I'm tinkering with a dice pool system and have a stumbling block.

The system involves rolling a pool of up to 6 d6s with a 50% chance of 'success' on any given die (3 of the sides have a symbol on then, 3 do not).

The target number is a number from 1-6. The player is attempting to get a number of successes equal to the target number, which is usually a Defense score or something.

So, if an attacker has 3 dice in their attack pool, and the target defence score is 2, they'd roll the 3 dice and hope for 2 successes.

These are the basic odds:

Sooo.... the basic problem is that any target number higher than your dice pool is an automatic failure. You can't roll 4 successes on 3 dice.

I'm trying to think of solutions to this before I jettison the whole thing and try something else. One is that maybe one of the sides on the attack dice is a critical success and counts as 2 successes? Or explodes? I've no idea how to calculate the odds for that though.

The system involves rolling a pool of up to 6 d6s with a 50% chance of 'success' on any given die (3 of the sides have a symbol on then, 3 do not).

The target number is a number from 1-6. The player is attempting to get a number of successes equal to the target number, which is usually a Defense score or something.

So, if an attacker has 3 dice in their attack pool, and the target defence score is 2, they'd roll the 3 dice and hope for 2 successes.

These are the basic odds:

TARGET NUMBER -> | 1 | 2 | 3 | 4 | 5 | 6 |

1 die | 50% | 0% | 0% | 0% | 0% | 0% |

2 dice | 75% | 25% | 0% | 0% | 0% | 0% |

3 dice | 87.5% | 50% | 12.5% | 0% | 0% | 0% |

4 dice | 93.8% | 68.8% | 31.3% | 6.25% | 0% | 0% |

5 dice | 96.9% | 81.3% | 50% | 18.75% | 3.2% | 0% |

6 dice | 98.4% | 89% | 65.6% | 34.4% | 10.9% | 1.6% |

Sooo.... the basic problem is that any target number higher than your dice pool is an automatic failure. You can't roll 4 successes on 3 dice.

I'm trying to think of solutions to this before I jettison the whole thing and try something else. One is that maybe one of the sides on the attack dice is a critical success and counts as 2 successes? Or explodes? I've no idea how to calculate the odds for that though.

**Crit x2**-- If a crit counts as 2 successes it just pushes the problem downhill. It makes it*less*of an issue, but now the impossible targets are those more than twice your attack pool.**Crit explodes**-- If a crit explodes, the total is potentially 'infinite' so there are no impossible targets (which is good--there should always be a chance, however slim). But does anybody know how I calculate those odds into a table like above?**Alternatives**-- make everything an opposed roll, so even on a pool of 1 vs a target of 6, there's a chance the defender will roll 0 successes. This slows things down a bit though, which is one reason I've never been super keen on opposed rolls, and the game does have a number of static target numbers for tasks which it would be thematically weird to make an opposed roll (the tree is opposing you climbing it?)
Last edited: