On mana crystal effects and efficiency

[Wildhorn]

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.

[DaFurryFury]

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.

[fas723]

To put some fuel on the fire, I'm not sure I agree with any one of you. 

1. It is quite obvious (apperently not every one here) that the crystal will give you bennefits directly from the trun after it is cast. Thus, you don't have to wait 5 turns for the crystal to pay of. Basically you can use the first earned mana the secound it is obtained.
2. Howerer, to say you would gain some leverage instantly (turn after it is cast) isn't correct either in my oppinoin. Think about it. How can a "stored" mana reserve be percived as worse then mana that will will be gather later? It is  just don't add up. To have mana available is way better then recive mana in the future.

I give you a few exampels:
Let's flip the thinking (it might be easier to see that way)
Let's say you have a incantation that cost you 0 to cast. If you could choose between these tow options what would you take:

- Gives you 5 mana (the no crystal example).
- Gives you 1 mana turn 1, 1 mana turn 2, ... , 1 mana turn 5 (the crystal example)

I bet no one will take option 2?
Question is; how many turns would you say option 2 requier for you to pick it over option 1?

Note: you will not save an action in the "no crystal" since it forces you to save the mana in order to make the example accurate, thus passing the action.

On the other hand, if you make a large net earn early by casting a crystal why not cast as amny as you can? Why not cast 6 crystals and 6 flowers? If the theori is correct that you will get the upper hand for each point extra channeling you have against your oponent no matter what, well just keep cast your crystals. To my this can't be true. Why? Not one signel crystal will put any threat to your oponent.

After I have been thinking about this for a while, my thoughts on this would be that it depends what you do and when you do it with your alternative action/mana instead of casting the crystal. If you just store it the crystal option will be superior earlier then 5 turns. If you invest in the mana for your strategy imideatly (turn 0, same turn as crystal would have come out) the gain over casting a crystal is at its maximum. With this said; if you are in between the two exampls and save these five mana to counter your oponent you have to do so prior to turn 5 to gain from it, otherwise the crystal is better.

Conclution: It depends when the 5 mana you have not cast the crystal with is used to know if it is better or not.

The discussion with starting mana pool can easily be see through if play with it a bit.
Let's say all mages start with 1000 mana, who would cast a crystal then? Correct, on one would since it would impact the game at all. Now we can reduce it to 500, and then 250, and then 100.... The closer to zero the better the crystal gets. So saying 10 is equalt to 0 is just not correct.

That was my 0.02$.
Hope it didn't offend anyone. 

(Sorry for all the spelling errors. It is early here in Sweden)

[gerni]

Hi guys, I just followed this thread loosely. Anyways, in my opinion (and that has been said) it makes little sense to look at calculations "in vacuum". Investing in channeling can give you a "game advantage" (besides the fact that it might get you a channeling advantage over your enemy). But that is not necessarily the case.

As already mentioned, there can be other advantages to aim for, i.e. "tempo" or "action" or "decision" advantages. You have to play to your mages/strategy's strengths.

Don't get me wrong, I really like theorycrafting or abstract scenarios to evaluate a card's impact. But in this case, I am not sure if it is helpfull (or outright possible) since the above mentioned side effects.

When planning a book, I tend to build around openings (and tradeoffs). I often ask myself:

• How can I get the most tempo/pressure on the enemy, while stay on par with his actions?
• How can I get the most actions while stay on par with channeling?
• How can I surprise my enemy? (force bad decisions)
• How can I be fexible to my enemie's actions?

according to my gameplan, a mana crystal might be a good or a horrible conjuration to play. You can't mold that into a formula.

As little sidenote (since this is theorycrafting), I think forcing hard decisions (playing unpredictable) is the way to win games.

[Gregstrom]

Actually... option 2 as given has a place, but it's pretty niche.  If you know your opponent has ways of destoying your stored mana, the drip feed is likely a better bet.

[DaFurryFury]

The reason that the original 10 mana that everyone gets has to be removed from the equation is because it increases the action potential of all mages and is equal between mages no matter what. Though you are correct in saying that the more mana you have the less impact mana crystal will have. You have to consider mana crystal on its own on any one turn, not just first turn. Thus, you must remove the original 10 from the equation when calculating its value.

