Card Design: An attempt at a comprehensive guide (A community effort I hope)

[Midnar]

Draw Cost in units of quanta? Do you mean a card-quanta exchange rate? I already worked on this. Assuming that Quantum Pillar, Nova, Supernova, Cremation and Immolation are balanced:

Nova: consumes 1 card to produce 12 quanta with usability 1/3 (based on quantum pillar). Exchange rate is 1:4 (maybe more, because the production of Nova isn't random, making it a bit more usable than QT).
Immolation: consumes 2 cards to produce 18 quanta. In a mono-fire deck, only 7 quantas are usable - exchange rate is 1:3.5. In a fire bow, those 7 quanta have a lower usability (because it's possible to draw only non-fire cards), and the other have a small usability - exchange rate is somewhere around 1:4.

Supernova: consumes 1 card and 2 quanta to produce 24 quanta with usability 1/3. Benefit=(24/3)-2=6. Exchange rate is 1:6.
Cremation: Same reasoning as Immolation. Exchange rate is somewhere around 5.

From this, I deduce that an unupgraded card is worth 4 quanta and an upgraded card 5-6. It seems extremely logical to me that an upgraded card is worth more quanta than an unupped one. As an example, (a Reverse Time card + 2 ) produce exactly the same effect as (a Rewind card + 1 ). Therefore a Rewind card is worth one more quanta than a Reverse Time card.

[OldTrees]

Draw Cost in units of quanta? Do you mean a card-quanta exchange rate? I already worked on this. Assuming that Quantum Pillar, Nova, Supernova, Cremation and Immolation are balanced:

No I was referring to how a 8|x Immortal creature is worth two 4|y Immortals and thus should have a casting cost more than twice the casting cost of the 4|y Immortals. (assuming the x and y were set at constant values that caused the resilience of the two sets of cards to be equal)

From this we can conclude that the "cost" to activate a card's value is equal to slightly more than the casting cost would indicate. I would like you to try to find a way to determine how much more.

[Midnar]

Draw Cost in units of quanta? Do you mean a card-quanta exchange rate? I already worked on this. Assuming that Quantum Pillar, Nova, Supernova, Cremation and Immolation are balanced:

No I was referring to how a 8|x Immortal creature is worth two 4|y Immortals and thus should have a casting cost more than twice the casting cost of the 4|y Immortals. (assuming the x and y were set at constant values that caused the resilience of the two sets of cards to be equal)

From this we can conclude that the "cost" to activate a card's value is equal to slightly more than the casting cost would indicate. I would like you to try to find a way to determine how much more.

I disagree with that. Methinks that if a creature is twice as powerful as another and have the same resilience, it should cost twice as much. That's how it is in the actual game by the way: Amethyst Dragon costs twice as much as Abomination - or, getting back to your example, Phase Dragon costs slightly more than two Immortals because it is slightly more resilient. Using 1 big critter instead of 2 small ones, you sure save a card, but you waste time, because it will come out later. Need speed? Play lots of small critters. Need a big punch with few cards? Play dragons. That how it always worked.

[OldTrees]

Draw Cost in units of quanta? Do you mean a card-quanta exchange rate? I already worked on this. Assuming that Quantum Pillar, Nova, Supernova, Cremation and Immolation are balanced:

No I was referring to how a 8|x Immortal creature is worth two 4|y Immortals and thus should have a casting cost more than twice the casting cost of the 4|y Immortals. (assuming the x and y were set at constant values that caused the resilience of the two sets of cards to be equal)

From this we can conclude that the "cost" to activate a card's value is equal to slightly more than the casting cost would indicate. I would like you to try to find a way to determine how much more.

I disagree with that. Methinks that if a creature is twice as powerful as another and have the same resilience, it should cost twice as much. That's how it is in the actual game by the way: Amethyst Dragon costs twice as much as Abomination - or, getting back to your example, Phase Dragon costs slightly more than two Immortals because it is slightly more resilient. Using 1 big critter instead of 2 small ones, you sure save a card, but you waste time, because it will come out later. Need speed? Play lots of small critters. Need a big punch with few cards? Play dragons. That how it works

I underlined your misunderstanding. I said the same resilience. The earlier a card can be played the higher the resilience because games have a finite length. So these two factors Draw Cost and Resilience due to Speed work against each other. But the question is how? By Sunday I should have a means to compare different cards after the  speed factors is removed. I would like you to design a comparison to investigate the balancing force (Draw Cost) when Resilience due to Speed is normalized.

[Midnar]

No I was referring to how a 8|x Immortal creature is worth two 4|y Immortals and thus should have a casting cost more than twice the casting cost of the 4|y Immortals. (assuming the x and y were set at constant values that caused the resilience of the two sets of cards to be equal)

From this we can conclude that the "cost" to activate a card's value is equal to slightly more than the casting cost would indicate. I would like you to try to find a way to determine how much more.

I disagree with that. Methinks that if a creature is twice as powerful as another and have the same resilience, it should cost twice as much. That's how it is in the actual game by the way: Amethyst Dragon costs twice as much as Abomination - or, getting back to your example, Phase Dragon costs slightly more than two Immortals because it is slightly more resilient. Using 1 big critter instead of 2 small ones, you sure save a card, but you waste time, because it will come out later. Need speed? Play lots of small critters. Need a big punch with few cards? Play dragons. That how it works

I underlined your misunderstanding. I said the same resilience. The earlier a card can be played the higher the resilience because games have a finite length. So these two factors Draw Cost and Resilience due to Speed work against each other. But the question is how? By Sunday I should have a means to compare different cards after the  speed factors is removed. I would like you to design a comparison to investigate the balancing force (Draw Cost) when Resilience due to Speed is normalized.

