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 from1star to4stars: .88 * .72 * .56 * 100 =35.48%

Chance to increase from4stars to7stars: .45 * .32 * .2 * 100 =2.88%

Chance to increase from7stars to9stars: .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 tryThis 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.34-35 times from 4 stars to succeed at getting one hero to 7 stars.

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.