11-08-2006, 01:10 AM
(This post was last modified: 11-08-2006, 01:25 AM by the Langolier.)
Sekel's post is completely correct, but imcomplete. The final probabilty is for ONE slot only, and griswold will sell you six. Additionally, at clevel 29 with the different ilvl for each slot, there may be a slight difference in probability for some slots. For now, we will just assume 0.00002405 for each slot.
For six slots, the probability for him to sell a KSOH (in a game) is:
1-(1-0.00002405)^6 = 0.001443 (or statistically 1 in 6930 games).
But don't get your hopes up. The probability to ACTUALLY have this item for sale in 6930 games is:
1-(1-0.001443)^6930 = 63.2%
So even if one hundred people shopped 6,930 games, only 63 of them would actually see a Kings Bastard Sword of Haste for sale. Once again, however, there is a "but". There is a fact that no one has mentioned, which makes virtually all of this completely pointless - the price cap! There are dozens of items Griswold will generate which will be discarded because they violate the price cap. Most notable are many awesome full plate mails with a suffix (excluding ages I believe). Furthermore, sometimes this cut-off is dependent upon the actual VALUES of the affixes chosen. For example, a Lord's Great Sword of the Heavens (81/12) is 100 gold short of the price cap. This means that it is possible to buy this item ONLY with those exact stats. With any other stat (inlcluding 82/12), it is too expensive. Now, a Lord's Great Sword of the Heavens can spawn with 60 different unique values (81-95 paired with 12-15). Since only the lowest possible is below the price cap, if this item is generated at griswold, only 59/60 times it will have to be regnerated (as opposed to every single time, or 60/60). At least, that what is assumed, but we don't have any information about that. This effect is even more prominent at Wirt. Just try calculating the price of an emerald tower shield of the tiger with varying values. 47% emerald is only possible with the lowest amount of life, 41. 46% is possible up to 44 life. 45% is possible up to 48 life, and so on. Same thing goes for various ruthless/merciless long battle/war bows of the heavens.
There is no information as to what happens when an item is discarded because of price cap, but probably the slot in question simply generates another item. The problem then is when this happens (since another item is generated) it essentially has the same effect as if there were *7* slots in that particular game. And what if he generates two items that are two expensive, now he has generated virtually 8 slots worth of items - which will increase the probability of him selling the sword. The problem is how often can you say he generates an item that is too expensive? And if he generates an item that will be below the price cap with some values, but not with others, what is the ratio between them?
Since that ratio of keeping/discarding an item is dependent upon the quality of the affixes selected and because it is unique for any item that the cap falls in between the price range, it is extremely difficult to calculate the affect of the price cap on probability at town shops. Believe me, if there were a way, I would have done it already.
It is also worth noting that Griswold will NEVER use an ilvl of more than 30, which that there is no difference between shopping at clvl 31-50.
Edit: Ok, Nystul beat me to the punch on the last part.
For those interested, if you include the effect of the price cap, the problem because conditional probability, and is very complicated. Technically it affects more than just having to regenerate the item, but the actually probability of the sword iteself, so it no longer is 0.00001405 per slot. I am working with a professor on some conditional probabilty for monster generation, so if I can apply it to shopping I will report about it and may even get motivated to make a calculator for it.
For six slots, the probability for him to sell a KSOH (in a game) is:
1-(1-0.00002405)^6 = 0.001443 (or statistically 1 in 6930 games).
But don't get your hopes up. The probability to ACTUALLY have this item for sale in 6930 games is:
1-(1-0.001443)^6930 = 63.2%
So even if one hundred people shopped 6,930 games, only 63 of them would actually see a Kings Bastard Sword of Haste for sale. Once again, however, there is a "but". There is a fact that no one has mentioned, which makes virtually all of this completely pointless - the price cap! There are dozens of items Griswold will generate which will be discarded because they violate the price cap. Most notable are many awesome full plate mails with a suffix (excluding ages I believe). Furthermore, sometimes this cut-off is dependent upon the actual VALUES of the affixes chosen. For example, a Lord's Great Sword of the Heavens (81/12) is 100 gold short of the price cap. This means that it is possible to buy this item ONLY with those exact stats. With any other stat (inlcluding 82/12), it is too expensive. Now, a Lord's Great Sword of the Heavens can spawn with 60 different unique values (81-95 paired with 12-15). Since only the lowest possible is below the price cap, if this item is generated at griswold, only 59/60 times it will have to be regnerated (as opposed to every single time, or 60/60). At least, that what is assumed, but we don't have any information about that. This effect is even more prominent at Wirt. Just try calculating the price of an emerald tower shield of the tiger with varying values. 47% emerald is only possible with the lowest amount of life, 41. 46% is possible up to 44 life. 45% is possible up to 48 life, and so on. Same thing goes for various ruthless/merciless long battle/war bows of the heavens.
There is no information as to what happens when an item is discarded because of price cap, but probably the slot in question simply generates another item. The problem then is when this happens (since another item is generated) it essentially has the same effect as if there were *7* slots in that particular game. And what if he generates two items that are two expensive, now he has generated virtually 8 slots worth of items - which will increase the probability of him selling the sword. The problem is how often can you say he generates an item that is too expensive? And if he generates an item that will be below the price cap with some values, but not with others, what is the ratio between them?
Since that ratio of keeping/discarding an item is dependent upon the quality of the affixes selected and because it is unique for any item that the cap falls in between the price range, it is extremely difficult to calculate the affect of the price cap on probability at town shops. Believe me, if there were a way, I would have done it already.
It is also worth noting that Griswold will NEVER use an ilvl of more than 30, which that there is no difference between shopping at clvl 31-50.
Edit: Ok, Nystul beat me to the punch on the last part.
For those interested, if you include the effect of the price cap, the problem because conditional probability, and is very complicated. Technically it affects more than just having to regenerate the item, but the actually probability of the sword iteself, so it no longer is 0.00001405 per slot. I am working with a professor on some conditional probabilty for monster generation, so if I can apply it to shopping I will report about it and may even get motivated to make a calculator for it.