On mana crystal effects and efficiency

[ACG]

Sorry, that question was misworded. What does your equation represent? What is (x-5)+(0.5*x) equal to?

Edit: Just reread your statement - it seems that you are saying that this is the "value" of the mana crystal. What is the relationship between the value of the mana crystal and the state of the game? Can you give an example of the value of another card so we can see how you are computing it? For instance, what is the value of Barracks?

[DaFurryFury]

The end value number is simply an abstract representation of a card. The number exists simply because we want it to. When applying the possible uses of this card, we might compare one card's value index number to another's. So to pick one out of a hat let's use Goblin Grunt.

A grunt cost's 4, has 4 life, and an attack of 3. I have yet to do a full valuation of a creature card so I'm just going to say that each life has 1 value and each attack die has 1 value. In this case that mean that a life or a die is equal to 1 mana in terms of comparing to mana crystal. so grunt's equation might look something like this: (-4)+(4+3y). Y=number of times he has attacked during the game. If we assume that goblin grunt attacks every turn you can translate y to x or turns after it was cast in the same way we did with mana crystal. This is of course excluding the factor of the possibility that it literally can't attack for a certain instance and thus the value over the time of the game would decrease.

But for the sake of experimentation, we can estimate. So let say a game last 8 rounds and the grunt is able to attack on 5 of those rounds.

Mana Crystal (7-5)+(0.5*7) = 5.5
Goblin Grunt (-4)+(4+3y)   = 15

In this case the goblin grunt was worth nearly 3 times more than the mana crystal, but that is likely a flawed outcome due to that attack dice are not necesarilly equal to mana or action potential. Could be more, could be less, but it's all theoretical. What my argument says is that the increased action potential that mana crystal gives you increases the game value of itself.

[Wildhorn]

Basically, your formula is (T-C)+(A*T)

Where:
T = number of Turns
C = crystal mana Cost
A = totally subjective variable that you call "Action potential".

[DaFurryFury]

The A is the VALUE of increased action potential. Not action potential itself. There would also be a variable for the value of the mana it gives you back but it's usually 1 so I left it out since 1 times anything itself. So the equation might look like this expanded a little more. (B*T-5)+(A*T)
B=value of mana
A=value of action potential

So theoretically each unit of A or B could be increased or decreased at will to represent various possible valuations of each element that the mana crystal gives you. The hard part here is how we relate A to B. I use the template that mana gained should be directly inverse to mana spent so that makes B equal to 1 just like each mana spent on the card. So then we have to decide at what ratio is the action potential bonus is to the mana. My current model says that action potential is worth half of possible mana usage. So that's why its .5.

[ACG]

I think I know what the problem has been in this discussion - we are not talking about the same thing at all.

You have created a model to give you the "value" of a card. The problem is that it is not possible to assign a value to a card, due to the complexity of the resources in the game, and therefore this analysis does not tell us anything useful.

To have a meaningful discussion about payoffs in Mage Wars, we have to stick to things that can be measured. Mana fits this bill perfectly, since it has an explicit value. Life/Damage can likewise be easily analyzed. Actions are trickier to analyze, and attacks even more so, since they sometimes have traits. Traits are impossible to value objectively.

What the no-early-payoff perspective has been arguing is that strictly in terms of mana, the mana crystal pays off by the 5th turn after casting, which is a straightforward calculation (if we neglect future discounting, which complicates matters more than I want to get into). This analysis treats the net mana gain/loss as the value of the crystal.  Include actions into the analysis, and it takes at least 6 turns (possibly more) to pay off, but the exact number cannot be given since there is no objective way to translate actions into mana that applies to all situations.

To illustrate a "model" based on this (Warning: this is a thought experiment - I am not proposing this as an objectively true model), consider the following:

1. Since meditation amulet values a full action at 3 mana, and moving is clearly less important than action (not always true, note), let the value of a quick action be ~2 mana.
2. Aside from costing an action and providing mana, the crystal has no other significant benefit, so we may neglect all other properties (we could look at spellpoint cost, but there is no clear way to relate that to mana, so we'll assume that the player has an arbitrarily large spellbook).

