There are some games that feature randomness that is partly controlled by the player. For example, deck building games (dominion etc) let you choose which card

There are some games that feature randomness that is partly controlled by the player. For example, deck building games (dominion etc) let you choose which cards to add to your deck, then cards cycle through deck -> hand -> discard pile, finally shuffling discard pile to become new deck. There is randomness in the order of cards drawn from your deck, but it can be influenced by your decisions of what cards to add to your deck during the game, and you are guaranteed to draw each card in your deck once as you successively draw hands and cycle through your deck, before shuffling. I am very much enjoying playing "slay the spire", which takes this deck building mechanic and mashes it up into a roguelike. There is additional variability in random encounters, rewards, and what moves enemies do, but part of the fun is figuring out how to best exploit or mitigate the situation you end up in with the hand you are dealt, and trying to tilt the odds of the kinds of hands you'll get in future. Helps that games are usually short (eg win in an hour if everything goes well, die quickly and restart a new run otherwise) Another example is a game where each player has two moddable d6 : the values of the faces of each players dice can be individually upgraded/replaced , as one of the core mechanics of the game. ("Dice forge"?)