The ideal start is basically the most mana-efficient technique to create a mana farm. The first thing one should focus on is creating a single mana gem, but even before that, they should create 3 traps, all with grade 4 RO gems by transmuting both grade 3 R and O gems onto your 6 other grade 3 gems; then combining these (max stats is assumed), and combine one particular RO gem with two other Reds and two other Oranges (which are created through gem transmutation) so there is a splash radius of greater than 15, so it hits 5 targets. Put these in a trap. Anger the first wave as many times as possible (without angering with your grade 2 R and O).
This guide will focus on how to create ideal start with the greatest accuracy possible. The important stuff for this guide is in bold, if you want to hear the mathematical reasoning and stuff like that, then read the whole guide
New Terminology Used
Pool limit - the amount that you could spend where you would break even on the mana increase of a mana pool.
Grade 3 mana gem - an grade 3 RO gem with 222 firing speed, 8.4 mana steal in a tower, and 30 splash in a tower.
Grade 6 mana gem - a grade 6 RO geme with 279 firing speed, 8.4 mana steal in a tower, and 30 splash in a tower.
Before you use this guide, it is strongly recommended that you have read the thread on 10 billion points made easy. Unless you have actually made 10 billion points, that is. This guide assumes that you are using 7000 mana per grade 3 mana gem, which is very close to the minimum amount necessary. We are using the last track because it has the greatest opportunity for mana earning, with 103 traps, about 50% more than any other level. This directly affects mana pool multiplier.
Part I - Grade 3 track
The formula for pool limit is ( 20 * #mana gems (for trap cost) ^ 2 + 7000 * # mana gems ) / 20. This reduces to:
m^2 + 350 m
Where m is the number of gems.
If this number is less than the cost of pooling, then you should create a grade 3 mana gem. If this number is greater than the cost of pooling, then you should mana pool.
Step 0 - Do necessary gem transmutations to create what is described above.
Step 1 - Create a maxed mana gem. It should be 10.4 mana steal in trap with at least 30 splash radius in a tower, so it hits 6 targets. It should have a 222 firing speed.
Step 2 - It is best to mana pool until you have 6000 max mana - you get a 5% bonus on all your mana-earning. Why 6000? 7020 / 20 = 351, so we will pool until the mana cost of pooling exceeds 351. Create another mana gem.
Step 3 - Mana pool to 11,000 max mana - Pool limit = 704. Create another mana gem.
Step 4 - Mana pool to 16,000 max mana - Pool limit = 1059. Create another mana gem.
Step 5 - Pool to 19K - the cost is greater than 1416. Create another mana gem.
Step N in this part - Follow this pattern by pooling up to where the pool cost exceeds 350 * # + #^2 of mana gems. Anger more than is sustainable to ensure that all your traps are being used at all times. Continue this until all the traps are covered in Grade 3 RO gems (except for Grade 3s in the beginning). You should have 83,000 mana pool at the end of this.
Part II - The Grade 6 track
We will now upgrade these gems to grade 6. This allows the cap to go from 533 firing speed to 670. This is 25% more efficient than before for another 4000 mana per upgrade. What does this mean? Each mana pool is worth 5.25 current mana gems, because there are about 105 places on the track. And by doing this, each of these are worth 0.25 mana gems, so we pool until the cost of pooling exceeds 84,000. This means you should pool until 93,000 mana.
Step II.N - Every upgrade adds 0.25 gems to the stakes, so this becomes 84,000 for pool limit, then 84,200 as you add another, then 84,400, and so on. .... You will be upgrading your gems multiple times before you mana pool. Keep track of the number of upgraded gems and your pool limit. You continue this until you have completely covered the map with Grade 6 mana gems. Pool limit for step 2 = 84,000 + 200*# of gems already upgraded to 670 firing speed
Build and place 3 R/B gems at the very start of the track to condense the monsters further and allow more monsters to be on the track. You might consider using prismatics (beware of lag) and purple gems in the beginning because of armor, but after a certain point, the extra damage is trivial and not worth the mana.
Part III - the maximum revenue
Now, we will begin replacing the traps with ROL (Red-Orange-Lime) gems. Why? Because this is the gem combination which ensures the maximum amount of mana steal. You may have heard of the ROY gem. How can this be better? It has 670 firing speed and a 70% chance of double hit, so it averages 1,139 hits. This is better than 1071 hits for a ROY gem. Furthermore, it can be constructed easier, because I have problems with the firing speed of ROY gems. It is not as mana efficient for construction as the grade 6 RO gem, but since we have run out of traps, this is the most efficient method of producing mana. It steals more than 45% more mana than the normal RO gem.
