Bonus Heroes - Break Even Points

astrp3

Since the math of the bonus heroes/favorite system will change over time as more 4*s are added, I thought it might be interesting to post some numbers on how many 4*s you need to favorite to have the same or better chance at drawing a specific one than you did under the old system.

First some basic numbers for heroic tokens:

Chance of drawing a 4*: 7.1%
Total 4*s in token stores: 43 (assuming Mordo and Coulson are the only two not in the stores)
Old chances at drawing a specific 4*: 0.165%
New chances at drawing one of the 12 4*s in the store: 0.592%

New chances at drawing a specific 4* not in the store:
With 1 favorite: 0.355%
With 2 favorites: 0.178%
With 3: 0.118%
With 4: 0.089%
With 5: 0.071%
With 31 (all 4*s not currently in the store): 0.011%

Note that the chance of drawing a specific 4* given a specific # of faves will not change as more 4*s are added.

Break-even point for favorites as # of 4*s increases (i.e. how many 4*s should you favorite to have an equal or better chance to get a specific one as you did under the previous system). NOTE: This assumes that you are not favoriting one of the 12 4*s already in the stores.

Currently, the break-even point is 2 (i.e. if you keep 1 or 2 favorites, you will have an equal or greater chance at getting a specific one that you did before).

With 60 total 4*s (excluding new ones), the break-even point will be 3.
With 80 it will be 4.
With 100 it will be 5.

I could do the same for elites and legendaries, if anyone cares (not sure if the b-e points will be different)