RTI(∞) Tab

Road to Infinity refers to both the Road to Infinity challenge, and the tab it unlocks.

= RTI Tab =

Unlocked by beating the Road to Infinity challenge. It increases various stats through two tabs: Levels, using Clones (similar to Might); and Pets/Stats, using Pets.

Similar to Might, the power of RTI persists through rebirths in the form of permanent levels. This is a permanent buff to your stats. You can also get a temporary buff to your stats by leveling the respective RTI element. These are called temporary levels and reset to 0 when you rebirth. Temporary levels roll over and become permanent levels depending on the amount of time spent in the rebirth. You can see the rate at which your temp levels become perm levels in the Lvl (temp)/Lvl (perm) tooltip in the RTI tab. Conversion rate increases by 0.25% every minute until it reaches 100% at 6hr 40min, and then slowly climbs by 0.1% every minute until 300% at 40hr. Below is a graph showing the efficiency of permanent level gains.

The amount at which perm/temp levels affect your stats depends on your RTI base multiplier and your pets assigned to RTI. This multiplier goes up by 1% for each minute into the rebirth, at a max of 100%. This cap can be raised by defeating P Baals over v100 in the RTI challenge. More in-depth info can be found below.

The total effect of RTI on a given stat can be seen on the Pets/Stats tab.

What To Focus On
Each of the elements on the RTI tab boosts a source of power, but some should often take priority over others depending on playstyle and the challenge you are in. These are ranked in the order many in the community consider order of importance, but some will come down to opinion.
 * SpaceDim: One of the most important elements, and spending time leveling up perm levels on this element will be very beneficial in the long run for many areas of the game due to the versatility of SpaceDim bonuses.
 * Building Speed and Creation Speed: Because these are multipliers to your BS/CS, their value to you is largely dependent on your other sources of BS and CS. These become very powerful and can somewhat replace some of the need to purchase BS/CS with God Power.
 * Divinity: Being a multiplier to Divinity gain, this one is very powerful. Very helpful for challenges like DGC, UfCC, and others requiring large amounts of Div.
 * God Crystal: This one appears to start out somewhat weak, but can really benefit you in longer rebirths. Not super important, but is another great source of GP.
 * Creating: Once you unlock RTI, Creating will often be your main source of Attack power and max HP. Because of this, boosting it any way you can will allow you to take down stronger gods.
 * Mystic: A boost to your main source of surviving fights with gods? Of course you should level this one up! Not as important as the other bonuses listed above, really becomes strong with a pet slotted into this stat.
 * TBS: Not crazy, but provides a nice boost in power. Very helpful for climbing challenges like the RTI challenge.
 * Physical/Battle: These two stats really get left in the dust in longer rebirths. Still level them a bit for some perm levels since Battle has some use in shorter rebirths for regen after completing MQC and Physical can be good for NDC and other creation-limited challenges.

= Pets/Stats = Allows pets to be allocated, increasing the effect of specific RTI Boosts. The total RTI multiplier for each stat can be seen here.

The general formula to determine the multiplier boost is: $$1 + (\text{Temp Level Multi} \times \text{Perm Level Multi} - 1) \times \text{Pet Multi} \times \text{Time Multi}$$

The temporary and permanent level multipliers vary depending on the boost.

The pet multiplier is determined by which pets are equipped in the RTI tab.

The time multiplier starts at 0.00 and increases by 0.01 per minute after rebirth, up to a max of 1. This is increased by 2% (additively) per P.Baal defeated above P.Baal v100 in the RTI challenge. I.e.: $$\text{Time Multi} = \frac{\{ 0 \dots 100 \} \, \text{Minutes}}{100} \times \left( \frac{\text{RTI Score}}{50} - 2 \right)$$

Pets can be equipped to the RTI page to increase the multi given by specific boosts in RTI (pet multi) and the level speed of specific boosts. This is determined by the pet's class and class level. Good RTI pets are pets that have a high class bonus, like Elf or Bottle.

