I think if you want to make your point, you will need to provide an example of something that you can do with a mana crystal (within the first 5 turns of casting) that you could not do had you not cast the crystal, because it has already been pointed out that there are things you can do without the crystal that you cannot do with it. If you cannot find an example, it means that during the first 5 turns, not casting a crystal is better, since the options it provides encompass all the options the crystal provides and more. You need such a counterexample to make your point convincing.

I am going to film my example video soon and here are the things I'm going to go over.
My perspective (of added channel ability)
The opposed perspective (Primarily the mana bonus)
The things that mana crystal allows that you didn't have access to before. (Which is what you have just asked.

Basically there is a rundown of three major elements you work with at the beginning of the game.
Your channeled mana
You starting mana (10)
The ability to carry over mana between turns

These are all elements that change the model used if you incorporate any of them.
Basically my conclusion will be this;
Mana Crystal allows you to summon larger creatures and cards without the need to use your starting, non-replenishable mana, or the need to sacrifice action potential from one turn to carry to the next.

I define action potential, literally, as the stuff you can use to do things. In respect to casting, the primary measurement of action potential is mana. I use the term action potential over mana because it is more clear in the respect that mages do not have to use it and that the value of action potential does not change when it is used, it simply is moved.

my point is that your math does not include the reduced flexibility of bringing the flowers, that's why i challenge your math.

It does actually. The negative clause of the mana spent is the reduced flexibility, because every card has this. As zorro was mentioning that if you drop 2 mana crystals you can't summon Adramelech on second turn, however this is also true of any card that you can cast. If you cast 2 of something else that effects the board differently you also don't have any more reduced flexibility than casting mana crystal. So, in the long run what this says is that whether or not you cast mana crystal did not make it so you cant summon that other big card, it's that you spent any mana at all. That is an effect of playing cards not playing mana crystal, thus the only negative inclusion needed is the mana spent on mana crystal.

The table made by zorro is the best representation IMO, because it doesn't omit anything and is perfect in it's simplicity, it just says how much mana has each mage available to invest into altering the game state by any given turn.

The reason his model is not good is because it assumes that the opponent mage doesn't spend any mana. Where in a real game this is, in fact, possible, it mean that the other mage has sacrificed board presence to save his mana for what we can only assume is a really big spell that could possibly equal the board presence of everything the other mage played beforehand. Since the board presence is another variable when comparing two mages we have to equal them out by having both mages play cards that have similar board presence, and the only measure we have of that is mana cost since we see the function of smaller cards having less action potential and more expensive ones having more.

If one mage casts a mana crystal and the other mage doesn't cast anything and moves forward, thus improving his board position (more zones to target, more space to run away etc) and then spends one mana of the saved mana each turn afterwards, thus simulating the channeling +1, both mages will have spend the same amount of mana by turn 6

In the long run what mana crystal REALLY does is allow for one player to play cards with larger potential. Although, as we have mentioned, there is a secondary way to get cards out with larger potential which is saving mana turn by turn. This is where the actual value of mana crystal comes into play because it allows for the +1 channeling each turn to get out a creature or other spell with larger potential than before. Even if both players spend the same amount of mana then the player with mana crystal will still come out on top because he will have either played larger potential cards faster than the other would have, or he will have more mana left over.

Now since were talking about the subtle reductions in flexibility, I want to show you this. It is true that playing mana crystal (as well as any other card) reduces your flexibility, but the original argument was about how quickly mana crystal "pays itself off" before giving you only positive benefits. The original model was after turn 6 but I argued that it pays itself off sooner because of the benefit of having 1 extra mana each turn. So I used a Valuation of the card to functionally express the benefits over time. If you go to this calculator (https://www.desmos.com/calculator) and input this expression (X-5)+(1*X) which represents my model, you will see the x-intercept of 2.5 which represents how many turns after it is cast to "pay itself off." This even allows for some room for error if you think the benefit of having 1 extra channeling is less than the actual mana gained. If you do think this try putting in .5 where the "1" is and you will see it takes only a little over 3 turns instead of 2.5.

Of course a crystal will give you more options (more mana) in the future, but not during turn 2, 3, 4 or 5. If you value the extra mana provided by 1 crystal during turn 2, you have to value the extra mana of not casting it turn 1, of the potential value of saving that mana from turn 1 to 2.

In my model it does actually benefit you turn 2-5 because you have 12 mana to spend on those turns instead of 10. If you save your mana than you are simply moving the action potential of one turn to the action potential of the next, you aren't adding anything you just end up moving it because you have forgone the potential of a previous turn. So you cannot simply "simulate" the mana crystal as you say. There just happens to be another means of getting those larger cards out. Does that make sense?

But please accept different points of view as not just ignorance,

I'm sorry, I do try my best. Both you and Mortuss have shown care and thought in your arguments against me and I respect that, but I'm sick of it when others just re-iterate what they've said while just ignoring any new evidence that I come up with. That's what true ignorance is.

