True chance of achieving "safe" Star levels

[Klepto]

Just ran some quick calculations for these. Would like to expand on this if/when possible to include chances above 9 stars:

Chance to increase from 1 star to 4 stars: .88 * .72 * .56 * 100 = 35.48%
Chance to increase from 4 stars to 7 stars: .45 * .32 * .2 * 100 = 2.88%
Chance to increase from 7 stars to 9 stars: .14 * .10 * 100 = 1.4%

As you can see, achieving 5 stars or so is fairly trivial, but actually succeeding at achieving 7 stars or higher is incredibly difficult and involves tremendous luck given that your chance to succeed at consecutive rolls drastically decreases once you've achieved the 4 star mark.

The really sad part here is that since getting 4 stars is pretty much easy unless your luck is terrible, getting 7 stars seems initially like it wouldn't be that much harder but your true chances are actually very slim.

With average luck, you will theoretically have to try 34-35 times from 4 stars to succeed at getting one hero to 7 stars. This means with average luck you will need well over 100 blue medals for each hero you achieve 7 stars with. 250-300+ blue medals is very likely.

Even if you obtain half of those medals for free from Labyrinth and Guild Chests, 100 blue medals at an "average" cost of 4 gems apiece is still 400 gems or $35-$40.

That's the true cost of a 7 star hero, on average. Whether you get the gems from daily Count/King's Bounty or buy them, or get them in the Arena/Labyrinth, you will spend $35-$40 of gems on average (or more) to get a 7 star hero. Even this is a lowball estimate on cost. Use your money (and gems) wisely, and treat stars and blue medals as a perk, not as a goal.