However, since you mentioned it I will go over what the 10 mana does to the effect of the card. Mage wars is game almost completely centered around "action potential." That is what you can do in one turn. So in this example I won't be talking about mana crystal I will be talking about two mages, one with 9 channeling and one with 10 channeling.
On any one turn now matter what round it is the increased action potential is equal to the channeling of each mage. If you have any mana more than your channeling on your turn its because you chose to withhold some potential on a previous turn to use it this turn. But in the end it always equals out. The mage with 9 channeling might have more mana than the mage with 10 but that will only happen in a case where the Mage with 9 decided to not use his potential and the Mage with 10 played a larger turn than the Mage with 9.

What the 10 mana does is increase both mages action potential for the first turn. However this 10 mana is non replenishable. Only the 9 or 10 you channel is replenishable. So lots of people tend to hold on to this mana for later turns. Once that 10 mana is spent you are completely reliant on your channeling. So basically instead of mana crystal allowing you to play more than the opponent, it allows you to play more than your opponent without dipping into that non-replenishable supply. So even though an opponent could potentially play more than you, you still come out on top since you spend less than your opponent out of the original 10. So that's why you have to remove the 10 from the equation. It doesn't change any of the actual math. It simply adds a little to each side without advantage to one or the other, even if it changes how you might spend your first couple turns.

So I understand your confusion. Hopefully this clears it up some more.

[wtcannonjr]

[...] 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?

[Wildhorn]

The reason that the original 10 mana that everyone gets has to be removed from the equation is because it increases the action potential of all mages and is equal between mages no matter what. Though you are correct in saying that the more mana you have the less impact mana crystal will have. You have to consider mana crystal on its own on any one turn, not just first turn. Thus, you must remove the original 10 from the equation when calculating its value.

No you can't consider mana crystal on its on on any one turn, because a game has a finite number of turns. You can't manipulate data to fit your needs.

If a game last 6 turns, no matter what you can say, mana crystal will have zero benefits. You spent more mana than you will ever get back.

And what you do not seem to understand is that a player not spending the mana on a mana crystal can fake the equivalent of a mana crystal for the 5 next turns, but if needed, can spend the "remaining" mana.
That's why a mana crystal doesnt give any benefit before the 7th turn, because the same result can be simulated until the 7th turn but in case of emergency the stored mana can be spent.

[DaFurryFury]

[...] 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?

[DaFurryFury]

On the other hand, if you make a large net earn early by casting a crystal why not cast as amny as you can? Why not cast 6 crystals and 6 flowers? If the theori is correct that you will get the upper hand for each point extra channeling you have against your oponent no matter what, well just keep cast your crystals. To my this can't be true. Why? Not one signel crystal will put any threat to your oponent.

You bring up an interesting point as it is true that mana crystal has no payoff if you don't use the mana you're given. Though, I think the answer is in that sentence. "No payoff if you don't use the mana." By the same respect my channeling value has no meaning unless I spend it meaningfully. If I spend it on more mana crystals I will simply be gaining more mana to spend on what we would assume are other things to meet my ends.

It's like investing in the stock market. I give money away so I can gain money with which one would assume that I spend on food, living, and entertainment. But i leave a little so I can continue to gain more money to spend on other things.

[zorro]

I think you are also having trouble understanding my original points.

If i undestand what you say, your calculations try to include not only the mana cost, but the ongoing flexibility. But please accept different points of view as not just ignorance, my point is that your math does not include the reduced flexibility of bringing the flowers, that's why i challenge your math.

As a (naiff) example, if you drop two flowers first turn, you can not drop adramelech second turn. If you are a warlock and drop 1 crystal fist turn, you can´t drop Lord of Fire protected with Nullify second turn. That's reduced flexibility. Anyway, having more mana allows you to use more and/or more powerfull spells.

Hypothetical arguments about players for some reason setting aside ten mana on round 1 in order to drip-feed it into their usage over the next 10 rounds feel contrived to me. 
[...] 
Arguing about long-term disposal of starting mana may be missing the point.

But I think we all agree that, in a given turn and considered alone, haven X+Y mana is always better, and provides for mor flexibility, than having just X. So hypothetical arguments can be usefull to avouid the incredible complexity of considerign every posible card.

