb/100. You observe that over 10000 hands you won 1.15 bb/100 with a s.d of 2.1bb/hand. With this underlying distribution you are actually most likely to be one of the -1bb/100 players even with this observed data, simply because most of the population is and the data is not conclusive enough.
Having thoroughly confused you with those examples back to the point in hand.
It is *impossible* to know how likely you are to have 6% or less ROI without knowing what the population distribution looks like for the games you are playing. i.e., what percentage of the population as a whole has 0-1% ROI, 1-2% ROI, 2-3% ROI and so on. Obviously the mean is going to be around -9% ROI but what the spread of the data looks like I'm not sure. I suspect a normal distn with mean -9% and s.d about 15%. Then again it might not be normal at all in which case we are totally ****ed in terms of calculating this without a computer simulation.
If anyone has a better idea of an estimate for the population distribution of Sng players ROIs let me know as the problem has piqued my interest.
burden2 - I need to know the standard deviation of your ROI per event to be able to estimate your actual ROI from the sample and the population distribution. If you know how to calculate this please post it in the thread, otherwise just post the numbers of each finish you had (i.e. number of 1st, 2nd, 3rd, and 'noncashes'). I'm pretty busy at the minute but as it's a very interesting mathematical problem I will do it on Monday when I have a day off, if you post the info needed.
What I can say without looking at your s.d is that I suspect it will be more than 50% likely your ROI is 6% or less, assuming my population distribution is reasonably correct. After all you will be 15% above the population mean even with 6% ROI, which is 1.0 s.ds, so only 15.9% of players are better than this. The sample of 300 games is (I suspect, without seeing the s.d. its impossible to be sure), so small, that Bayes theorem will say you are still likely to be in the <6% bracket. It's similar to the ring game example mentioned above. Statistically it's known as 'regression to the mean'. Your actual longterm score is likely to be closer to the mean than any observed sample (only likely, not certain).
In fact it would not totally amaze me if given a sample of 300 games at 15% ROI you still have like reasonable non-zero chance to be a losing player (say 10% chance or so).
p.s. mean -9% s.d. 15% puts a breakeven player at +0.6s.d. Then we would have 28.4% of all players being better than breakeven. Does this sound about right to those of you who play 1 table SNG?
Last edited by Pyromantha; 07-10-2009 at 07:03 PM.