Item: Frostshard

I was inspired to design an item that had a similar feature to vorpal sword's instant kill (with conditions). I tried to balance Frostshard using vorpal sword as a baseline. I figured that if vorpal sword had a 5% chance to instant kill, that I would double the chance for Frostshard and not include the +3 hit/dam rolls. Here's my table from AnyDice:

Frostshard needs two critical hits in a row to instant kill. The second attack must be made before the start of your next turn (hence this sword is best used by fighters with extra attack), but is made with advantage since the target is petrified. To reach the 10.40% chance of instant kill, I set the crit range to 17-20. Also, since vorpal sword ignores slashing resistance, I thought that I would copy that effect by giving Frostshard +1d8 cold damage (which is a longsword's damage dice).

The icing on the cake for Frostshard is its wand-like property. All in all, this sword is probably overpowered, but only playtesting can tell.