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Author Topic: On mana crystal effects and efficiency  (Read 67838 times)

zorro

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On mana crystal effects and efficiency
« on: October 03, 2014, 02:40:53 AM »
Hi!

I wanted to take this topic apaprt from its father since it went pretty off topic. Original post can be found here, but ere is the start of the discussion on the mana crystal:

To break the values down further I'll explain it like this.

Mana Crystal gives the controller increased channeling, not mana. Channeling by extension gives you mana. So the (time of game-5) does give you it's effectiveness on a simple terms level. However, don't confuse channeling with just getting mana because Channeling has another benefit. That is, it increases the amount of mana you may cast on any given turn. In the long run my opponent may have gained much more mana than I but I was still able to cast larger spells earlier because I'm gaining mana faster, as opposed to slower but consistent.

Here's a turn by turn count.
Lets say 2 mages have 10 channeling.

Turn 0 = 10 mana <------ for the sake of removing values we don't need because the starting value is the same for everyone and it doesn't change the math at all.

Turn 1 = Channels 10 mana.(10) Plays mana crystal (-5). End Turn = 5 mana left. [For the sake of simplicity each turn both mages will spend 5 mana so that I can illustrate the concept of acceleration and not simple mana totals]
Turn 2 = Channels 11 mana.(16) Plays card (-5) End turn = 11 mana left
Turn 3 = Channels 11 mana.(22) Plays card (-5) End Turn = 17 mana left
Turn 4 = Channels 11 mana.(28) Plays card (-5) End turn = 23 mana left

Player 2
Turn 1 = Channels 10 mana.(10) Plays card (-5) End turn = 5 mana left
Turn 2 = Channels 10 mana.(15) Plays card (-5) End turn = 10 mana left
Turn 3 = Channels 10 mana.(20) Plays card (-5) End Turn = 15 mana left
Turn 4 = Channels 10 mana.(25) Plays card (-5) End turn = 20 mana left

Hopefully you see the pattern by now as the ever increasing ratio starts to benefit the owner of mana crystal. This ratio is described by the clause in my equation being (X*1) where x = the amount of rounds that the mana crystal is in play. "1" is a placeholder because these equation could describe the same relationship if multiple were in play.

So in conclusion, not only does the card grant you mana after turn six (which really is just a bonus for the main benefit), you gain a rate of gain bonus over your opponent which allows you to play larger more quickly. Even though you "wasted" 5 mana. Though by my calculations the "value" of mana crystal is zero after 2 and a half turns so each turn after turn 3 is when you start to reap benefits.

Now let me jump the gun here and ask myself, "why is the ratio bonus as equal to the flat mana gain bonus that takes place after 6 turns?" Well, the fact that the ratio bonus is equal is only relative to how much of an advantage it gives me over the other player. So in my opinion the values are equal, but maybe you aren't like me and think the ratio increase is worth only half that of the bonus mana crystal gives you after 6 turns. So plug in ".5" where the "1" is on the equation. The result is that it still only takes 3.33 turns to "pay itself off." Even if you put in ".25" its still a better outcome than the typical 6 turns that people think.



I hope that long winded explanation helps you to understand my point of view a bit. The old simple model isn't really wrong it's just not completely right and downplays the effects of mana crystal and the benefits.

Duh man, you maths are wrong again.

You make both mage cast 5 mana spells, but the thing is that 1 of these spell for first mage is the mana crystal. You need to compare with someone not casting a mana crystal.

So it is:

Turn 0 = 10 mana <------ for the sake of removing values we don't need because the starting value is the same for everyone and it doesn't change the math at all.

Turn 1 = Channels 10 mana.(10) Plays mana crystal (-5). End Turn = 5 mana left.
Turn 2 = Channels 11 mana.(16) Plays card (-5) End turn = 11 mana left
Turn 3 = Channels 11 mana.(22) Plays card (-5) End Turn = 17 mana left
Turn 4 = Channels 11 mana.(28) Plays card (-5) End turn = 23 mana left

Player 2
Turn 1 = Channels 10 mana.(10) (not casting mana crystal) End turn = 10 mana left
Turn 2 = Channels 10 mana.(20) Plays card (-5) End turn = 15 mana left
Turn 3 = Channels 10 mana.(25) Plays card (-5) End Turn = 20 mana left
Turn 4 = Channels 10 mana.(30) Plays card (-5) End turn = 25 mana left


You see, player 2 has 2 more mana.

