When to use shard-covers

MadScientist

When you have a character that acquires enough shards to increase a cover but is not yet champed, it is usually preferable to save this extra cover until you can decide exactly which color is needed later. However, sometimes one or more shard-covers can be used early without changing the probability to champ the character without wasting a cover.

For example, if the covers are distributed 4/4/3 and you have a shard-cover available, you can immediately make the character 4/4/4 as any next cover will make him champable.

To help you make these decisions I have compiled a table that shows all equivalent cover/shard-covers distributions up to 4 shard-covers. You can read the table as follows: A character with a 5/5/1 covers distribution and 1 shard-cover waiting has the same probability to be champed with the next (random) cover as a character with a 5/5/2 distribution. This probability is 33.33% (you just need one copy of the third cover in any case).

############ 1 shard-cover ###########

------------+-----------+-------------
distribution| equivalent| probability
------------+-----------+-------------
  551+1     |  552+0    |  33.33%
  542+1     |  543+0    |  66.67%
  533+1     |  543+0    |  66.67%
  443+1     |  444+0    | 100.00% 
------------+-----------+-------------
  550+1     |  551+0    |  11.11%
  541+1     |  542+0    |  33.33%
  532+1     |  533+0    |  44.44%
  442+1     |  443+0    |  77.78%
------------+-----------+-------------
  540+1     |  541+0    |  14.81%
  531+1     |  532+0    |  25.93%
  441+1     |  442+0    |  48.15%
------------+-----------+-------------
  530+1     |  531+0    |  13.58%
  440+1     |  441+0    |  25.93%
------------+-----------+-------------<br>

  

  

########### 2 shard-covers ###########

------------+-----------+-------------
distribution| equivalent| probability
------------+-----------+-------------
  550+2     |  552+0    |  33.33%
  541+2     |  543+0    |  66.67%
  532+2     |  543+0    |  66.67%
  442+2     |  444+0    | 100.00% 
  433+2     |  444+0    | 100.00%
------------+-----------+-------------
  540+2     |  542+0    |  33.33%
  531+2     |  533+0    |  44.44%
  522+2     |  533+0    |  44.44%
  441+2     |  443+0    |  77.78%
  432+2     |  433+1    |  88.89%
------------+-----------+-------------
  530+2     |  532+0    |  25.93%
  521+2     |  522+1    |  29.63%
  440+2     |  442+0    |  48.15%
  431+2     |  432+1    |  70.37%
------------+-----------+-------------
  520+2     |  521+1    |  18.52%
  430+2     |  431+1    |  48.15%
------------+-----------+-------------<br>

  

########### 3 shard-covers ###########

------------+-----------+-------------
distribution| equivalent| probability
------------+-----------+-------------
  540+3     |  543+0    |  66.67%
  531+3     |  543+0    |  66.67%
  522+3     |  543+0    |  66.67%
  441+3     |  444+0    | 100.00% 
  432+3     |  444+0    | 100.00% 
  333+3     |  444+0    | 100.00%
------------+-----------+-------------
  530+3     |  533+0    |  44.44%
  521+3     |  533+0    |  44.44%
  440+3     |  443+0    |  77.78%
  431+3     |  433+1    |  88.89%
  422+3     |  433+1    |  88.89%
  332+3     |  333+2    | 100.00% 
------------+-----------+-------------
  520+3     |  522+1    |  29.63%
  511+3     |  522+1    |  29.63%
  430+3     |  432+1    |  70.37%
  421+3     |  422+2    |  74.07%
  331+3     |  332+2    |  92.59%
------------+-----------+-------------
  510+3     |  511+2    |  19.75%
  420+3     |  421+2    |  58.02%
  330+3     |  331+2    |  77.78%
------------+-----------+-------------<br>

  

########### 4 shard-covers ###########

------------+-----------+-------------
distribution| equivalent| probability
------------+-----------+-------------
  530+4     |  543+0    |  66.67%
  521+4     |  543+0    |  66.67%
  440+4     |  444+0    | 100.00%
  431+4     |  444+0    | 100.00%
  422+4     |  444+0    | 100.00%
  332+4     |  444+0    | 100.00%
------------+-----------+-------------
  520+4     |  533+0    |  44.44%
  511+4     |  533+0    |  44.44%
  430+4     |  433+1    |  88.89%
  421+4     |  433+1    |  88.89%
  331+4     |  333+2    | 100.00%
  322+4     |  333+2    | 100.00%
------------+-----------+-------------
  510+4     |  522+1    |  29.63%
  420+4     |  422+2    |  74.07%
  411+4     |  422+2    |  74.07%
  330+4     |  332+2    |  92.59%
  321+4     |  322+3    |  96.30%
------------+-----------+-------------
  550+4     |  511+2    |  19.75%
  410+4     |  411+3    |  59.26%
  320+4     |  321+3    |  87.65%
------------+-----------+-------------<br>

  

  

111MCH111

MadScientist said:

When you have a character that acquires enough shards to increase a cover but is not yet champed, it is usually preferable to save this extra cover until you can decide exactly which color is needed later. However, sometimes one or more shard-covers can be used early without changing the probability to champ the character without wasting a cover.

For example, if the covers are distributed 4/4/3 and youavailable, you can immediately make the character 4/4/4 as any next cover will make him champable.  

  

I like your effort in the calculations, however the next cover is NOT always random. Most shards come from a feeder 3*. And that feeder will also give a specific cover at 3 champion levels. So sometimes you already know what color the next cover will be. Just also take a look at your bonus shard hero feeder progression.

MadScientist

In all the combinations listed above, there is *no* possible combination of covers you could get that would allow you to champ the character if you would have saved the shard-cover. However, knowing exactly what covers you are going to get allows you to use the shard-cover even in situations not listed above.

To illustrate the first point, let's take some examples from above:

Going from 532+2 to 543+0. There are three possible covers you could get:

1. One of the first color. In both situations you cannot use the covers and have to save it.
2. One of the second color. In the first situation, this puts the character at 542+2 and can be champed. In the second situation, this puts the character at 553+0 and can be champed.
3. One of the third color. In the first situation, this puts the character at 533+2 and can be champed. In the second situation, this puts the character at 544+0 and can be champed.

Going from 331+3 to 332+2. You would need three more usable covers to champ the character. There are only two possibilities where you could not champ the character:

1. Getting three covers of the first color. In the first situation, this puts the character at 531+3 with one saved cover. In the second situation, this puts the character at 532+2 with one saved cover. In both situations, you now need one cover of the second or third cover to champ the character.
2. Getting three covers of the second cover. This is equivalent to 1.