Incrementy

Incrementy is a mechanic that is unlocked through Booster Upgrades. It is an increasing number (grows quadratically, in a similar fashion to ${\text{time}}^{2}$) that is produced only when the Ordinal is ψ(Ω) or larger. Incrementy is reset when a Factor Boost/Collapse is performed, starting a Challenge/Omega Challenge, or resetting Booster Upgrades or the current Collapse run.

Incrementy production

The full, detailed formula for the determined Incrementy production is

Changes	Content	Details	Notes
	game.ord/1e270	Base Incrementy Production
power	sqrt(OC6 completions)		Capped at sqrt(1.1), if you completed OC6.
multiply	2rIU2 bought		The 2 can be changed by the effects of OC2 or its reward. In Incrementyverse, the 2 can be changed by the effect of SFU101 if you have this Function. Everything except this one will be no effect while in Incrementyverse
multiply	Dynamic Factor cap		If you have IU8.
multiply	log10(ℵ2 Power)		If you have AU5.
multiply	(Dynamic Factor cap)x	x = min(0,min( (C8)/2, (C8+1)/4, (C8+5)/8, (C8+17)/16, (C8+49)/32))) where C8 is your C8 completions.	Doesn't apply if you are in Challenge 8.

The full, detailed formula for the determined Incrementy production is:

$({\frac {\mathrm {Ord} }{1\mathrm {e} 270}})^{\mathrm {OC6B} }\times (\mathrm {OC2} +2)^{\mathrm {IU2} }\times \log _{10}(\aleph _{2}+10)^{\mathrm {AU5?} }\times \mathrm {DFC} ^{\mathrm {IU8?} +\min {(0,\min {(\mathrm {{\frac {C8}{2}},{\frac {C8+1}{4}},{\frac {C8+5}{8}},{\frac {C8+17}{16}},{\frac {C8+49}{32}}} }})\times (1-\mathrm {C8?} )}$

where:

$\mathrm{Ord}$ represents the value of the game.ord variable in the game's code, $\mathrm {IU2}$ represents the amount of Incrementy production upgrades that have been bought, $\mathrm {DFC}$ represents your current Dynamic Factor Cap, $\mathrm {IU8?}$ is 1 if you have IU8 (Dynamic Factor cap multiplies Incrementy gain) and 0 otherwise, $\mathrm {AU5?}$ is 1 if you have AU5 (ℵ₂ boosts Incrementy gain) and 0 otherwise, $\mathrm {C8?}$ is 1 if you are currently in Challenge 8 and 0 otherwise, $\mathrm {\aleph _{2}}$ represents your ℵ₂ Power, $\mathrm {C8}$ is Challenge 8 completions, $\mathrm {OC2}$ is -1 if you are in OC2 and your OC2 completions otherwise, and $\mathrm {OC6B}$ is your OC6 bonus, which is ${\sqrt {\max {(1,\min {(\mathrm {OC6} ,1.1)}}}}$ where $\mathrm {OC6}$ is your OC6 completions. The Bold part is Base Incrementy production and Underline part is Incrementy production multiplier.

Besides providing a passive boost to Tier 2 Automation, Incrementy can be used to upgrade its own bonus.

Incrementy boosts Tier 2 Automation through the formula $\mathrm {log} _{10}(\mathrm {i} +10)^{{1.05}^{\mathrm {IU1} }}\cdot {1.2}^{\mathrm {IU3} }$, where $\mathrm{i}$ is your current amount of Incrementy, $\mathrm {IU1}$is the amount of Incrementy Raised upgrades that have been bought and $\mathrm {IU3}$ is the amount of Incrementy Multiplier upgrades that have been bought, they will be hardcapped at 1e120 if you are not in Incrementyverse. In Incrementyverse, the 1.2 can be changed by the effect of SFU102 if you have this Function.

Table of Incrementy Upgrades

Below is a list of all Incrementy upgrades. The first three upgrades do not require the Incrementy extension Booster Upgrade and can be bought as many times as you can.

Upgrades pre-Extension

Incrementy Upgrades

Upgrade	Description	Cost	Cost Multiplier	Other Details
rIU1	Base Incrementy multiplier is raised to the 1.05	1.00e5	1.00e5	The formula is simply $\mathrm {n} ^{1.05^{\mathrm {u} }}$, where $\mathrm{n}$ is your Incrementy multiplier (without the 3rd upgrade pre-Extension), and $\mathrm{u}$ is how many times you've bought this upgrade.
rIU2	Double production of Incrementy	1.00e3	1.00e3	Cost and cost scaling is squared in OC4
rIU3	Multiply Incrementy multiplier by 1.2	1.00e9	1.00e9	The formula for Incrementy multiplier from this upgrade is simply $\mathrm {i} *1.2^{\mathrm {u} }$, where $\mathrm{i}$ is the Incrementy Multiplier, and $\mathrm{u}$ is how many times you've bought this upgrade.

