One more thing to note. I remove the beginning 10 mana in my examples because, i believe, that it is there to slightly weaken the effects of things like mana crystal. Higher channeling is an increasing benefit that when left unchecked will lead to one sides, almost undoubted, victory. The 10 mana is put there so that the player wth less channeling will have something to react with and isn't fighting an uphill battle the whole time. Once that original 10 mana is spent though, it's gone forever and you are solely relying on your channeling values.

@zorro - Thanks for moving the discussion by the way.

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

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

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

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.

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.

I think my original question was answered for the most part so I don't mind derailing the discussion a little on the mana crystal thing.

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.

I might post more about this in a separate thread but I feel like I would be put on a spit over a fire for pretty much telling an entire community that they are wrong about anything no matter how small. Haha

But when considering what an opponent might throw at you, wouldn't you want at least a couple heals (just as an example) because you might either want to keep a big creature alive or use it on several. I do know cards like mage wand and enchantment transference has widened my spell range, but those are cards specifically made to extend a spells effect.

These are some really neat comparisons. I'm relatively new to mage wars but have been playing Go for several years with my bro. Go has always been one of the greatest examples of game theory as far as give and take is concerned, but translating that same idea to sente and gote is kind-of genius! Even though the two ideas are loosely the same, they serve two greatly different models of thinking.

Anyway this has inspired new strategies and ideas for me. I've always known that several games can be alike at the core, but I have always thought of Mage Wars as more like chess. Though your thoughts make me think that Go is more applicable since it's such a game of pace and less about tactical positioning. (Not to say that positioning has no presence)

Thanks for your thoughts!

When can Dancing Scimitar make its attack? I ask because it doesn't say like other abilities that will say "before or after a friendly creature's action." I assume it cant happen during an enemy attack. Can you confirm this?

Okay now I'm confused again..... Sorry
I thought from the beginning it was accepted that 1 wall (not extended) is played such that it is touching 3 zones, blocking 2 zones from entering 1 of the zones determined by which direction it's oriented. Thus Los is blocked across two zone edges with the one wall (not extended).

But do you mean to say that a wall is placed between only 2 zones thus blocking movement and sight from the 1 direction?