How can I reduce the planar die "whiff factor" with house rules?
This is inspired by the action-choosing mechanism from Speculation.

Start of game setup:


Get six objects that can represent planeswalk/chaos/nothing: colored marbles, Scrabble tiles, popsicle sticks with symbols drawn on them, etc.
Place the objects in an opaque bag.


When the player wants to "roll":


The player pays the cost for rolling and chooses an item from the bag without looking.
If a Nothing item is removed, set it aside on the table.
If a Planeswalk or Chaos item is removed, perform that action and return all the items to the bag.


This reduces the likelihood of whiffing over time.


Normal 4/6 chance on the first roll.
3/5 chance after the first whiff.
2/4 chance after the second whiff.
1/3 chance after the third whiff.
No chance of whiffing after four whiffs.


This seems to well satisfy criteria 1, 3, and 4. Admittedly, it's not much faster than regular rolling, if you discount the fact that on average you'll get a favorable result faster than if you had used a die.