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Upgrades post-Extension

Post-extension Incrementy upgrades, unlike the pre-extension upgrades, can only be bought once and require the Incrementy extension Booster Upgrade.

Extended Incrementy Upgrades

Abbreviation	Description	Cost	Other Details
eIU1	Manifolds are 3x as effective, and gain a flat 5e8/s Tier 2	5.00e15	At past version, the cost is used to be 1e17 and 1e16, the effect also used to be Boost Tier 2 up to 1e8 and then gain a flat 1e8/s
eIU2	Manifolds are 26% more effective	2.00e22	Having 6 Manifolds with this upgrade and the previous will give a total of a 10.001x boost to Dynamic Factor.
eIU3	Reduce manifold requirement scaling	4.00e23	The formula before getting this upgrade is $3^n$, but it reduces to $2^n$ with this upgrade. You usually double your Manifold count as you obtain this upgrade, in late game, you should get around 58% more Manifold than without this upgrade
eIU4	Dynamic increases 100x faster	1.00e19	Growth to max: 4500s (1h 15m) goes down to 45s with this Incrementy Upgrade. Useful for Challenges 3, 4 and 5. Also slows down Dynamic Factor decrease in Challenges 6 and 7.
eIU5	Dynamic Factor cap multiplies Incrementy gain	1.00e25	Formula is $\mathrm {i} *\mathrm {dfc}$, where $\mathrm{i}$ represents the amount of Incrementy you gain per second (with the rebuyable Incrementy Upgrades), and $\mathrm {dfc}$ represents your Dynamic Factor Cap. In past versions with Incrementy Cap, it also multiplies the cap.
eIU6	Double the OP from Markups and gain a flat 1e15/s Tier 2	1.00e27	Useful for reaching the requirements for Challenge 8. This Upgrade used to be Incrementy also boost Tier 1 and slow down decrementy.

Conclusion

Incrementy is very useful mid-game, when you unlock the extension Booster Upgrade. Additionally, Incrementy becomes the main currency end-game within the Incrementyverse event.

Trivia

• In past versions, they have a Incrementy cap which is 1.000e25 * (Dynamic Factor cap)^IU8, IU8 = 1 if you have IU8, and 0 otherwise, however it's now removed before the game is moved to GitHub to reduce timewalls.
• In past versions, if the cost is over 1.000e257, the display will mess up and take a post-ψ(Ω) appearance much like OP, and if the cost is over 1.798e308, the display will be normal, but can't be buyable even if Incrementy uses ExpantaNum, now both was fixed along with Incrementy Upgrade costs using ExpantaNum.
• Incrementy may be the longest relevant feature in Ordinal Markup.
• Change about Incrementy, Incrementy/s and Incrementy Upgrade cost from 3 to 2 decimal places:
  1. v0.24: Due to Non-repeatable Incrementy Upgrade cost doesn't getting formatted, when it out, it always rounds to 2 decimal places.
  2. v0.30: Incrementy supports ExpantaNum, but it takes a different Number formatting.
  3. v0.31: Due to the addition of the getIncrementyRate(x) Function and it containing EN(x) (ExpantaNum(x)), it now uses 2 decimal places as formatting.
  4. v0.34: As players can surpass 1.000e257 Incrementy with its new released end-game mechanics and fixed strange Incrementy Upgrade cost, rIU costs are now using ExpantaNum. When you buy an upgrade, their cost also uses ExpantaNum, which allows players to buy Rebuyable Incrementy Upgrades that costs over 1.798e308 Incrementy.
• During v0.33, it was actually possible to exploit Incrementy amounts after getting BM2, which is Minimum Singularity in one tick, but this is now fixed.

At v0.32 and v0.33, even in Challenge 8, it is still applied.

This is changed most likely due to permanent nerf on Decrementy after SM1 and hinder the progress on Darkness stage onward.

Glitch

Note: This happened in a previous version but is now fixed.

Player in Challenge 8, but Dynamic Factor cap to Incrementy production isn't 1x

You can see IU1 cost display as 1.000e257 (cap in base 3) and IU3 cost display as g_BHO(10)