You start with 2 free slots for pets to be equipped into and you can purchase an additional 6 slots although the price is quite steep at 500k pet stones and 25k RTI permanent levels of each stat for each of the 6 purchasable slots. Alternatively you can also buy these extra slots with real money if you prefer at $4.99 each.

* Note that pets equipped to RTI automatically gain class exp. as long as they are equipped.
 * Assassin: Boost Physical and Battle
 * Defender: Boosts Mystic and Creating
 * Adventurer: Boosts TBS
 * Alchemist: Boosts God Crystal (this is soft capped and will decrease after 7 days)
 * Blacksmith: Boosts Space Dim (this is soft capped and will decrease after 7 days)
 * Rogue: Boosts Divinity
 * Supporter: Boosts Building Speed
 * Mage: Boosts Creating Speed

As of August 16, 2022, the best RTI pet for each class is: If you have Gray evo'd, the Children can make good alternatives to many RTI pets as they have a 0.8 class level bonus.
 * Assassin: Carno, then Lucky Coin or Mimic - this one is less important so anything goes
 * Defender: Mysterious Egg or Gnome
 * Adventurer: Seed or Aether. Portal is the best one that doesn't belong in growth camp. Earth Eater can be a good option if you don't have the ability/motivation to keep it fed for camps.
 * Alchemist: Bottle, then Void, then Taco, then Rose
 * Blacksmith: Elf. Generally worth putting the best blacksmith you have in here.
 * Rogue: Undine, or Cardboardbox if you don't want to use Undine
 * Supporter: Salamander, then Hourglass, then Flying Cloud (the best one you're willing to go without in dungeons/camps)
 * Mage: Sylph, then Balrog, then Witch.

Because RTI bonuses depend on class bonuses, you should not place wildcard pets or pets that are evolved to non-ideal classes in RTI if you have any alternatives available

Pets will also gain XP while in RTI. They earn Class XP only, with a formula of (Growth (maxed at 500k) / 50 * Mimic Multi) per hour. Before Dojo, if a pet has an Ego Sword (or higher/lower tier) equipped, they will earn Class XP instead of the Dungeon XP it normally provides. Since Mimic gives a boost of 5% * CL to Class XP gains for pets in RTI, this makes Mimic a good choice for the Assassin slot. This has a trade-off since Mimic can become one of the strongest damage-dealing pets with enough Mimic Points

= Levels = This tab contains the RTI elements to boost, each increasing a stat depending on its permanent and temporary levels.

Temporary levels are gained over time by distributing clones to a boost, and are reset on Rebirth. The time to upgrade a level is: $$\frac{(\text{level} + 1) \times 100\,000\,000}{\text{rti score} \times \text{pet speed} \times \text{clones}} $$

RTI score is the highest P. Baal defeated in an RTI challenge. If 100 or more, instead use: $$(\text{rti_score} \times 2 - 100)$$.

pet speed is the speed bonus given by pets in the Pets/Stats tab. This only applies to certain boosts, based on the pet's class. If applicable, it is equal to: $$ \frac{\text{class level} + (\text{evo bonus x class level})^{0.8}}{100}$$

Example: A CL11 Frog Supporter has a pet speed of: $$ \frac{\text{class level} + (\text{evo bonus x class level})^{0.8}}{100}$$ $$= \frac{11 + (5.511\% \times 100)^{0.8}}{100}$$ $$= \frac{11 + (5.511)^{0.8}}{100}$$ $$\approx \frac{11 + 3.91728}{100}$$ $$\approx \frac{14.91728}{100}$$ $$\approx 14.92\% \, \text{Building Speed RTI boost}$$

Permanent levels are gained on Rebirth, based on minutes since Rebirth (T) and temp levels L: $$T < 6\text{h}40\text{m} \implies \text{perm levels} = \frac{L \times T}{400} < L \times 100\% $$ $$6\text{h}40\text{m} \leq T < 40\text{h} \implies \text{perm levels} = L \times \left( \frac{T}{1\,000} + 0.6 \right) \leq L \times 300\%$$ $$T >= 40\text{h} \implies \text{perm levels} = L \times 300\%$$