Then the (mana) value of a crystal as a function of turns X after casting is
[1 mana per turn]*[X turns]-[5 mana spent]) - [1 quick action = 2 mana] = X-7 mana
Therefore the crystal breaks even (has mana value = 0) only on the 7th turn after casting.

Obviously, there are a number of circumstances that could cause us to value a quick action differently, but the point is that each part of this model is tied to a measurable aspect of the game, even if the valuations are subjective and vary based on situation. Valuing a quick action as 2 mana is not based on a whim - it justifies itself by analogy to the meditation amulet. This model attempts to assign a mana value to the crystal, i.e. the amount of mana that the crystal is worth as a function of time. This is the sort of model that can be profitably discussed.

The reason that we do not accept your model is because "Action potential" does not appear to be tied to a measurable aspect of the game. The (X-5) part of your equation is clearly the mana cost, but we don't see how you get + 0.5*x. How did you you get 0.5, exactly? What is the logic behind valuing action potential at that? And how does action potential relate (in a direct way) to resources in the game?

Your model does not have a clearly articulated justification, and it is not clear what your model is measuring. If it expresses the mana value of  the crystal as a function of time, then what justification can you give for 0.5*x? If it is not the estimated mana value of the crystal, then what is it?

It is not possible to give a single number to any spell that represents its entire value. The mana crystal is possibly the simplest card there is, and we still can't give it an objective mana value, let alone an overall value. Others have tried to value cards in the past and have failed - there are just too many variables and too many possible game situations for any analysis to give an objectively true single value. The best we can do is to try to value aspects of spells - in the case of the crystal, we can analyze how long it takes to pay for itself.

[Satenus]

Objectively a Mana Crystal Effect (channeling +1) breaks even after X turns (X = Mana Cost) because only then you'll get back the mana spent and from then on it's pure gain. That is true, no arguing about it.

However, speaking of efficiency brings concepts that are not being taken into account in the discussion, and that is Plan, Objective and Purpose.

Efficiency means that the Objectives are met using the minimal possible amount of resources and time. The Objective of the game is to defeat the opponent, but there are many different possible Plans to do that. And inside each Plan, each single Card has its own Purpose.

So, if a player's Plan includes Mana Crystal Effect's Cards and has a clear Purpose for them, and the Objective is met, then we can say that the Mana Crystal Effect Card is Effective, if not necessarily Efficient.

In summary, in my opinion, a Card (or effects like it) cannot be evaluated in the void, it has an very complex game around it, and may find a place in the Winning Plan of any player.

What some players will see as a unworthy expenditure, others may see as an rewarding investment. 

[ringkichard]

(I want to start my making sure everyone knows that mana carries over from turn to turn. It's not like in MtG, where you lose your mana at the end of the turn. You don't need a 15 channeling to cast a 15 mana creature. All set on the basics? Good.)

--

Ok, if I'm understanding this debate right (I skimmed it, it's long) it comes down to the question "which is more important, total mana or mana/turn?"

Which is a bit like asking, "in a race, which is more important, distance traveled or speed."

So, some people are saying, "Duh, distance. The person who runs further is farther ahead, and winning."
And other people are saying, "No, speed is as important as distance, even before you catch up in distance, it's an advantage to be going faster. The faster player has an advantage, even if they're behind, and even if the race ends before they catch up."

To which I can only say that the Hare had an advantage in speed, but it was the Tortoise's advantage in distance that carried the day.

(Side note: It may be helpful to think of this in terms of calculus (which I studied a long time ago, please forgive any errors). Velocity is the derivative of position, and acceleration is the derivative of velocity.  Likewise, channeling is the derivative of total mana, and the number of mana flowers you cast or lose in a turn is the derivative of channeling.)



... But maybe there is some advantage to increased channeling, too? I haven't really thought this one out all the way through, but there's the issue of the step function of mana accumulation. Once you're down to 0 mana (which can happen easily) it is true that 10 or 9 mana a turn can leave you bottlenecked. If you have many ways to spend mana (e.g. familiar, spawnpoint, special abilities, activation, quickcast, revealing enchantments) your mana can quickly become the most scarce resource.

