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Strategems

A deckbuilding strategy adventure with a few surprises · By Playcebo

What if there were rational number stones?

A topic by MathCookie created 52 days ago Views: 229 Replies: 8
Viewing posts 1 to 6
(1 edit) (+2)

Prime factorization can be extended from just the positive integers to all the positive rational numbers if we allow negative exponents on the primes. For example, the prime factorization of 25/24 is 2^-3 * 3^-1 * 5^2.

So, what would negative exponent prime effects do in Strategems? Since these effects divide the energy cost of the stone, they have to be bad for you - and considering how strong dividing a card's energy cost by something like 53 is, some of the later effects need to be really detrimental to justify being able to reduce a stone with a cost in the upper four-digit range into something playable with 100 energy!

1/2. Burn a tile in this row or column. The fire lasts for three turns instead of two, i.e. it ends on your opponent's next next turn.

1/3. Your opponent gets to cycle a card

1/5. Freeze one of your stones in this row or column

1/7. Vulnerable: Cannot be placed adjacent to any fire, and if any of your stones adjacent to this one are frozen then this stone isn't valid for territory extending

1/11. Any empty tiles orthogonally adjacent to this stone are "blocked" from your color, meaning you cannot place stones on them but your opponent can.

1/13. All of the cards currently in your opponent's hand cost 13 less.

1/17. Any empty tiles diagonally adjacent to this stone are blocked from your color

1/19. Destroy adjacent stones of your color.

1/23. Any empty tiles exactly two orthogonal tiles in one direction away from this stone are blocked from your color

1/29. Exhaust this card.

1/31. Add a stone of the opponent's color in this row or column

1/37. Adds a 1/37 to your opponent's hand. Exhaust.

1/41. Invert all adjacent stones that are yours

1/43. The next card you play costs double energy

1/47. Cannot be played adjacent to an opponent's stone

1/53. Lose your next turn after this current turn (this stacks, so if you play two of these effects you lose your next two turns)

1/59. Adds one "stoneless card" to your deck (a stoneless card cannot be played, it's just deadweight in your hand)

1/61. Discard your highest card. If this is your highest card when you play it, it discards itself instead of letting you add it to the board.

1/67. Discard 2 cards. You cannot play this stone if you have less than two other cards in your hand when you play it.

1/71. When you play this card, you may only choose one of its prime factors to use the effect of (if it has any), not counting the 1/71 itself. (Both primes like 2 and reciprocals of primes like 1/2 count as one prime factor, so if you had 30/77 then you could choose 2, 3, 5, 1/7, or 1/11. The energy cost is not altered by this choice, only the effect).

1/73. Your opponent gets the effect of the next stone you play instead of you

1/79. Surround with stones in the opponent's color

1/83. Surround diagonal spots with stones in the opponent's color

1/89. Give a card to your opponent

1/97. May be played in any empty space. Your opponent gets to choose where this stone goes when you play it.

Some of these are not quite the opposite of their standard equivalent. 89/89 is just a better version of 3, 67/67 is just a better version of 9, 13/13 is plainly beneficial to the opponent, 2/2 still lets you burn some spaces, and 43/43 is just a better version of 43.

You couldn't actually make things like 2/2 or 89/89. Since this game is about prime factorization, the fractions always reduce to simplest form. In the deckbuilding, taking a 1/2 stone and multiplying it by 2 would just give you a 1.

I feel like combining this concept with the X-stone could be problematic. If you have 100 energy and play a single 1/97 you will then have 9699/97 energy and then playing the X-stone would require the game to figure out that 9699/97 = 3 x 53 x 61 x 97^-1. But if you instead play a single 1/97 and a single 1/89 and then the X-stone, the game will have to prime factorize 863114/8633 = 2 * 7 * 89^-1 * 97^-1 * 61651

I'm afraid 1/73 combined with the other fractional cards would be a tad broken, like 1/73 followed by 1/41, if i'm interpreting this right, would invert all opponent's cards.

Good point. Perhaps 1/73 should only apply to positive-exponent effects.

These effects, in general, feel a bit too strong; though it depends on how restricted you are from just including random rationals in your deck. Like, if you can just put a 29/71 in your deck, you kind of just win on the spot. Then again, with how your energy costs would be way lower, I guess the game would have to be balanced around you only having like 2 max energy instead of 100 anyway.

/11 is an interesting effect; I can see why you didn't want to just make it frozen opponent pieces, but it feels a little weird.

What's the exact opponent stone that gets added by /31?

Also, because you didn't specify, here's what I'd do for the other low prime squares:

/49: Cannot be placed if there is any fire on the board. Freezes itself.

/169: All opponent cards cost 169 less and all of your cards cost [this card's cost] more.

(+1)

Yeah, surrounding with opponent stones felt too strong of a downside for 1/11 (but not for 1/79 and 1/83).

Good point on 1/71 allowing you to bypass these downsides, maybe it should be changed so it still applies all the denominator effects but only lets you choose one numerator effect? That doesn't solve the 29/71 issue, though... but I'm of the opinion that 29 needs a nerf anyway (i.e. make it only usable once per turn, or make it only usable a few times total before it's discarded).

1/31 probably adds a copy of the same stone that you just played (albeit one that does not trigger its effects on play).

could 1/59's stoneless card be used as a partial-counter to 89, as you can't see which card you're picking? (and if so, she should have a special line like "What is this? Why do you have it? Take it back!" and bonus points if you actually can agree to her offer)