Long-term disposal of starting mana is just the point in dropping mana crystals, isn't it?. You dispose your starting mana in order to use it long term in a different distribution. You spend mana early to have mana later.


...

I will post again my table :

turn	Crystal	No-Crystal	diff
1	10	20	+10
2	22	30	+8
3	34	40	+6
4	46	50	+4
5	58	60	+2
6	70	70	+0
7	82	80	-2
8	94	90	-4
9	106	100	-6
10	118	110	-8
11	130	120	-10
12	142	130	-12

We can´t go into specific plays (minotaur, acid ball, whatever), since they are too many. We can look at available mana, wich will give us available options (we all agree?).

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.

By casting mana crystals, you reduce your total mana during turns 1-5, get in par turn 6, and get an advantage in mana and flexibility starting from turn 7. And will not be on par with the advantage provided by not casting them until turn 11.

Of course mana crystall gave you flexibility in other order, they give you mana for whatever (while a discount ring, for example, is more efficient, but lessflexible in that regard). But even while they can be usefull for some specific builds and plans, the do no pay off until at least turn 6 (and in my opinion, generally even later).

PS: typos...

[Mortuss]

So, I'm with Wildhorn and zorro.
The thing is, Mana Crystal doesn't affect the game state in any way (well, it blocks one zone in its exclusivity, but I don't think that is important). It gives you mana, which give you more options, but it doesn't threaten your opponent, nor does it negate any of the threats made by him.
There were many different models presented in the thread, so I'll try to talk a bit about some of them.
In the model where each mage spends 5 mana each turn, mage who cast the crystal indeed has more mana, but you have failed to mention the effect of the 5 mana card, that the other mage cast.

If you look at the crystal on turn by turn basis, assuming both mages spend all of their available mana each turn, mage without crystal gains huge boost in round 1, because he spend his mana on something stronger and more expensive, than the mage with crystal, who in turn gets a small advantage every turn afterwards by having one more mana available and thus having more options.

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

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 meat of the argument is this : mana is more valuable in the beginning of the game than in the later phases. If you can get a stronger board position and advantage early, it is likely that your opponent won't be able to pull back, even though he has more mana.
It is as fas723 has written (or at least what I think was his point), if you can use the 5 mana and action to get decisive board advantage, then you are better of without the crystal. If not, then the crystal will give you the advantage in time. 

[DaFurryFury]

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.

[Mortuss]

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.

That is not what the table says. The table shows how much mana you have available so far to alter the board state, including the mana you have spent to do so. By altering board state, i mean playing a card that either presents a threat to your opponent or negates a threat made by him. That means when I play a creature, it is mana invested in changing the board state, while mana invested in playing the crystal is not, since it is neither a threat nor a solution, it just allows you to play bigger threats later. So, for example, by the end of turn 4, the mage with crystal could have spent up to 46 mana to alter the board state, while the mage without the crystal could have spent up to 50 and that is why he has the advantage.
 

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.

No, the player with crystal cannot play larger potential cards faster. Lets take the turn 4 as an example again. The player with crystals could have invested up to 46 mana into threats so far, while the player without crystals could have invested 50 mana into threats. I think its obvious that 50 mana can buy bigger threats than 46 mana.

[zorro]

The table made by zorro is the best representation IMO, [...] 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.

Well, i tried to assume nothing, as mortuss said, appart from including the cost and direct effect of the mana crystal (which is very straight forward). I tried to abstract from specific cards and plays. My example of adramelech may have induced to think you the opossite - my bad.

I just value available mana, since I think more mana means more and more powerfull options anytime, be it bigger creatures, a more powerfull heal, or the chance of your face down enchantments being more things for your opponent to worry.  If we ignore the potential of extra mana for no-crystal player on first turns, it would be the same as ignoring extra mana of crystal player later turns - both players would try to cast the best possible spells for the current situation (and available mana) and get an edge from it.

Of course if your plan involves not using mana first turns mana crystal, it can be a great play - but assuming than casting it first turn lets you in a better position right from second turn is too much.

On a side note, the mana crystal as an advantage, the great flexibility of it's effect, but that come at a cost - which is that mana crystal is way less efficient than other spells, like discount rings or spawnpoints. I think most of the time a more focused option will be always more efficient.