I do minus 5 for all turns because this model assumes that the player plays something. Of course he will have more mana if he doesn't cast anything and I do. That's just how the game works. If he says he's not casting and waiting for a bigger turn that's fine, that is one of the strategies, but it's not pertinent to the acceleration model because in this case, as you suggest, I have gained my action back and potentially have more cards in play than he does. I just use 5 as a place holder. In a real game the turn values would be 5,2,7,13,etc.... but the model still holds as it refers to the ratio of mana gained in total over the opponent without other influences.

Does that make sense?

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zorro

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Re: On mana crystal effects and efficiency
« Reply #1 on: October 03, 2014, 03:04:30 AM »
I also dont thing the return of mana cristal is #turns-5, for the same reasons as DaFurryFury, but with opposite conclusion. I think on turn 6 if you have played mana cristal first turn you are still way behind the player who did not casted it.

Let's consider 10 base channeling, and playing two mana crystal first turn (for maximizing example value)

No-Crystal-Player
turn 1: 20 mana and 2 actions - for whatever
[...]
turn 6: 70 mana - for whatever

Crystal-Player
Plating two mana crystals you have:
turn 1: 10 mana and no actions - for whatever
[...]
turn 6: 70 mana - for whatever

First of all, is not (number of turns - 5), but (number of turns - 6) since the turn casted does not provide channeling. On turn 6 you are on par mana wise (just two lacking quickcast later). You have no exponential value increase, since no-crystal-player may not use its 10 mana advantage and just keep it for getting high availability, if you value that. If you want to consider high mana availability as a bonus on turns 7+, i think you have to take into account less mana availability during turns 1-5, during no-crystal-player has an advantage.

turnCrystalNo-Crystaldiff
11020+10
22230+8
33440+6
44650+4
55860+2
67070+0
78280-2
89490-4
9106100-6
10118110-8
11130120-10
12142130-12

I think the double mana crystal does not really breaks even until turn 11. Then the crystal-player have 10 more mana availble, but yat the cost of being on disadvantage during turns 1-6... which i consider have more impact than turns 7-11.

No-crystal player have 10 mana to cast a creature first turn. That creature have 6 turns to run onto the opponent and hit him (or even the crystals!) three times before the end of turn 6. It can be Timber wolf, Skeletal Sentry, or even a General Signet Ring plus Orc Butcher (you even got a discount ring then!). You have to take into account the 4-dice hitter actions during first turns. Sure, by turn 6 crystal player can cast it's own 4-dice creature, and by turn 10 a second one... But all in all i consider first turnhs more important and having more impact (you can disturb opponent's plan)
« Last Edit: October 03, 2014, 03:10:31 AM by zorro »
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Schwenkgott

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Re: On mana crystal effects and efficiency
« Reply #2 on: October 03, 2014, 05:54:19 AM »
I think the double mana crystal does not really breaks even until turn 11.

I think there is a slight error in your comment. It does not matter how many mana crystals you cast. After 5 rounds, you will have more mana than without the mana crystals.
Meaning: When you cast them in round 1 and start to benefit from additional channel in round 2, you will have more mana in round 7.

I consider the other effect from more channeling more important though.
You always want to spend the mana you have per round as effective as possible. That means, you want to spend it all (bring it on the board). If you do not cast mana crystals, you have (only) 10 mana per round. The saved mana from the crystal lets you cast something big in round 1. Assuming you spend all your mana for that, in round 2 you channel 10 mana. But this is limiting your options, you cannot cast something for 11 mana.
The crystal mage is only limited in round 1, because he casts a crystal, but in every round that follows, he may make use of 11 mana, so he has more options to react to his opponent.
« Last Edit: October 03, 2014, 06:00:53 AM by Schwenkgott »
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Re: On mana crystal effects and efficiency
« Reply #3 on: October 03, 2014, 06:15:53 AM »
I think you have to look at this game more from a turn by turn perspective.
Meaning, what did my opponent do this turn and how did I counter it ?
Did I get ahead in this exchange ?
Mage Wars is very much about reacting to what your opponent does and trying to get ahead in this exchange.