Now, of course, if you didn't cast a mana flower, and instead attacked,  you'd have 5 extra mana and wouldn't be as bottlenecked.

And this is where the pro mana flower logic breaks down for me: If I save the mana, instead of spending it on a Flower, the next turn I have far more options available than even +1 channeling would give me. It seems like we've been ignoring the opportunity cost of the mana.

[DaFurryFury]

And this is where the pro mana flower logic breaks down for me: If I save the mana, instead of spending it on a Flower, the next turn I have far more options available than even +1 channeling would give me. It seems like we've been ignoring the opportunity cost of the mana.

Please watch the video I posted to better understand my points. I know you're new to the conversation but you are regurgitating information that has been said and I have reacted to in detail. https://www.youtube.com/watch?v=oqMV0wBFu54

You have created a model to give you the "value" of a card. The problem is that it is not possible to assign a value to a card, due to the complexity of the resources in the game, and therefore this analysis does not tell us anything useful.

This is incorrect. You can assign a value to anything and, in concept, it's actually pretty easy. By analyzing traits and giving each certain effect value by ratio you can create an index number to represent a card. My analysis does not include every single trait that the mana crystal holds but rather the most important ones. This does not give the most accurate index number but it's good enough for the relationships we are trying to draw between cards, because the only application of the index numbers we can create is only relevant in comparison to each other. To say that it is impossible to create index values of a card is to say that you cannot compare goblin grunt to adramelach and definitively determine which is more useful. You are correct in saying that there are a ton of elements to consider when doing this but just because the solution isn't simple, doesn't mean it's impossible. I also find it curious that you deny the existence of such a process then immediately attempt to due one with your meditation amulet example. (Which is interesting by the way, I like it. So much that I may include it by concept in my own valuation to make it more accurate. However I'm not sure I totally agree with your valuation of a quick action. Actions are often in flux because one possible and often feasible action is to do no action at all. But I digress.)

Now to answer the action potential question. Action potential IS measurable, it is what a card has the ability to do, more or less. Now this is a complex concept as it is "potential" meaning it has not done what it has the ability to do. Mana crystal, rather than increasing it's own action potential, increases your mage's action potential, and that is where I'm getting the .5 by physical account. It increases the amount of stuff the mage can do on a per turn basis. The fact that .5 is the number .5 is because I believe that, by ratio, the increase in action potential is worth half of that of each mana it gives you back. So basically, the card's index value increases by 1.5 each turn after it is cast until the end of the game which is the only point in time which you can fully and accurately asses the index value of the card. That is why we must use variables in it's value assessment equation.

So perhaps you are correct in saying my valuation is not complete objective, but it's also not objective from the stand point of each mage as well. Especially until we include a clause concerning spell points and those heavy on zone-exclusives.

So in conclusion, no, my valuation is not simple and is far from totally complete, but that doesn't mean that it is irrelevant. Isn't that what progress is anyway? Finding something that works until we prove it wrong and then we refine it further so it works again.

[Sailor Vulcan]

You should probably read that one article on resources. Can't remember what it's called. What it basically said was that there's an order in which starting resources like mana/channeling get converted into final resources (damage/life).

In fact, I suspect the entire game state at any one point in time can be described as follows:


(Spellbook points+positions/ranges+stats+traits+usable abilities-discounts +or- initiative)_friendly

–(Spellbook points+positions/ranges+stats+traits+usable abilities-discounts +or- initiative)_enemy

Where "discounts" refers to any resource discounted, not just mana. Using this definition, casting the spell rouse the beast would be converting mana into an action discount.

Also removing cards from your spell book is treated the same as subtracting spell book points.


All this said, some of these variables are really just sets of variables that have been grouped together for the sake of being concise. It's not impossible to calculate the value function of a spell. But by the time you've calculated it, it will probably have already changed. Unless you have a really good computer and no life.

