Board Thread:General Discussion/@comment-25968376-20150709075810/@comment-25968376-20150724120859

(Sorry, I don't have a video showing the ticks)

Just taking pure energy into account, doesn't matter if they're from potions or revives. Doing some calculations, I basically set up the following formula:

$$\displaystyle T = \frac{E_B+E_E \cdot n_{Tee}}{\frac{1}{(1+ SED)^{n_{Tsed}}} \cdot EL}$$ where $$T$$ is time expected to run, $$E_B$$ is the base energy, $$E_E$$ is extra energy from treasures, $$n_{Tee}$$ is number of treasures with extra energy, SED is slower energy drain, $$n_{Tsed}$$ is number of treasures with SED, and EL is energy loss per tick. So what we want which values of SED gives a higher T than EE. To make this easy, we can assume that both n:s are the same. Anyone want to solve this? My head is spinning from all the math already :)

As an example: Cookie has 500 base energy an episode has 4 energy drain/tick. A comparison between 3 treasures that just give extra energy, vs 3 treasures that just give SED. So what we want to solve is

$$\frac{500+E_E \cdot 3}{1 \cdot 4} > \frac{500+0}{(\frac{1}{1+SED^3}) \cdot 4} $$

Now as an example, we can plug in and compare the values of T we get for 3x cocktail vs 3x muffin at +9. Once again I chose a cookie with 500 base Energy and running on an episode with 4 energy drain per tick.

For the cocktails we get: $$T = \frac{500 + 40 \cdot 3}{\frac{1}{1.1^3}\cdot 4} = 206 $$ seconds.

For the muffins we get $$T = \frac{500 + 90 \cdot 3}{\frac{1}{1.07^3}\cdot 4} = 235$$ seconds.

However, look what happens when I change the SED value of the cocktail. Just a slight increase, from let's say 10% to 15% already gives us about 235 seconds, which is the same as the muffin! And how about a 20% value? 267 seconds! Whereas an increase in recovery isn't so dramatic. 20 extra energy for the muffin only resulted in T=254, only 19 seconds increase. The mathematical analysis is that the power factor (x^n) in the SED makes T grow much faster than adding extra energy, which is a linear growth.

Conclusion: In this particular case, I'd recommend 3x muffins but with a 25% slower energy drain boost for maximum run time. But as soon as we see treasures with 15% or higher SED, use those instead!