Back in the mid 1990s, we played a variant on Magic: the Gathering for a while. We didn't pay it for long because it wasn't 'proper' Magic, and most of the other people we tried to get involved in the games just couldn't handle it.
The variant was simple. Every time a creature attacked or defended you rolled a d4, the power and toughness of the creature were boosted by the result. If a 1/1 creature rolled a 4, it might take down a 4/4 creature that rolled a 1... it might walk away unscathed from a conflict with a 3/3 creature who rolled a 1. There would only be a 1 in 16 chance of it occurring, but there was still the outside chance of a upset. Similarly, once a creature managed to score a hit on a player the player rolled a d4 to reflect a potential mystical barrier that might absorb some or all of the hit. The dice were only rolled at the end of the conflict, when everything is being resolved.
The simple concept made certain abilities more powerful, others less powerful, and changed a number of fundamental dynamics in the game. Zero cost ornithopters became potential nightmares bringing lethal strikes from above.
To counterbalance a bit of the added danger, we specified that a creatures cost an extra colorless mana... and while this generally worked, it was a case that for every rule we added in to balance things out, another aspect of the game would become unbalanced.
It was a fun idea, but needed to be integrated into the game from the beginning, because when we were adding it in, the game was already a fine tuned engine. The variant was fun for a while, and it added a degree of novelty, but after a while it became very easy to abuse.