[DaFurryFury]

If you can link me to that I would be interested in taking a look. Sounds interesting. One of my favorite studies of mage wars theory is the study in GO. Worth a look and if you are familiar with the game of Go it makes mage wars seem so simple. http://forum.arcanewonders.com/index.php?topic=11042.0

Also, I don't think a valuation of the entire game in necessary to calculate a value index of a single card. They have to be able to be separate entities to be able to be compared I think. The game state valuation is interesting, it probably is usable for discussing combos of cards and increased and decreased effectiveness of such based off of game position, mage, and various other elements. I.E: The mana crystal player may be at more of a disadvantage if the opponent plays several ranged creatures and spells to quickly destroy the mana crystal.

[Borg]

Also, I don't think a valuation of the entire game in necessary to calculate a value index of a single card.

IMO it's not possible to calculate a single value for each card as each card's value changes all the time.

The Value of Vampirism changes greatly depending on :
1- How many attack dice do you roll
2- How much life has the target left
3- is the opposing creature living or non living etc ...

A Spell like Force Hammer has a different value depending on whether the target is a conjuration or not ...

[ACG]

Now to answer the action potential question. Action potential IS measurable, it is what a card has the ability to do, more or less. Now this is a complex concept as it is "potential" meaning it has not done what it has the ability to do. Mana crystal, rather than increasing it's own action potential, increases your mage's action potential, and that is where I'm getting the .5 by physical account. It increases the amount of stuff the mage can do on a per turn basis. The fact that .5 is the number .5 is because I believe that, by ratio, the increase in action potential is worth half of that of each mana it gives you back. So basically, the card's index value increases by 1.5 each turn after it is cast until the end of the game which is the only point in time which you can fully and accurately asses the index value of the card. That is why we must use variables in it's value assessment equation.

The point of my example was to illustrate what I mean by justification and measurement. When you make a model, you need to justify where each number comes from. It is obvious where x-5 comes from, but it is not clear where 0.5*x comes from. How did you arrive at the conclusion that action potential is worth 0.5 per turn? ("I believe it is" or "it feels right" is not justification) You say that it is measurable, but "stuff that a card has the ability to do" is not quantifiable. To explain how you arrived at 0.5, you need to be specific about what contributes to this and why. In my example, I showed one attempt to give a mana value to a quick action by analogy to the mana value of a full action suggested by the meditation amulet. Regardless of whether it is true, this is a justification, and the formula contains only measurable quantities (amount of mana and number of quick actions).

It is impossible to measure action potential, because it is not a resource in the game. Actions are resources. Mana is resources. Each spell card is a resource. Each attack that a creature has is a resource. Mage Wars does not have anything called Action Potential, which means it is a derived quantity. But you haven't given us a way to derive it, so it is of little use in analysis.

And when we talk about value, we absolutely need to specify what type. You can only value something in terms of other things - a carton of eggs is worth $3, or a pound of acorns, or a gallon of water, but not "4". I have been analyzing the mana crystal by putting a mana value on it ("mana value"). Putting an abstracted index as a value makes it impossible to analyze something because it is unclear what the number means.

As others have stated, value fluctuates constantly in mage wars, so the payoff time may vary. But I have yet to see an example of a situation where the crystal pays off in fewer than 5 rounds.

[fas723]

This is incorrect. You can assign a value to anything and, in concept, it's actually pretty easy. By analyzing traits and giving each certain effect value by ratio you can create an index number to represent a card.

I really admire your patient in this topic DaFurry! All the credits to you for that! 
About a year ago I made a creature evaluation that were supposed to end up with an equation where you could calculate the mana efficiency of each one. It included all aspect of a creature (health, armor, attacks, traits, etc) with a mathematical method that didn't use any arbitrary assessments at all. I still think I got quite close and I'm still thinking about how to improve it. However it encountered a lot of resistance just like this topic has done.  The main reasons it failed was two:

- People didn't agree with the model (specially the trait evaluation)
- People didn't understand the how the model worked and how to read the results.

The topic kind of ended with a loose end since it was hard to get buy in, very much like this one. You can read about it hear if you like:

http://forum.arcanewonders.com/index.php?topic=13360.0

Now when I read this thread my suggestion to you is to try and make a model were you don't select any value by yourself. Let the model calculate them / assign then for you. The value of your coefficient "A" (action potential) must be proven somehow. Not just set to number. That will give you buy in I think.