We will be doing two things here: We will be creating grade 10 ROL gems - these require 16 Grade 6 gems each, and with gem transmutations, that means a little less than 6000 per gem, so that's about 95,000 per gem for 45% more effectiveness of 1 gem.
The new pool limit formula: [ (number of mana gems RO)+(number of mana gems ROL)*1.447] * 95,000 (this is the cost) / [20 (mana pool increases the mana gain by 5%) * 0.447 (for the increased effectiveness) ].
Part IV. - Finally starting to build firepower
Here, we want to things - to build up your firepower, and also to build your multiplier.
Build a grade 15 prismatic gem. Drag a Red on it. Drag a Cyan on it. Drag a Lime on it. Drag a Yellow on it. You now have a correctly aligned prismatic. I would recommend building firepower with two super-gems. This allows you to alternate between building firepower with one and then the other.
Combine with multiple grade 6s. When you combine, drag it ONTO another gem, so it doesn't become misaligned. Each combination increases the firepower by 40-55. A whole sheet averages about 2000 max damage increased.
Part V - Placing your prismatics
Put your prismatics in a trap. This sounds stupid, but it actually deals 5x more damage in a trap. A few reasons why.
In a trap, you can hit up to 5 targets at once.
Triple damage is not shown, but you can have about a 30% chance of triple damage in a trap. It has been tested.
More range and firing speed means that you can fire about 3.5 x faster than in a tower.
A 66% chance of double hit means this is firing even faster. Note: there has been speculation that there is a possibility of more than one extra hit.
Before you put your gem in a trap, it is necessary to hue the gems - this allows the maximum damage to be dealt. On the last level, the optimum hue is 195, which can be achieved by dragging this gem onto several Cyan gems. Hue is dependent on the gems added. The Hue # corresponds to a number of degrees on a circle, ranging from 0 to 360 and once it reaches 360 it starts over at 0 (so a hue of 0 and a hue of 355 are very, very close together), and when two gems are combined, the Hue is the bisector of the angle created by the two radii of the original gems.
Part VI - On angering
Angering actually relates to the Pascal triangle, but that's completely different. Basically, it is a multinomial equation and an infinite product. It affects Hp geometrically:
(1+grade angered * 0.05)(current hp of wave)
It affects armor geometrically as well:
Initial armor * 1.25^#of angers OR Armor + 2. Whichever is higher
It affects Score in a infinite product (which can be reduced to a multinomial equation)
(1 + 0.15*grade) / (# of anger already done + 1).
If you anger with grade 7 or higher, then the score will keep on increasing by more than it increased the last time - any less, and it will have a limit. Keep this in mind when angering. Anger with as high grade gems as you can as long as you can be consistent - Angering with a Grade 15 and then Grade 8s is not as good as angering with Grade 11s consistently.
How much should I anger?
All that matters with angering is the Monster Health.
Your limit / wave is this: Each wave takes about 60 seconds, so using this, then ...
Total monster health capacity for a wave = 2,600 * active prismatic tower damage or 13,000 * active prismatic trap damage. This assumes that there can only be one extra hit. If there can be multiple extra hits, then the number is 3,000 * active prismatic tower damage or 15,000 * trap.
I anger boss waves to about 3-5x this, The wave preceding and 2 waves following this, I anger to half capacity.
Armored waves get 1.5 x this.
Normal waves get 1x this.
Runner waves get 0.5x this.
Swarm waves get enough so that they get through your traps, so that's about 10 million health of the total wave.
It is important to adjust this - if you find that monsters are leaking once or twice only, you can risk a greater score and higher banishment by angering more. If the banishment costs are high, then it's probably better to back off by 1 or 2 gems (any more would make things too easy. Overangering is not a huge problem.
Please note that the advice to anger is way off in this guide. Angering is the most difficult aspect of the game because you can anger with any grade, with different results for each grade angered. Furthermore, angering needs to be done on a case-by-case basis. I suggest "superangering" boss waves that give tons of score, especially those with only 2 monsters (twin bosses). As a rule of thumb: you get the most score with the least initial monsters - runners, monsters, and armored waves are equal in the score they give for the given wave. However, a wave of 8 armored gives roughly twice as much score as a wave of 16.
Other threads to see:
All 229 waves
10 billion points made easy
All 512 waves [if you really want a challenge]
Unrelated footnote because textile broke
Here is a savefile where I maxed stats with just one map.