New tournament, new way to frustrate players. ?

After the training tournament with a 16900 treshold for the Suwaï champion no free player can get before it ends, we now have the champion chase tournament with a 2500 threshold.

How many shards should we open to get 2500 points according current shards rates 

Again way too much for a free player !  Maths below with Y being the number of shards you would have to open.

Summary :

• Green shards : between 1483 and 2200
  
• Blue shards : between 24 and 47
• Purple shards : about 32
  
• Sacred : between 7 and 9

Worst case scenarios (no champion is void)

If we go with green shards,

2500=0.986 x Y + 0.014 x 10 x Y

2500= Y (0.986 + 0.14)

Y= 2 500/1.126

Y = 2 220

If we go with blue shards

2500=0.83 x Y x 10 + 0.16 x Y x 250 + 0.01 x Y x 500

2500=8.3 Y + 40 Y + 5 Y

Y = 2500/53.3

Y= 47

Purple shards

2500=0.915 x Y x 50 + 0.08 x Y x 350 + 0.005 x Y x 650   (==> purple always gives void)

2500=45.75 Y + 28 Y + 3.25 Y

Y = 2500 / 77

Y = 32

Sacred shards

2500= 0.94 x Y x  250 + 0.06 x Y x 500

2500 = 235 Y + 30 Y

Y = 2500/ 265

Y=9

Best case scenarios (every rare, epic and legendary is void champion)

Green : 

2500=0.986 x Y + 0.014 x 50 x Y

Y = 2500 / 1.686 = 1483

Blue

2500=0.83 x Y x 50 + 0.16 x Y x 350 + 0.01 x Y x 650

Y = 2500 / 104 = 24

Purple

2500=0.915 x Y x 50 + 0.08 x Y x 350 + 0.005 x Y x 650

Y = 2500 / 77 = 32

Sacred

2500= 0.94 x Y x  350 + 0.06 x Y x 650

Y = 2500 / 359 = 7