[fas723]

Also, I don't think a valuation of the entire game in necessary to calculate a value index of a single card.

IMO it's not possible to calculate a single value for each card as each card's value changes all the time.

The Value of Vampirism changes greatly depending on :
1- How many attack dice do you roll
2- How much life has the target left
3- is the opposing creature living or non living etc ...

A Spell like Force Hammer has a different value depending on whether the target is a conjuration or not ...

Not sure I agree 100% here. To me the only value a card can have is in terms of mana. AW has release Vampirism as a enchantment and had set a fixed value to the trait. So in this aspect the trait value is quite clear. And that goes for many other trait as well.

With that said, the effect of Vampirism will be very different depending on the current play state (not to be confused with value of the trait/card)

[Sailor Vulcan]

Also, I don't think a valuation of the entire game in necessary to calculate a value index of a single card.

IMO it's not possible to calculate a single value for each card as each card's value changes all the time.

The Value of Vampirism changes greatly depending on :
1- How many attack dice do you roll
2- How much life has the target left
3- is the opposing creature living or non living etc ...

A Spell like Force Hammer has a different value depending on whether the target is a conjuration or not ...

Not sure I agree 100% here. To me the only value a card can have is in terms of mana. AW has release Vampirism as a enchantment and had set a fixed value to the trait. So in this aspect the trait value is quite clear. And that goes for many other trait as well.

With that said, the effect of Vampirism will be very different depending on the current play state (not to be confused with value of the trait/card)

The value of a card just equals its mana cost? That is just not true. This is not fullmetal alchemist. There's no rule of equivalent exchange where the output resources (the stuff that gives it value) must always be equal to the input resources (actions/mana).

Case in point, meditation amulet costs 4 mana and a quick action to cast. After that each round you can choose to use a full action (the equivalent of two quick actions) to gain three mana. In terms of mana alone, it breaks even after only two uses. If you were only measuring it by mana, it would get more valuable over time. However, no matter how many times you use it, meditation amulet actually never breaks even in terms of actions and mana combined. It is a net loss of actions/mana over uses:

-4 mana-1 quick action
+3 mana-1 full aciton (~2 quick action)

=~(-1 mana-3 quick action)

+3 mana-1 full aciton (~2 quick action)

=~(2 mana -5 quick action)

+3 mana-1 full aciton (~2 quick action)

=5 mana -7quick action

So meditation amulet's total output never exceeds the total initial investment. You're losing actions faster than  you're gaining mana. That's why meditation amulet is a lot more useful in builds with lots of creatures as opposed to solo builds. A net loss of your mage's action is less detrimental when you have multiple other creatures that can take actions (more than your opponent).

Does leather boots (cost 2 mana) have the same value as crown of protection (cost 2 mana)? It still varies, of course, but if you're a priestess, that uses creatures other than herself that don't already have more than 3 or 4 innate armor, then it very often does not have the same value. Crown of protection can increase armor by more than 1 over time, but only on non-mage creatures (whose survival often isn't as important as the mage's). Leather  boots can increase armor by only 1, but can be used on the mage, and cannot be used on any non-mage creatures. Also, when do these two spells break even?

They both cost 2 mana and a quick action to cast. Then crown of protection costs 2 more mana and a quick action for each armor given. If we were talking purely in terms of total armor gained, crown of protection generally wins. If we're talking in terms of total net resources gained or lost, leather boots wins:

Leather Boots                      Crown of protection

-2 mana -1 quick action        -2 mana-1 quick action
+1 armor                              +0 armor

                                                -2 mana-1 quick action + 1 armor

                                              =-4 mana -2 quick action+1 armor
                                               
                                                 -2 mana-1 quick action +1 armor

= -2 mana-1 quick action          =-6 mana -3 quick action +2 armor
+1 armor           
+1 armor


No, the value of a spell does not just equal it's mana cost. TBH I think a card's spellbook point cost is probably a MUCH closer approximation of that.