You're trying to say that more speed means more resilience. But more speed means shorter games. Shorter games means creatures stay in play for less time.

Before stretching those tergiversations longer, we should agree on a definition of Resilience. From what you stated, I guess that you understand Resilience as "average number of turns the card stays in play". To me, Resilience is "average proportion of the rest of the game where the card remains in play". Let me illustrate the difference with an extreme example:

A momentumed 200|0 will last exactly 1 turn, but it will most likely stay in play until the end of the game (putting an end to the game itself). By the first definition (average number of turns the card stays in play) its Resilience is extremely low, and it deserves a casting cost of ~50. By the second definition (average proportion of the rest of the game where the card remains in play) its Resilience is extremely high, and it deserves a casting cost of ~400. Which one do you think fits best?

I knew that basing the resilience on hp alone was making a simplistic assumption. However, I would like to avoid any useless complication. Is taking atk and casting cost into account when calculating resilience really worth it? I don't think so, because such extreme cases don't exist in reality.

[OldTrees]

A standard definition of Resilience would be ideal.

When I think of Resilience it means to me the average number of turns the card is out / the average number of turns in a game involving the card in one deck. (aka some metagame considerations)

I do agree with the proportional definition of resilience (the thread in question used a turn based resilience to simplify it to make it easier for people to help me)

More speed means shorter games when you win (assumed 50%), same duration as before when you lose.
The proportional resilience of the card when you win is unchanged because it still takes the same number of card turns to win.
More speed means a card getting used on average at an earlier turn in the game regardless of the winner.
Since your opponent's TTW has not increased (except voodoo) then your card's average resilience
Hence the increase resilience is greater than the decreased resilience using proportion of the game as units.

As for whether including CC and Win Condition into calculating resilience:
Mostly I expect the result I get (by Sunday) to say that most CCs have almost identical but slightly different values. But at the extremes like 0,1,2,10+ I expect the value to be useful. Also from my experience people use a theory resource at different levels and in different ways. Ideally people would decide Resilience last with Power being decided first. As such it might be better to name it R(PC) but that doesn't sound as nice.

[Midnar]

I can think of 2 cases where there's a significant impact of casting cost and/or attack on resilience:
- A casting cost of 0 for an unupgraded creature. In PvP1, players generally don't have quanta during their first turn. Since there's no free creature control, playing a creature on the very first turn will give it one turn of quasi-invulnerability.
- An extra-high attack for an airborne creature. Sky Blitz OHKO wouldn't give the opponent a chance to get rid of it.

 From what I saw, people decide casting cost last with Power being decided first and Resilience somewhat neglected. C=PxR definitely sounds better.

[OldTrees]

C=PxR is what will work best for most card designers. I will still leave a note in an advanced sectioin that deciding P,C,R is the ideal order.

I agree that the border cases will be the only times that there would be a significant impact.
It is more there for completeness and because I already started on the excel sheet before you republished you great edit. Also the excel sheet is more accurate than QI in limited conditions.

But back on the topic of Draw cost:
Obviously C=PxR does not explain a 0 cost. If there were a 0 cost then either P or R would have to be 0 which would make a useless card like relic.

So obviously Cost must include some factor other than casting cost. In addition there is a card that refunds the draw (precognition). This is why I think that Cost=Casting Cost + some constant which I think is Draw Cost.

[Midnar]

But back on the topic of Draw cost:
Obviously C=PxR does not explain a 0 cost. If there were a 0 cost then either P or R would have to be 0 which would make a useless card like relic.

Remember that we are rounding the result at the end. As weird as it may sound, we can have PxR=0 while P≠0 and R≠0. Ball Lightning has 3 attack and 0.2 resilience (rough guess at the resilience of a 0hp creature). Photon has 1 attack and 0.67 resilience. In both cases, PxR rounds to 0.
When it comes to upgraded cards, a final cost of 0 is obtained for PxR≈1.

[Midnar]

So obviously Cost must include some factor other than casting cost. In addition there is a card that refunds the draw (precognition). This is why I think that Cost=Casting Cost + some constant which I think is Draw Cost.

While I definitely agree that Total Cost = Casting Cost + Draw Cost, I also think that the base value of having a creature in play (cremation/mutation/bond fodder) equals the draw cost.

[OldTrees]

So obviously Cost must include some factor other than casting cost. In addition there is a card that refunds the draw (precognition). This is why I think that Cost=Casting Cost + some constant which I think is Draw Cost.

While I definitely agree that Total Cost = Casting Cost + Draw Cost, I also think that the base value of having a creature in play (cremation/mutation/bond fodder) equals the draw cost.

Equating the additional cost to the value for having a creature in play might be accurate but does not help in the case of Spells.

So what is this base value compared to these other values we have? The reason to convert it is that there is a huge theoretical difference between CC/P=R and (CC+k)/P=R.

So what do you think a good estimate for k is? .5quanta? 1quanta?

Also thanks from reminding me about rounding with regard to 0 CC creatures.

[Midnar]

I think that a good estimate for k is 0 quanta for unupped creatures, and something between 1 and 1.5 for upped creatures (i.e. upgrade accounts for a -1 to -1.5 cost reduction, and no change to the base formula).