When to use shard-covers
MadScientist
Posts: 201 Tile Toppler
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>
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Comments
Going from 532+2 to 543+0. There are three possible covers you could get:
- One of the first color. In both situations you cannot use the covers and have to save it.
- 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.
- 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: