OtherSpace: Millennium Haggling System Probabilities

After looking at the current code for the haggling system, I was able to calculate the probability of getting a specific quality item and figured I'd post it as well as the calculations.

=Calculations= I used the formula displayed on the forums to figure out R and then S, namely R = (Cha+SS+4df)/2 and S = R*10, S then is the percent chance that it will become a fair, and so on and so forth. From now on, refer to S as a probability (a decimal). So it the value for Mediocre will be 1 - S, to get to a fair will be S, good is S^2, great is S^4, Superb is S^6, and Legendary is S^9. Keep in mind however, that the S^2 is the probability that one will get good or above, same with S, S^4 and S^6. So the probability of getting a Superb and having the item stay at Superb would not be S^6, but S^6 - P(legendary), and then Great would be S^4 - (P(superb) + P(legendary)), and so on and so forth up to and including fair. This leaves poor to be calculated, which depends entirely on the FUDGE roll.

To get the total probability of getting a certain item at a certain skill level, multiply the probability for that particular FUDGE roll times the corresponding probability for that quality. Calculate and sum all the probabilities of the FUDGE rolls and the quality probabilities to get the total probability. For poor, simply add the probabilities of the die rolls which would give one a poor (ie, R of less than 3).

And finally, the expected value for a given skill level is calculated by taking the total probabilities and multiplying them by their respective number, and then summing that. So You'd multiply legendary by 8, add that to (superb * 7) and so on. The number you get is the average item quality you should get at that level.

= One Great and One Good =

Expected Value
4.0095