Components
There are 10 different RTI components, granting boosts based on temp levels LT and perm levels LP:

$$\left( 1 + \frac{L_{T}}{1\,250} \right) \times \left( 1 + \frac{{L_{P}}^{0.3}}{25} \right) \times 100\%$$ $$\left( 1 + \frac{L_{T}}{1\,250} \right) \times \left( 1 + \frac{{L_{P}}^{0.3}}{25} \right) \times 100\%$$ $$\left( 1 + \frac{L_{T}}{1\,250} \right) \times \left( 1 + \frac{{L_{P}}^{0.3}}{25} \right) \times 100\%$$ $$\left( 1 + \frac{L_{T}}{12\,500} \right) \times \left( 1 + \frac{{L_{P}}^{0.3}}{250} \right) \times 100\%$$ $$\left( 1 + \frac{L_{T}}{1\,250} \right) \times \left( 1 + \frac{{L_{P}}^{0.3}}{25} \right) \times 100\%$$ $$\left( 1 + \frac{L_{T}}{3\,300} \right) \times \left( 1 + \frac{{L_{P}}^{0.3} \times 3}{200} \right) \times 100\%$$ $$\left( \left( 1 + \frac{L_{T}}{3\,300} \right) \times \left( 1 + \frac{{L_{P}}^{0.3} \times 3}{200} \right) - 10 \right)^{0.8} \times 100\% + 1000\%$$ $$\left( 1 + \frac{L_{T}}{5\,000} \right) \times \left( 1 + \frac{{L_{P}}^{0.3}}{100} \right) \times 100\%$$ $$\left( \left( 1 + \frac{L_{T}}{5\,000} \right) \times \left( 1 + \frac{{L_{P}}^{0.3}}{100} \right) - 10 \right)^{0.8} \times 100\% + 1000\%$$ $$\left( 1 + \frac{L_{T}}{5\,000} \right) \times \left( 1 + \frac{{L_{P}}^{0.3}}{100} \right) \times 100\%$$ $$\left( 1 + \frac{L_{T}}{10\,000} \right) \times \left( 1 + \frac{{L_{P}}^{0.3}}{200} \right) \times 100\%$$ $$\left( 1 + \frac{L_{T}}{10\,000} \right) \times \left( 1 + \frac{{L_{P}}^{0.3}}{200} \right) \times 100\%$$
 * Physical: Increases your Physical stat. Multiplies RTI bonus with:
 * Mystic: Increases your Mystic stat. Multiplies RTI bonus with:
 * Battle: Increases your Battle stat. Multiplies RTI bonus with:
 * Creating: Adds Creating as a stat you gain from pets. This is the average of you pet's physical, mystic, and battle stats multiplied by your RTI Creating multiplier. Multiplies RTI bonus with:
 * TBS: Increases your TBS critical damage. Multiplies RTI bonus with:
 * God Crystal: Increases the god power gained from God Crystal. Multiplies RTI bonus with:
 * After 1000% bonus:
 * There is a penalty to rebirths longer than 7 days of 2% per day. This means after 57 days into a rebirth, God Crystal RTI will no longer give a bonus.
 * SpaceDim Speed: Increases the leveling speed of all SpaceDim elements. Multiplies RTI bonus with:
 * There is a penalty to rebirths longer than 7 days of 2% per day. This means after 57 days into a rebirth, SpaceDim RTI will no longer give a bonus.
 * After 1000% bonus:
 * Divinity: Increases your divinity gain from the divinity generator. Multiplies RTI bonus with:
 * Building Speed: Increases your building speed. Multiplies RTI bonus with:
 * Creating Speed: Increases your creating speed. Multiplies RTI bonus with: