Five-Dice Hold Optimiser
Two rerolls left, a pair showing, and a straight half made — which dice do you keep? The honest answer needs an average over every outcome of every way of holding, and there are thirty-two ways to hold five dice. That is a few minutes of arithmetic per turn done by hand, and it is exact here: no simulation, no rule of thumb, just every result of every choice weighed by how likely it is.
What this generator does
Works through every distinct way of holding your dice, averages the score over every possible result of rerolling the rest — twice over, when two rerolls remain — and reports the hold with the highest average.
How to use this tool
- Enter what your five dice are showing.
- Choose what you are going for.
- Say how many rerolls you have left.
- Read which dice to keep, and how much better it is than the alternatives.
Understanding the controls
- What the dice show
- The five faces in front of you. Order does not matter, so 1-2-3-4-6 and 6-4-3-2-1 give the same advice.
- What you are going for
- The category you intend to score. The best hold for a straight is often the worst hold for a set, which is exactly why this is worth calculating.
- Rerolls left
- One or two. With two, the calculation looks a move ahead: it assumes you will hold optimally again next time.
Common use cases
- Deciding what to keep in a five-dice game
- Settling an argument about whether to chase a straight
- Learning why keeping a pair usually beats keeping a single high die
- Checking your instincts against the actual numbers
- Teaching expected value with a decision people care about
How this generator works
Every possible five-dice hand is one of 252, and the results of rerolling any number of dice form a distribution that can be written out in full. The recommendation's average is recomputed from scratch and compared against every other hold before it is shown, and the outcome probabilities are checked to add up to one — a missing outcome would quietly bias every figure on the page.
Randomness and fairness
Nothing is random. The same dice, target and rerolls always give the same advice, because it is a calculation rather than a simulation.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- One category at a time. A real turn weighs several open categories at once, which is a much larger calculation.
- It maximises the average score, not the chance of hitting the category outright — those differ for the straights.
- Bonuses that depend on the rest of the scoresheet are not considered.
- Five six-sided dice only.
Privacy and your data
The calculation runs in your browser. Nothing about your game is transmitted or stored.
Related generators
- Push-Your-Luck Stopping CalculatorThe pot at which rolling again stops paying, worked out exactly for any die and any busting face.
- Dice Countdown RollerRolls six dice, sets one aside, rolls the rest — the whole countdown to a single die, laid out as a sheet.
- Weighted Dice RollerBuild a loaded die by setting each face's weight, roll it, and see how far the results drift from what the weights promise.
- Dice Probability CalculatorThe exact distribution of any dice total — every outcome counted, not simulated, with the odds of rolling at least a given number.