Choices at the Die Roll

One of the things I always liked about Legends of the Five Rings rpg was the Roll & Keep system for die rolling. If you are unfamiliar with it, most contests allowed the player to roll a number of dice, but then they could only use a certain number of them; the chosen dice gave the total of the die roll. Usually the player would always choose the highest die rolls (since rolling high meant greater success), but there were times when a player would actually want to roll poorly. I remember once in a game I was running, the party leader wanted the rest of the group to do something a certain way and pulled rank on them. One of the players purposely chose the lowest rolls she made and thus "failed" in the task...and accomplished her real goal of denying the party leader.

Not many game systems allow player choice at the die roll. Sure, they get to choose the color of their dice. Sure, they can make sure to roll a d8 for damage instead of a d6 because they are using a long sword instead of a short sword. But that is about it for die choice. There are not a lot of systems that allow for die choice at the time of die resolution with any sort of meaningful impact.

I recently picked up the Oubliette rpg. It uses an interesting die mechanic wherein the player gets a pool of dice. The player then rolls the dice, keeping the highest roll. However, before the roll the player can choose to remove dice from the pool and instead gain a +1 to the total for each die removed (up to a limit). Here the player is presented with a choice of how many dice to roll (upping the chance of a higher roll) or adding to the overall total (and thus lowering the chance of rolling high on the remaining dice). I'm sure there is a mathematical break-point where keeping some dice outweighs rolling more dice, and vice versa, but it still presents the player with an interesting choice. Personally I like the concept of allowing for meaningful choice at the actual die roll.

Can you think of any other game systems that allow for choice at the die roll?