Benefits of each? The best thing I can think of is how charm can be revealed between attack phases but minor heal gives you an extra die.

What are some of the best uses of charm over minor? And visa versa?

Quote from: DaFurryFury on October 05, 2014, 09:27:06 AM

[...] Mage wars is game almost completely centered around "action potential. "

I like this viewpoint. What methods are available to evaluate decisions we make about potential actions?

This is a concept that is as wide as the amount of cards available to play in the whole game. It's quite daughnting to think about and here's why. In all the examples that I've given to now are limited to the mage's action potential and only with respect to his ability to cast cards. Though we all know that casting is not all a mage is good for. He/she has abilities to support other units and "boost" their potential or even boost their own potential but in respect to attacking or defending.

In reality, when I am calculating the "value" of a card I have to take into consider every trait that the card has including its type, life, armor, even its sub-types. However, in the mana crystal example I am judging its value based solely on its channel return. This relates to action potential in that mana crystal, instead of having action potential on its own, it boosts the mages action potential.

Now when discussing action potential with creatures is yet another complete conversation. You have to take into account what the average damage is and its survivability and tons of other stuff that I'm not ready to conquer yet. In addition a creature's action potential can be manipulated by incantations and enchantments. It's just a whole other ball game when calculating theoretical values of other card types.

Does that explain a little more on what I mean by action potential?

When choosing a base method of finding the value of a card I use the basic equation -M+R
M=mana spent
R=Return

The problem is that "r" can mean 1000 different things. In mana crystal's case the return is based over time and how much it gives you with both mana and action potential. So that's where I get (-M+time)+(1*time). How you evaluate this from an action potential standard is often up to the player and how he uses the gain from the card.

So maybe that can help guide you when making your own calculations?

Quote from: DaFurryFury on October 04, 2014, 10:54:56 PM

Anyway, in my perception, people who disagree with mathematical value just because they don't understand it completely seem ignorant to me. Not to be mean... However, I do not mind at all if the evidence isn't enough for someone to put the card in a spellbook because that is all up to the indevidual to decide if it's worth it. I don't have mana crystals in all decks I just wanted to show how the value of the card can be expressed by a different model.

Coming up with a formula like Z+2X-Y (Z=mana when casted, X=number of round since casted, Y=mana cost of the mana crystal) to represent the value of mana crystal is ignorant. The formula is Y+X-Z.

Okay, dude, really.... I think you're the only one left that disagrees. And that's fine. Think what you want but it seems at this point you are just ignoring facts because you don't want to be wrong. I've done all I could to try and reasonably explain my points to you. Whether or not you change your mind is not important to me. I just like valuating cards using theoretical mathematics because it helps ME understand the game at a deeper level. I just felt like sharing my findings to see what other people could gain from it. I plan on applying the same theories to other cards and when I present my findings im sure you will be there to contradict me for fun. Until then I'll stay silent on my discussion to you.

If anyone else has any questions about how I set up my equations and what it means I will be happy to oblige.

I meant to make this post awhile back, sorry bout the delay. I used my design of the hex board and it went fantastic. To reiterate the board is in this setup.

A1 A2 A3 A4 A5
   B1 B2 B3 B4
C1 C2 C3 C4 C5
Start zones are A1 and C5

This setup made the games feel no different from the basic board whatsoever. So yay proof of concept. One of the only differences is that there are two extra spaces. This can mean a lot when it comes to zone exclusives but since the "board halves" are still accessible in two moves by any mage it changes little. A mage that relies on zone exclusives has almost no extra advantage either way. This formation also makes it so warlord doesn't have any disadvantage with his outposts.
Walls have already been discussed. I feel like the best way to do it is the "two prong" method as it allows you to make a wall across the whole board using three walls.
I found no other real change in gameplay as far as 1v1 goes. If I were to do any more I would likely use the shape originally discussed.

Anyway just wanted to update that hexes make a good substitute if you like them better even for 1v1. I just don't like squares since they can't do circle representation real well. But in a game like this it really doesn't change a whole lot I've found.

But since the card reads "the controller gets plus 1 channeling" and not "controller gains 10 percent of mana of whatever he currently has during upkeep", the percentage point is rendered moot. It doesn't matter how much the controller has, he will always gain 1 extra mana in addition to any he would get before.

But that isn't the point. It doesn't matter what is cast. Given infinite mana the players will cast the biggest things they can as soon as possible, but since you don't get infinite mana, you have to choose to wait to cast big stuff or cast smaller things more frequently. A card like mana crystal gets you 1 channeling closer to having infinite mana so you can cast the bigger stuff faster. My equation doesn't take into account what the opponent casts because it doesn't have to, it only is pertinent to the mana crystal and your channeling.