Talk:Enigma/@comment-24986675-20140925135714

Some information about the stacking of the item Small Enigma.

Small Enigma will get your cooldown[1] stacked MULTIPLICATIVELY[2] by 5%. Here's the formula:

CDnew = 0.05 + (1-0.05) * CDold

A list of values recording the amount of Small Enigmas and the related cooldown.

Please notice there's synergy[3] between Small Enigma and Rapid Mitosis on reducing cooldown.

[1] CD (CoolDown) of your is stored as a variable whose value is 45, since most of the  in this game have a 45-second CD. So for those whose CD is not 45 sec, such as Captain's Brooch (135 sec), you just need to do a simple math (triple the result of the CD formula here) to get the 'real'  CD.

BTW, all integer numbers on CD timers (including and also all Abilities) are rounded from decimals. For example, 2 on timer means the remaining time is between 1.5(included) and 2.5(excluded) seconds.

[2] Actually, the stacking of this item works a little different from other multiplicative stacking items (such as Boxing Gloves and Rapid Mitosis). For those items, the value of the variable CD is increasing. Small Enigma, however, has a decreasing value. I'm using the word MULTIPLICATIVELY only because their formulas are in the same structure: Sthnew = Rate + (1-Rate) * Sthold.

Strictly, the stacking effect of Small Enigma item should not be called MULTIPLICATIVELY. I'm not gonna put a boring math class here. To be simple, the basic reason is all other 'multiplicative' stacking items have a starting value 0 (and aiming at, most of the times, 1), but Small Enigma has a starting value 45 (and also aiming at 1).

I personally think the authors of this game have made a tiny mistake here for using the wrong formula. Their original idea is probably giving a simple formula: CDnew = 0.95 * CDold.

I'm bringing this boring section neither to be critical of the formula nor to be critical of the authors, only because it leads to a 'BUG' in the following section [3].

[3] The synergy works perfectly fine before the CD is still above 1 sec (or to be strict, the value of the variable CD is still above 1). However, Small Enigma will become a negative effect, i.e. increasing the CD rather than decreasing it, when the CD goes below 1. This should be a 'BUG' since the game has been using a wrong formula (explained above in section [2]).

For example: given the formula CDnew = 0.05 + (1-0.05) * CDold. When your CDold is 5, the CDnew = 0.05 + (1-0.05) * 5 = 4.8 -- This is correct because 4.8 is less than 5

When your CDold is 0.5, the CDnew = 0.05 + (1-0.05) * 0.5 = 0.525 -- This is wrong/bug because 0.525 is greater than 0.5

This BUG will NOT happen when:
 * You only have Small Enigma.
 * You only have Rapid Mitosis.
 * Your CD is still greater than 1.

This BUG WILL happen when:
 * Your CD is less than 1, which can be caused by:
 * Pick up more than 96 Small Enigmas and then a Rapid Mitosis.
 * Pick up more than 79 Small Enigmas and then 2 Rapid Mitosis.
 * Pick up more than 52 Small Enigmas and then 5 Rapid Mitosis.
 * Pick up more than 52 Small Enigmas and then 5 Rapid Mitosis.

The reason of this BUG is the formula of the CD always has a output going towards 1, no matter the input is greater or less than 1. When less than 1, the formula works similar to those multiplicative increasing items.

Besides, this BUG doesn't really bother you a lot, since with a 1-sec CD, you can easily crash the game already ^_^