How to use the tabletop hit, wound and save calculator
- Enter the number of attacks and choose the die used.
- Enter the roll needed to hit, to wound and for the target to save. Pick a reroll rule for hits and wounds if you have one.
- Enter the damage each unsaved wound causes.
- Read the expected hits, wounds, unsaved wounds and damage, and the table of how likely each number of unsaved wounds is.
Formula
Chance to hit, wound or save on a die = (faces - target + 1) / faces, between 0 and 1
An attack gets through = P(hit) x P(wound) x (1 - P(save))
Unsaved wounds follow a binomial distribution with n attacks and that chance
Expected damage = n x chance x damage per wound
Each stage is independent, so thinning the attacks one stage at a time gives the same distribution as using the combined chance once.
20 attacks on a six-sided die
Hit on 3+ is 66.667 percent, wound on 4+ is 50 percent, and a 5+ save fails 66.667 percent of the time. One attack gets through 22.2222 percent of the time. From 20 attacks the expected hits are 13.333, wounds 6.667 and unsaved wounds 4.444. The chance that none gets through is 0.6563 percent, the chance of at least 5 is 46.7731 percent, and of at least 8 is 5.6533 percent.
Rerolling missed hits raises the hit chance to 88.89 percent, so the expected unsaved wounds become 5.926, or 11.852 damage at 2 damage each. With no save allowed, every wound counts.
How the stages combine
Many tabletop games resolve an attack in three rolls: one to hit, one to wound and one for the defender to save. Each roll thins the number of attacks that continue. The page multiplies the three chances for one attack and then counts how many of the attacks get through. Because the rolls are independent, you can think of it either way and get the same answer.
To compare dice that are added together see the dice probability calculator. For success-counting dice use the dice pool calculator, and for movement and ranges on a hex map the hex grid calculator.
Expected value and spread
The expected number of unsaved wounds is only the average. Real results scatter around it, and the standard deviation shows how much. With a small number of attacks the spread is large compared with the average, so the table of chances is a better guide to what might actually happen on one turn.
Assumptions and limits
- Each stage is a fair die, and a roll succeeds when it is the target number or higher.
- A target of 1 always succeeds, and a target above the number of faces can never succeed, which for the save means no save is allowed.
- Rerolls apply once, and a rerolled 1 only matters when the target is above 1.
- Extra attacks, rules that change the roll needed and ignored wounds are not modeled.
Frequently asked questions
How do I calculate expected wounds from attacks?
Multiply the number of attacks by the chance to hit and the chance to wound. With 20 attacks at 66.7 percent and 50 percent that is 6.67 wounds.
How is a save applied?
The defender succeeds on the roll needed or higher, so the chance that a wound is not saved is one minus that chance. A 5+ save fails 66.7 percent of the time.
What does rerolling misses do?
Each miss is rolled once more, so the chance becomes p + (1 - p) x p. A 66.7 percent hit chance becomes 88.9 percent.
Why show the chance of none getting through?
It tells you how often the whole attack fails. With 20 attacks and a 22 percent chance each, that happens about 0.66 percent of the time.