The campaign takes place in Cormyr and one of the players is a War Wizard, an official military position. The War Wizards operate out of Mage Keep and this player wants to go there find some Magic Item Formulas. I have been trying to figure out the map all day and can't. Just stuck.
So let's assume 1 in 100 practitioners at Mage Keep create, find, reinvent, or otherwise obtain a magic item formula. Let's assume mage keep over its whole history has had 50,000 practitioner members. That means that 500 practitioners in the whole history of Mage Keep have contributed to their collection. I got this far. Let's assume it's possible to get the same magic item formula as a result more than once but the chance of finding that specific formula falls by 50% every time it comes up as a result. Lets assume a pool of 1,000 possible unique magic items. After all that, we need to remove 33% of the total to account for the destruction wrought by the spell plague. How many unique magic item formulas does Mage Keep have?
Could anyone help me with the math?
EDIT #1: I mean it would be easy to say that each practitioner contributed an average of 2... 500 Mages, 1000 unique magic items... But there would definitely be more ways to make magic items, you know? Like maybe this Bag of Holding formula requires Phase Spider Silk, while another formula requires the flesh of a Githyanki warrior. How would I figure that out...
Not to ruin your fun of doing it via math, but you could just not worry about it. The wizard will ask for a specific formula. You just have to decide if they have that one. And the answer to that is whether or not you want to give it to them, not whether some math tells you it’s there. Just decide. Don’t overthink it.
How many do you want it to have is exactly the number it will have :) Trite but true. If someone searches for a specific magic item formula - give them a chance to find it. Come up with a table for each level of rarity of magic item formula. Keep in mind that finding a formula is not the same as finding the item. Some items could require a wish spell to create for example. In addition, some might be impossible to create and others you may not want in your game. In both cases, any die roll automatically fails to find the formula.
PS based on your numbers you have 500 characters with a magic item formula and over 1000 possible magic items with duplication possible. If each contributes one then the maximum possible number of magic item formulae is 500/1000. However, you want to also reduce this by 1/3 - this means that the maximum number of magic item formulae remaining is 333. If you arbitrarily reduce this further for the possibility of duplication you end up somewhere between 200 and 250 distinct magic item formulae out of a possible 1000. So you could use 20-25% as your base chance for the keep to have any particular magic item formula.You could increase that if some mages contributed more than one formula.
However, that doesn't address the question of rarity or plot driven item formulae - for example if the characters need a formula for an item for a specific quest then you can just put it in the keep - you don't need to roll - the characters just need to find it.
The bottom line is really that, as DM, you do not have to calculate anything - you design and build the world - the numbers you are trying to figure out are just a guideline to give you an idea of how many might be found but you can and should just make it up to fit the narrative of the story you are playing. If it is just a character looking for a formula for a specific magic item then decide (a) would this item fit in your campaign or would it be disruptive - if disruptive then the formula can't be found and it is an automatic fail ... (b) do you WANT the character to have the possibility of creating this magic item as a plot point - then the check to see if the formula exists automatically succeeds ... if you are indifferent then roll the percentage you worked out above to see if they find the formula. In all cases you roll the dice and then just tell the character the result - all cases appear identical from the player perspective - but the DM is the one in charge of the game, not the dice.
It is also possible that while an entire formula is what it takes to make the macguffin there are partial formulas floating about. Those were the contributions of the mages as well, just that they are incomplete.
The PC could find two or three of these incomplete formulas and figure out that they work together in some specific way that requires a special ingredient or catalyst. (Queue quest music.)
They find the catalyst, combine the formulas, and produce the macguffin or effect. Yeah!
The effect has unforeseen deleterious effects. Now the PC needs to undo the thing that they did because they are the only one who knows what they did in the first place. (Queue quest music.)
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The campaign takes place in Cormyr and one of the players is a War Wizard, an official military position.
The War Wizards operate out of Mage Keep and this player wants to go there find some Magic Item Formulas.
I have been trying to figure out the map all day and can't. Just stuck.
So let's assume 1 in 100 practitioners at Mage Keep create, find, reinvent, or otherwise obtain a magic item formula.
Let's assume mage keep over its whole history has had 50,000 practitioner members. That means that 500 practitioners in the whole history of Mage Keep have contributed to their collection. I got this far.
Let's assume it's possible to get the same magic item formula as a result more than once but the chance of finding that specific formula falls by 50% every time it comes up as a result. Lets assume a pool of 1,000 possible unique magic items.
After all that, we need to remove 33% of the total to account for the destruction wrought by the spell plague.
How many unique magic item formulas does Mage Keep have?
Could anyone help me with the math?
EDIT #1: I mean it would be easy to say that each practitioner contributed an average of 2... 500 Mages, 1000 unique magic items...
But there would definitely be more ways to make magic items, you know? Like maybe this Bag of Holding formula requires Phase Spider Silk, while another formula requires the flesh of a Githyanki warrior.
How would I figure that out...
Not to ruin your fun of doing it via math, but you could just not worry about it. The wizard will ask for a specific formula. You just have to decide if they have that one. And the answer to that is whether or not you want to give it to them, not whether some math tells you it’s there. Just decide. Don’t overthink it.
How many do you want it to have is exactly the number it will have :) Trite but true. If someone searches for a specific magic item formula - give them a chance to find it. Come up with a table for each level of rarity of magic item formula. Keep in mind that finding a formula is not the same as finding the item. Some items could require a wish spell to create for example. In addition, some might be impossible to create and others you may not want in your game. In both cases, any die roll automatically fails to find the formula.
PS based on your numbers you have 500 characters with a magic item formula and over 1000 possible magic items with duplication possible. If each contributes one then the maximum possible number of magic item formulae is 500/1000. However, you want to also reduce this by 1/3 - this means that the maximum number of magic item formulae remaining is 333. If you arbitrarily reduce this further for the possibility of duplication you end up somewhere between 200 and 250 distinct magic item formulae out of a possible 1000. So you could use 20-25% as your base chance for the keep to have any particular magic item formula.You could increase that if some mages contributed more than one formula.
However, that doesn't address the question of rarity or plot driven item formulae - for example if the characters need a formula for an item for a specific quest then you can just put it in the keep - you don't need to roll - the characters just need to find it.
The bottom line is really that, as DM, you do not have to calculate anything - you design and build the world - the numbers you are trying to figure out are just a guideline to give you an idea of how many might be found but you can and should just make it up to fit the narrative of the story you are playing. If it is just a character looking for a formula for a specific magic item then decide (a) would this item fit in your campaign or would it be disruptive - if disruptive then the formula can't be found and it is an automatic fail ... (b) do you WANT the character to have the possibility of creating this magic item as a plot point - then the check to see if the formula exists automatically succeeds ... if you are indifferent then roll the percentage you worked out above to see if they find the formula. In all cases you roll the dice and then just tell the character the result - all cases appear identical from the player perspective - but the DM is the one in charge of the game, not the dice.
And if they can make the item once, they can make it a hundred times, and sell them to other mages/adventurers and retire rich.
It is also possible that while an entire formula is what it takes to make the macguffin there are partial formulas floating about. Those were the contributions of the mages as well, just that they are incomplete.
The PC could find two or three of these incomplete formulas and figure out that they work together in some specific way that requires a special ingredient or catalyst. (Queue quest music.)
They find the catalyst, combine the formulas, and produce the macguffin or effect. Yeah!
The effect has unforeseen deleterious effects. Now the PC needs to undo the thing that they did because they are the only one who knows what they did in the first place. (Queue quest music.)