Opening the game with a Crystal/Flower can be a good play for instance to counter a situation where you're channeling less than the opposition.

Suppose you channel 9 and your opponent channels 10 mana.
This means that in ( for example ) a 15-turn game you will channel 15 mana less than your opponent.

By playing a Crystal/Flower on T1 you make a 1-time 5-mana investment to even the channeling from T2 on. Sure you invested 5 mana on it but you countered an opposition's advantage with it for every following round.

Following that same Logic, playing a Crystal/Flower can also give you an advantage if you had the same channeling rate to begin with.

As I already mentioned, the game is about making the best plays in any given round, countering your opponents's actions and trying to get an edge on him and playing a Crystal/Flower at some point may be just that play.

EDIT ADDED

And consider this situation :

A Mage Channeling 9 mana per turn wants to spend 10 mana every turn.
He can do this for 10 turns ( until his starting 10 mana are used up )
From turn 11 on he will no longer be able to spend 10 mana a turn as his mana pool is empty and he channels only 9/turn.

That same Mage playing a Crystal/Flower on T1 upping his channeling to 10 can spend 10 mana every turn all game and has 5 remaining mana to boost.
« Last Edit: October 03, 2014, 06:50:49 AM by Borg »
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zorro

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Re: On mana crystal effects and efficiency
« Reply #4 on: October 03, 2014, 06:48:35 AM »
I think there is a slight error in your comment. It does not matter how many mana crystals you cast.

Yeah, you are right. I used double mana crystal just to have mana to cast a lvl 2 creature with the no-crystal-mage :)


When you cast them in round 1 and start to benefit from additional channel in round 2, you will have more mana in round 7.
[...]
I consider the other effect from more channeling more important though. [...] Assuming you spend all your mana for that, in round 2 you channel 10 mana. But this is limiting your options, you cannot cast something for 11 mana.


Let's asume the no-crystal-mage donīt spend it's extra mana first turn, and he just keep the mana as extra chaneling.  In my table (with double crystal), it's equivalent to having +10 channeling turn 1 for the non-crystal mage, +8 turn 2, +6 turn 3, etc. On turn 6, both mages have virtually the same channeling. (non-crystal mage can spend two of the ten mana saved from first turn on turn's 2-6). Starting from turn 7, crystal mage has extra channeling. On turn 11 crystal-mage will have an (acumulated) 10 chaneling advantage, and then he compensates the first turn 10 channeling advantage of no-crystal-mage.

The crystal mage is only limited in round 1, because he casts a crystal, but in every round that follows, he may make use of 11 mana, so he has more options to react to his opponent.

Thats my point! crystal mage has little extra options to react from turn 2 (+1 mana), but non-crystal mage has huge extra options on turn 1. Non- crystal mage keep having extra options until turn 6, and crystal mage will not have an edge of extra options until turn 11, where he would have compesated the first 1-5 turns with less options with the last 7-11 turns with more options.

Mage Wars is very much about reacting to what your opponent does and trying to get ahead in this exchange.

I almost agree, is about getting ahead... but i think generally better make your opponent react your moves, and that's why I value more the virtual +5 channeling  on the first turn (plus action!), than a +1 channeling from turn 2 that will not give you an advantage until 5 turns later.

Since i consider pretty more critical the first turns, i find really difficult to find usefull the mana crystal - specially, when you have different options as discount ring who are cheaper, or spawnpoints, who offer a great advantage in actions.

Of course, i tend to consider start the most critical point, and then to play traying to finish my setup as early as possible.
« Last Edit: October 03, 2014, 08:11:11 AM by zorro »
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kiwipaul

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Re: On mana crystal effects and efficiency
« Reply #5 on: October 03, 2014, 06:58:58 AM »
Really it is not the mana that is the point but the strategy of your mage.  Wizard has a lot of spells to increase their mana and reduce the mana or channeling of the other.  Note that Mana flowers or crystals will also be more expensive for some to add into their books. 

