Tornado Prestige

Tornado Prestige or "T" is the third and final prestige in Idle Spiral. It resets P-prestige, P-upgrades, r value and r upgrades.

Tornado prestige gives some bonuses in Δr/z , and Regenerate While Resting% , some flat of *a* to *e* variables, based on the amount of R you have when you tornado prestige.

On top of that T prestige also unlocks many unique bonuses and unlocks challenges, shown in the table below. (you can go further than the maximum tier, but this does not unlock anything right away)

Below the Table you will find Additional Information about Certain Rewards

**Additional Information**

T21: The New Integral Part
The New Integral is added to the calculation, it becomes visible after doing a P Prestige, this integral comes with two new "P" Upgrades
those being +0.01 α and +0.01 β

The effect of the Integral depends on those two new Variables

Due to the form of the Integral being

∫
0
a

2

x
b

d
x

\int\limits\_0^a 2x^b dx

Increasing α always results in an Increase in Δr
while Increasing β can result in either an Increase or a Decrease in Δr

Community Member Kloppie5 has found a generall „Rule of Thumb“ for when to upgrade β

„When α<1.20 Upgrading β is always Negative, When α>1.65 Upgrading β is always Positive“

The Effect of Increasing β and α can be seen in the Following Desmos Graph:
https://www.desmos.com/calculator/cykdd9dc4z
You can Use this Graph by Inputting your α value and seeing wether increasing β (The X Axis) will have a positive or a negative effect

Further analysis of T21:

TL;DR: Rule of thumb 2.0: Don't buy b until you have a>1.65. Past that, just buy b as if it is a normal upgrade.

∫
0
a

2

x
b

d
# x

2

a

b
1

b
1

{\displaystyle \int\limits\_0^a 2x^b dx = {2a^{b+1} \over b+1}}

We want to analyze how changing b affects the value, so

d

d
b

2

a

b
1

b
1

=

2

a

b
1

(
b
1

)
2

(
(
b
1
)
ln
⁡
a
−
1
)

{\displaystyle {d \over db} {2a^{b+1} \over b+1} = {2a^{b+1} \over (b+1)^2} ((b+1)\ln a - 1)}

Increasing b will increase the result when the above formula is positive.

Variable a and b come from p upgrades. The part

(
b
1
)
ln
⁡
a
−
1

{\displaystyle (b+1)\ln a -1}

decides whether the value is positive, and buying upgrades can only cause it to increase. After it becomes positive, it can no longer go back to negative. So the question is, at how much a, it starts to be worth buying b?

The price scaling of a and b are static, a is 1Sx\*1.25^x, b is 1Sp\*1.4^x. So it's possible to calculate how much b you can buy when you have a given amount of a.

Assuming the cost to next level of a and b is equal, so

# b
0.6632
a
0.1312

{\displaystyle b = 0.6632 a + 0.1312}

Instead of buying b one level at a time, you should buy it from 1 to the target value at once. This is because early b levels are harmful.

a
2

<

2

a

b
1

b
1

{\displaystyle a^2 < {2a^{b+1} \over b+1} }

 ->

2

a

b
−
1

>
b
1

{\displaystyle 2a^{b-1} > b+1}

 ->

a

0.6632
a
−
0.8688

−
0.3316
a
>
0.5656

{\displaystyle a^{0.6632a - 0.8688} - 0.3316a > 0.5656}

The result is around a = 1.62, and b = 1.20

This means at a = 1.62, buying b from 1 to 1.2 will make your r gain roughly unchanged. It's recommended to wait a bit more.