Re: Moving Up Is Hard To Do
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How close would we be, with a standard dev of 15/100 and a 95% confidence level?
I'm asking because I don't know, not just to be a smartass, but I'm curious, because I'm hopefully going to be moving up limits soon. [img]/images/graemlins/smile.gif[/img]
Edit: 99% confidence level too, if you don't mind.
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Even I know the answer!!! [img]/images/graemlins/grin.gif[/img]
Assuming that after 100,000 hands you have a winrate of 3 bb/100, and a SD of 15 bb/100, the .95 confidence level is:
[2.070307452, 3.929692548]
so, we can be almost an entire bb/100 off from our "true" winrate. (I think).
The .99 CI is: [1.778176881, 4.221823119]
And that's even bigger.
So basically, you can never really know your "true" winrate.
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Yes, but you have to remember that it's a bell curve, so you're far more likely to be near the middle of that range than near the edges. In fact, without further evidence of the actual parameters, you must assume that your sample mean is the most probable value. I'm not saying it IS the parameter value... just that it's more likely to be the actual value than any other value in that range due to the inherent probabilities in bell curves.
What you're describing is the 95% and 99% CIs, so it's "possible" that your actual winrate is really outside that range....but not likely. The odds are that it's nearer to the sample mean.
If you do a linear analysis of your variance and find that each block of 5k hands is statistically similar in variance (there is a test for this) to the others, then you can assume that your winrate after 20k hands is your actual winrate for that type of play. Some would argue that 10k is enough if you're a very consistent player.
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