Beastmaster will swarm, perhaps with his lair or not
Warlock will rush possibly, (or not)

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Re: On mana crystal effects and efficiency
« Reply #6 on: October 03, 2014, 07:32:50 AM »
Thats my point! crystal mage has little extra options to react from turn 2 (+1 mana), but non-crystal mage has huge extra options on turn 1. Non- crystal mage keep having extra options until turn 6, and crystal mage will not have an edge of extra options until turn 11, where he would have compesated the first 1-5 turns with less options with the last 7-11 turns with more options.
I don't agree that the crystal mage has less options.
He still picks 2 cards per round and as long as his ideal choices can be paid for he loses no options at all.
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zorro

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Re: On mana crystal effects and efficiency
« Reply #7 on: October 03, 2014, 08:08:17 AM »
Non- crystal mage keep having extra options until turn 6, and crystal mage will not have an edge of extra options until turn 11, where he would have compesated the first 1-5 turns with less options with the last 7-11 turns with more options.
I don't agree that the crystal mage has less options.
He still picks 2 cards per round and as long as his ideal choices can be paid for he loses no options at all.

Same way, as long as his ideal choices can be paid without the extra mana from the crystal, he not need the crystal either at all. But since you donīt know in advance wich will be to maximun cost of your ideal choices, and usually expensive cards bring bigger effect... i think we both agree that having more mana increases your options (that's the whole point in casting mana crystal, isnīt it?).

Once that is stablished, I also consider that having more options during firsts turns is more important than to have them during last turns.

Really it is not the mana that is the point but the strategy of your mage.  Wizard has a lot of spells to increase their mana and reduce the mana or channeling of the other.  Note that Mana flowers or crystals will also be more expensive for some to add into their books.

Also i agree partially. Mana is not the strategy, but a way to bring out your strategy. My point is that mana flower-cristal (almost always) just delay your strategy, and i think there are (almost) always better alternatives, since the opportunity cost of casting a mana crystal is usually understimate. Whatever your strategy is, as soon as you bring it out, the better, be it rush, swarm, or whatever, the sooner you bring it out, the sooner your opponent has to deviate from their plans to cope with you.

PS: my replies are just because i consider this topic interesting - specially since same arguments bring us to totally opposite conclusions :)
« Last Edit: October 03, 2014, 08:14:18 AM by zorro »
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Re: On mana crystal effects and efficiency
« Reply #8 on: October 03, 2014, 09:35:13 AM »
I'm with Schwenkgott here.

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. 

I think that in a regular game I'm likely to have very little mana in reserve by the end of round 3 - the rest will have gone into assets of some sort (creatures, conjurations, enchantments...) or attacks/incantations.  Arguing about long-term disposal of starting mana may be missing the point.

What I get if I put 5 of my initial mana into a mana crystal instead of some other asset is added ongoing flexibility.   The Crystal provides not so much extra mana as extra liquidity of mana.  My extra channelling means that every round after casting it I get extra flexibility in my casting decisions.  I doubt I'm alone in preparing a contingency Teleport, Agony or something in order to react to an enemy's moves, or keeping back mana so I can reveal a Nullify or Rhino Hide at the last minute.  Keeping back a contingency mana supply for those spells is an overhead on my total mana supply, and reduces my flexibility - worse than that, not keeping back that contingency mana tells my opponent that he can cheerfully drop a lightning bolt on that creature of yours with a face-down enchantment because I can't do anything to stop him. 

So, if I have a Nullify lying around, and am waiting for the opportunity to reveal a Rhino Hide or possibly cast a Teleport or Force Push, maybe 5 of my mana is being held for that over most of the turn.  I could use some of that reserve during final quickcast, but I'm probably going to want it back next round.  My channelling in real terms is down at 7 or 8.  In these terms, getting 1 extra channelling is a much bigger deal - I may only have to save for 2 turns to bring out that Iron Golem, instead of 3.  And as noted above, it's not a case of saying 'If you hadn't spent that mana on a Crystal you'd have your Golem by now' - that mana would have gone on a Hand of Bim-Shalla (or maybe I summoned a Basilisk instead of a Blue Gremlin - the point is that my initial mana gets spent on something).

