What's your opinion about Mutant? Please, talk me about your experience...

My friends think this is a broken character and they want to fix it.

Mutant has the most singular abilities in the game:
She begins with random status. She just roll 2 dice at the start of the turn losing 1 life. The only certain ability is to avoid to be turned into a Toad LOSING 1 LIFE instead; I think it's a very good ability, because to become a toad really sucks.

Mutant's values are 2strength/2craft/3fate/5life

Estimation of starting status:
Strength: 3,16
Craft: 3,66
Fate: 3,55
Life: 5,5 -> Note: this is a character who spend life to activate her principal ability
Spells: 0,33

Mutation ability: LOSE 1 LIFE to roll 2 dice
2,77% 2) -1s and -1c
5,55% 3) -1s or -1c
8,33% 4) -1life !Danger!
11,11% 5) -1fate
27,76% Bad things

30,54% 6-7) heal 1 life and replenish 1 fate
30,54% Pretty good things in the most of cases
If you have more than 5 lives and more than 3 fates it's a bad thing because you have just lose a life.
If you have less than 5 lives and more than 3 fates, nothing happen. If you have more than 5 lives and less than 3 fates, now you have a fate instead a life.
If you have less than 5 lives and less than 3 fates, you get a fate

13,88% 8) +2fates
11,11% 9) +2lives
25% Very Good things

8,33% 10) +1s
5,55% 11) +1c
2,77% 12) +1s and +1c
16,65% Very ignorant level-up!

Now, think about light fate and dark fate.
Mutant is an evil character, so the Graveyard is a pretty choice to represtinate fate.
Mutant will probably use light fate for bad things (27,7%) [2-5]. In the best of the hypothesis we have 1+4 = 5. Light fate to 1. Reroll 1 in a 6. 6+4 = 10 = gain a strength.
Mutant's opponents will probably use dark fate for ignorant level up (16,65%) [10-12]. In the best of the hypothesis we have 5+5=10. Dark fate to 5. Reroll 5 in 1. 5+1 = 6 = heal 1 life, repristinate 1 fate.
If Mutant rolls 1+6=7 (16,66%), there is a chance she uses a light fate to 1.
= 1 6
Otherwise, there is a chance for mutant's opponents to use a dark fate to 6.
= 1 6
But, keep in mind: we don't know if mutant's opponents have dark fate to use against mutant during the game.

Notes:
- It's better if Mutant mutates with at least 3 lives (or 1 light fate)
- Fates and Lives are the fuel for his ability... 8 and 9 roll in the 25% of cases.
- Dark fate isn't a guarantee
- If mutant turn alignment in good it can be easily broken (good mutant+chapel+poltergeist = omg)
- No Toad is a great thing

I've only seen the Mutant once, and we hadn't introduced the Light/Dark Fate yet, so I can't speak to how much we would attempt to sabotage the Mutant with Dark Fate. I will say that odds are the Mutant isn't going to get too much out of its mutations, as most times it's just going to be gaining lives or fate. In addition, lives are a lot harder for the Mutant to replenish, and while Fate can certainly fix a bad roll, using up your lives is significantly more dangerous. Our Mutant spent a large portion of the game at two lives due to mutating followed by a couple of bad encounters, and wasn't able to do much of anything other than explore for several rounds. I don't think it's so terribly unbalanced; it basically swaps the positions of the good rewards in the Temple, making it easier to fuel mutations, but harder to get anything really substantial in the long run out of it. The bads are also really, really bad.

However, we did (by chance) stumble upon one scenario where the Mutant really shines: A Hero Rises alternative ending card. Odds are really good that the mutant is gaining at least 1 fate on their roll (44% by your calcs), thanks to fate replenishment turning to gains if you're already past max fate, plus replenishments from visiting the Graveyard. While the other two characters in the game were still struggling to get past the halfway point, the Mutant had her full fate and was only hesitant to go on because she had been stuck at two lives for almost half of the game. Once she healed up even a little, she made a beeline for the Crown and won handily.

The last game that we played, it wasn't an issue. Stepson had the mutant, and used all the lives he could to adjust his stats. Then he couldn't get to any place to heal his lives and died in combat.
I think it took something like ten turns to happen. I very much enjoyed looting the spot where he died. (mwahahahaha)