Wow, joined over 2 years ago to get your first post here, I feel honored
Some constructive criticism early on: It seems like you didn't prepare too well for presenting the information. Following and understanding all the ideas would be easier for us if you prepared what you were going to say for each slide ahead of time and practiced it. It's difficult to follow your train of thought when you're correcting yourself and getting your words and numbers jumbled...feels like you improvised it.
That's always how I give my talks. The slides are well prepared, I know what I'm gonna say, but I don't have any notes written down, as to not sound robotic. I makes it sound much more natural as i get some ribs in I hadn't thought of. For example the "well, because we're not Russ Hamilton" was a thing that just came up on the fly.
I do acknowledge that I might have some extra difficulties "winging it" as I am not a natural english speaker, so I first have to organize my train of thought from german -> english. If I were to do dry runs and too many notes it would just take too much time for me and at some point I have to draw the line. Time is money, too, unfortunately.
With regard to the Gambler's Fallacy, would the assumption that ones - EV will be balanced out in successive all-in situations be more correct as the sample siZe of hands played approached infinity? And is the main reason it's a fallacy due to the fact that the gambler is in a very finite number of situations? I ask this because, looking at the p(k) vs (k) distribution graph on the probability slide, it would appear that the number of (k) values above and below the average weigh each other out. Looks like if you had so many '12' values you could expect, eventually, to have about as many '8' values and so on.
Yes, in the long run the samples even out. If you look out over the events as a whole over a significant sample you will see them even out. However, there is no predictability over what the next experiment (hand, even hand sample) is gonna bring. Even if you know all parameters and probabilities. The fact that you JUST had a winning or losing hand has no bearing on what the next hand is gonna bring. Global view versus "next hand" view.
However, when predicting parameters based on an observed sample, there is such thing as "regression to the mean" IF the first observed values are extreme in relation to the underlying true distribution: http://en.wikipedia.org/wiki/Regression_toward_the_mean
That is a bit counterintuitive, but it just states that the observed distribution is probably wrong and you will go back to the actual distribution quite quickly.
As an example, say you lose at a clip of 30bb/100 the first 1000 hands you ever play. That losing rate is extreme and yes, you may expect not to lose at that clip for the next 1000 hands. It will not even out the next 1000 hands, though ;-).
I appreciate all the work you put into it and I look forward to the next episodes!
Thanks and thanks again for the constructive criticism.