Originally Posted by adventurebound
Zach...please explain the calculus of K?


Glad you asked:
Here's the equation again:
BR needed = 3.5*top prize  10*expected ROI +3.792833*k
If this were not an estimate we wouldn't use only top prize, but we would use all the prizes, probability of winning each one, and calculate the probability of busting to determine the BR needed. Instead we simply use the top prize assuming that we will be in different payout structures in a somewhat bell curve. The ROI normalizes it as if you have a high ROI you will be further to the right (towards the top prize) and if you have a low ROI you will be further to the left.
Now what we do is integrate the curve, and we take the area under a certain amount of money to be total money. Since it is a normal curve all the probability adds up to one, so the area under the curve is an approximate weighted average of the money and our probability. It's been calculated that even the most rigged site only takes $3.792833 from an average player, so someone with a 0 ROI and 100% rigged will need $3.792833.
But we still don't know if k is linear, quadratic, etc. We know two points, so we need to determine the order of k. Since we realize poker is rigged and although we can't explain it we know when poker is x% rigged, we just kept playing until we had a session where we just knew it was 50% rigged. We lost exactly $1.90 which is half of the 100% number rounded. So we determined that k is linear and we can use the formula included. It has been extensively tested and scientifically proven. Let's use it to determine the approximate BR needed if we assume that Stars, as we know it is, is 100% rigged, and our ROI will be 10%:
BR needed = 3.5*top prize  10*expected ROI +3.792833*k
BR needed = 3.5*5520.68  10*0.1 + 3.792833*1
BR needed = $19,326