# Talk:Diamond Flask

## Contents

## Discussion of Effectiveness

It would be useful to document the actual effectiveness of this flask, as that is not immediately obvious. A mod may consider adding the discussion or parts of it to the main page.

Let us call the total crit chance (including gear, charges, etc.) the *crit* chance, and the crit chance obtained by drinking the flask, the *lucky* crit chance.

The *lucky* crit chance is mathematically described as: *lucky = 1 - (1 - crit) ^{2}* or

*2crit - crit*. It is useful to analyze the

^{2}*lucky*crit chance in terms of relative and absolute difference to the original

*crit*chance.

### Relative Increase

Relative increase = *(lucky-crit)/crit = 1 - crit*

In other words, the distance of *crit* chance to 100% is the effective multiplier you are getting through the diamond flask. E.g. with 70% *crit* chance, the flask will give you a 30% increase (just like a **30% more critical strike chance** modifier would), for a total of 91% *lucky* crit chance.

But this is misleading for small numbers: if you have a 10% *crit* chance, a 90% increase will mean only 19% *lucky* crit chance, which -- while almost doubled -- is generally too low for critting.

### Absolute Increase

Absolute Increase = *lucky-crit = crit - crit^2*

This gives us an overview of the largest absolute effect of the flask, depending on our *crit* chance (see the graph at google). Immediate observation indicates that the flask is the most effective when our *crit* chance is exactly 50% (*lucky* crit chance is then 75%). The absolute increase in total crit chance is symmetrical on both sides of the curve and approaches zero the closer you get to 0 or 100% *crit* chance.

### Cut-off crit chance for diamond flask

What is a meaningful cut-off for *crit* chance when using the diamond flask? Obviously, yielding a *lucky* crit chance beyond 95% is meaningless so this should always be taken into account. In practice, the decision also depends on how useful another flask would be in place of the diamond flask.

To calculate the *crit* chance based on desired *lucky* crit chance: *crit = 1 - sqrt(1-lucky)*. For 95% *lucky*, *crit* needs to be ~ 77.6%, and for 90% *lucky*, *crit* needs to be ~ 68%*. See also the graph at google (inverse of the Absolute Increase formula).*

Another decision could be to consider the flask only if it has the effect of at least **X% more critical strike chance**, which is to have *crit* at most *100% - X%* (inverse of the Relative Increase formula). E.g. for the flask to have at least **30% more critical strike chance** effectiveness, *crit* may at most be 70%.