Saying that casting a Mana Crystal gives you less options in your early turns is only true in as much as any 5 mana spell you cast gives you less options - whatever you cast is your option.  The payoff of a Crystal is greater channelling, the payoff of a Bitterwood Fox is a fast but vulnerable creature, the payoff of Agony is that one enemy creature is made less effective.  They all cost 5 mana and an action, they all give you something.  The crystal is harder for the opponent to remove than the others, and its benefit is more flexible.

On reflection, another issue here is that all these calculations only look at the RoI on the Crystal, not the RoI on the other spells that might be cast.  That's not an even playing field - everything you cast gives you something, or you wouldn't be casting it in the first place.  Just because the RoI on channelling boosters looks like it can be easily calculated doesn't mean you can gloss over the RoI of the alternatives.  The only spells you cast that provide an instant return on their investment are incantations and attacks - to compare the numbers on the Crystal with an empty assumption of an instant RoI on the alternatives isn't good practise.


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Re: On mana crystal effects and efficiency
« Reply #9 on: October 03, 2014, 11:23:05 AM »
 :'(
I do minus 5 for all turns because this model assumes that the player plays something. Of course he will have more mana if he doesn't cast anything and I do. That's just how the game works. If he says he's not casting and waiting for a bigger turn that's fine, that is one of the strategies, but it's not pertinent to the acceleration model because in this case, as you suggest, I have gained my action back and potentially have more cards in play than he does. I just use 5 as a place holder. In a real game the turn values would be 5,2,7,13,etc.... but the model still holds as it refers to the ratio of mana gained in total over the opponent without other influences.

Does that make sense?


No. Because in your example:

Player 1: Cast 1 mana crystal and 3 Acid Ball
Player 2: Cast 4 Acid Ball

Then you tell me player 1 has more mana than player 2. Of course, you casted 1 less Acid Ball than player 2.

Player 2 has done more than Player 1.


That's the probleme with people thinking Mana Crystal give you some hidden mana-generation, they always give example where Player 1 cast the crystal and player 2 cast something else. But the thing is if you want to compare casting mana crystal vs not casting mana crystal... well, compare casting mana crystal vs not casting mana crystal, NOT casting mana crystal vs casting something else.
« Last Edit: October 03, 2014, 11:25:32 AM by Wildhorn »

sIKE

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Re: On mana crystal effects and efficiency
« Reply #10 on: October 03, 2014, 01:39:06 PM »
Well you can't say this and maintain your argument. What is the persuasive argument here?

Should I cast a Mana Flower to increase my channeling and leverage it benefits vs. it is a cost sink and you don't make a return on you investment for 6 turns.

If you choose not to cast Mana Flower this means you will cast something different I am guessing that Acid Ball was chosen as an example as it has the same mana cost as the Mana Flower.  So:

1 * Mana Flower (5 mana) + 3 * Acid Ball (5 mana ea.) = 20 Mana

4 * Acid Ball (5 mana ea.) = 20 Mana

the next round the player who cast the mana flower would have 1 more mana than the other player (assuming their base channeling rate was the same).

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Re: On mana crystal effects and efficiency
« Reply #11 on: October 03, 2014, 01:40:48 PM »
...no.  My choice in the deployment phase is between Mana Crystal and one of 50 other cards, not between Mana Crystal and no card.  If I want to think about comparative benefits between one card and any other card, I don't want to compare one card with nothing.  That doesn't let me make a value judgement.  It doesn't even let me judge some sort of absolute benefit, unless and until I have evaluated every other card in the same way.  Comparing Mana Crystal with a non-specific 5 mana spend doesn't say much either, but at least it doesn't pretend that the only other choice I have is sitting on my behind waiting to be eaten by zombies.

Edit: ninja'd by sIKE...

