The 'purely dependent on the skill of the player' is not possible with random effects. There is always the bad luck or the lucky draw possible that swings the state for the unlucky player. But you can make the probability for it low.



Give the Player a choice from several random options (as in a cardgame). Make them replenish only after they are fully/mostly depleted. So you have to decide wheter to use 'good' options now or later on, etc.

There is a not widely known board game (dog - don't ask me why it's called thus) that uses cards for determining the amount for the move, replenishing the hand only after it is fully used up, and giving one card less with each distribution. Very interesting concept I think.

Just my 0.02$