Math Help needed for a 52 card deck based resolution system.

[BerzerkerUnit]

Aloha, here's a link to the full document (which is in a passable Alpha state). World Break (https://docs.google.com/document/d/1VW-bZbcfsU23nCBuRnM80PbpE50hJiyJZ7rbKOz-BnE/edit?usp=drive_link)

My request for math help breaks down like this:

Difficulties for tests range between 8 and 20. with ~12-13 being the norm.
20 requires assistance or magic etc. Average Stat for a player is 3.

One of the subsystems for magic is for crafting items. My current idea is that in order to craft the item you need to use a Face Card to bind the magic to it. So the more items you make, the fewer Face Cards your deck will have. That feels like a solid trade off. But what should the numeric values be for such a thing?

If we assume an item provides its bonus to a limited purpose, like boots of speed that let you run fast without tiring. How much faster should they let your run?
Movement is physical Trait x 4 yards- so average walking speed is ~12 yards. Would double be too much? What if it only applied to the Dash Action?

If it makes a sword magic, what should the static bonus to attack or damage be?

I would still love any feedback you can give. Thanks!

If someone can break down... wait, maybe I can think this through.

Removing a face card will bring the average value of the deck down by a certain amount. I can just double or triple that based on how narrowly the item's effect can be applied.

[rel]

sorry, the link is rather long and wordy, and I'm having trouble parsing it. Any chance you could give cliff notes of the resolution mechanic?

[BerzerkerUnit]

Stats are rated 1-6.
For non combat you draw a card and add card value. Ace=1, face cards are 10.

Some features may allow you to draw multiple cards and choose. Some may allow you to draw multiple cards and stack(sum of card values in the stack).

My question was, if creating a magic item requires you to assign a face card to it while it stays magical (removing it from your deck for the duration) what kind of static bonus should that grant?

Right now I’m thinking +1 to a broadly defined category of things, and +2 or +3 for a more narrowly defined category.

[Yakk]

E(draw) is (1+2+3+...+9 + 10*4)*4/52 = (10*11/2+30)*4/52 = 340/52, or 6.53846...

Taking out a face card (a 10) reduces the E(draw) by *about* (10-6.5)/52, or (a bit more than) 1%. (330/51 is 6.471.... 320/50 is 6.4, 310/49 is 6.327..., )

Swapping a face care for a +1 always would be a massive boost. You can also see this by what it does to the deck - take the deck, remove a face card, then *promote every card by 1*. The promoted 9s more than replace the missing 10. Eliminating the aces is great. And now your remaining face cards are 11s.

[rel]

E(draw) is (1+2+3+...+9 + 10*4)*4/52 = (10*11/2+30)*4/52 = 340/52, or 6.53846...

Taking out a face card (a 10) reduces the E(draw) by *about* (10-6.5)/52, or (a bit more than) 1%. (330/51 is 6.471.... 320/50 is 6.4, 310/49 is 6.327..., )

Swapping a face care for a +1 always would be a massive boost. You can also see this by what it does to the deck - take the deck, remove a face card, then *promote every card by 1*. The promoted 9s more than replace the missing 10. Eliminating the aces is great. And now your remaining face cards are 11s.

That's my analysis too. A +1 is worth a lot more than your chance of drawing a natural 10 going down slightly.

[BerzerkerUnit]

That's my analysis too. A +1 is worth a lot more than your chance of drawing a natural 10 going down slightly.

In which case the bonus should be very niche or cost some other resource.

Let's look at a pretty classic example: Flaming Sword

So maybe the flaming quality only triggers if the same suit is used for the action.

So if you created it with the King of Hearts, the Flaming effect only triggers if the card you use for the attack is a heart.

Now you're at a little less than a 25% chance to activate it... Maybe you can bind more face cards to make it more likely.

As I've developed the concept a little more I'm thinking the bonus will either require the observance of a taboo, or the bonus will only apply in pursuit of a goal.

The Suit trigger could be a mechanic the represents something like requiring a particular maneuver to trigger the flames (EX: only when slashing left to right).

Alternatively it might only trigger when attacking known Members of the Phantom Troupe.



I'm also not sure the card promotion analogy is entirely accurate. I'm not counting Aces as face cards, they're a 1, so you can't get them out of the deck, and while you will cycle cards faster, but you're still reducing your chances to get a 10. The more items you create, the fewer 10s you can draw. If you're drawing 3 cards/5 cards per round in combat, I think you'll start to feel those missing face cards soon enough, no?

[Yakk]

With a +1, the "Aces" are "worth 2" (1+1).

Without a +1, your draw plus mod is (1,2,3,4,5,6,7,8,9,10,10,10,10) x4. With a +1 it is (2,3,4,5,6,7,8,9,10,11,11,11,11) x4 minus (11). You "lose" a 10, but your 9s are now worth 10 and your other 10s are worth 11, and the lowest you can draw is Ace(1)+1 = a 2 before the +1.