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Re: On mana crystal effects and efficiency
« Reply #12 on: October 03, 2014, 01:44:54 PM »
If you're going to quote me please do so completely. You're missing the most important point that I made when breaking down the equation. I also explain that the values of cards are only relative to each other. Since this is NOT actually an exact value, and is only a representation of what the value might be, I gave an estimate of when the card "actually" pays itself off because that is where the discussion started when you said you thought it started to pay off at round 6. My theory is the it pays itself in under half that.

My original post
Quote
It's clearly a common fallacy on these forums that the returns for a mana crystal is only directly related to the mana it gives you back. That is true only in the sense of counting mana. To properly evaluate the "value" of mana crystal you must look at it's "real" returns. I define "real" as the return a spell gives you after it pays itself off plus it's immediate effects. This manifests itself in many ways but mana crystal is pretty simple in that it just gives you mana back.
So to boil it down, the total converted value of mana crystal is (Length of Game - 5 [Mana Cost] + [Increased amount of Channeling * Length of Game]. If you're a math nut you will like this expression; (X-5)+(1*X) So if you put that expression into a graphing calc (https://www.desmos.com/calculator) you can see the "x intercept" which shows approximately how many turns it would take for it to pay itself off. (2.5) Which is less than 3 turns if you calculate it this way.
Now I'm going to try to answer a question which I think several of you will have. "Why/Where are you getting the second half of the equation which adds an originally un-thought of positive?" Well, it represents the value of increased channeling that you gain because it's not just a card to give you more mana. It's a card to allow you to summon 1 mana worth of a larger spell during that turn. Plus it's effects stack when you play a small turn to save because you gain more with the larger channeling.

Side-note: If you put the equation into the graphing calc I linked you to, you will see the "y-intercept" which represents the amount you spend on the spell. Yay Mathmatics and Game Theory!

Now I understand this is a really big rant that several of you maybe didn't read, but people keep telling me the effectiveness of cards based off of it's effect on the surface without taking into account a card's value over time.

Wildhorn
Quote
The formula is wrong because you add twice X, which gives 2 mana per turn while crystal only gives one.

The right formula is ((X*1)-5)


If you want an example:

Give 5$ to a djinn and 1$ will appear every day in your pocket. That's how mana crystal work.

But your formula is: Give 5$ to a djinn, 1$ appear in your pocket every day... But the djinn also give you 1$ per day.

Me again
Quote
My equation does not calculate how much mana it gives you. It's a more abstract representation of the overall value. Both mana gain and action potential of the increased channeling. Since it increases channeling and does not give you just flat mana, it's value is exponential based on the amount of turns taken and the increase of mana per turn instead of mana per game. If you calculate just mana per game yes you are correct but that's not where the true value of mana crystal lies.


You have to realize that it doesn't matter what you play or what the opponent plays. So long as you both are playing the game then the equation works. You don't even have to equate it to mana crystal. You can put the same idea toward a mage with 9 channel and another with 10. The only difference is that the mage with 10 didn't pay for his extra channeling and pays off at turn zero.
« Last Edit: October 03, 2014, 01:54:56 PM by DaFurryFury »
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Re: On mana crystal effects and efficiency
« Reply #13 on: October 03, 2014, 01:55:30 PM »
This doesnt even make sense. You can't compare apple and orange.

Your example make as much sense as if I was comparing Acid Ball and Mana Crystal to see which one give a better armor reduction ratio.

What I am telling you is, if both mage have 50hp and start with 0 mana and have a channeling of 10 and we cast a spell that deal X dmg and cost X mana (where X is the amount of mana you have) you will die before me because on 5th turns I will have 50 mana while you have 49.

sIKE

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Re: On mana crystal effects and efficiency
« Reply #14 on: October 03, 2014, 03:09:03 PM »
This doesnt even make sense. You can't compare apple and orange.

Your example make as much sense as if I was comparing Acid Ball and Mana Crystal to see which one give a better armor reduction ratio.

What I am telling you is, if both mage have 50hp and start with 0 mana and have a channeling of 10 and we cast a spell that deal X dmg and cost X mana (where X is the amount of mana you have) you will die before me because on 5th turns I will have 50 mana while you have 49.
I don't understand what you mean here at all. 50 mana while you have 49?
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