40k Dice Calculator

Multiply the attacks by the chance to hit, the chance to wound and the chance the save fails, then by the damage of each attack, then apply Feel No Pain and count which models actually die. For attacker: 10 attacks, bs 3+, s4, ap 0, d1. target: t4, sv 3+, 1 wound per model. that comes to 1.11 unsaved wounds on average — but the average hides the spread: 30.8% of the time those ten shots do nothing at all, which is why the calculator draws the whole distribution.

Compare the attack's Strength with the target's Toughness: twice the Toughness or more wounds on a 2+, greater on a 3+, equal on a 4+, less on a 5+, and half the Toughness or less on a 6+. An unmodified 1 always fails and an unmodified 6 is always a critical wound.

AP is subtracted from the save roll before it is compared with the armour save, so AP -2 turns a 3+ save into a 5+. The invulnerable save is checked without AP. It is one roll: the defender passes on whichever of the two it beats, so in practice the better save is used. An unmodified 1 always fails.

Cover no longer improves the save. A ranged attack against a unit with the benefit of cover has its Ballistic Skill worsened by 1, so a 3+ shooter hits on a 4+. Ignores Cover removes it, and Psychic attacks can ignore the penalty.

Re-rolling 1s only gets back the one face that always fails; re-rolling failed hits gets back every miss. Hitting on a 4+, re-rolling 1s hits 58.3% of the time and re-rolling failed hits 75.0%. A die is only ever re-rolled once.

A critical hit (an unmodified 6, unless something lowers it) can trigger both: Sustained Hits adds extra hits that roll to wound as normal, and Lethal Hits lets that critical hit wound automatically. In 11th edition Lethal Hits is a choice, not automatic.

A critical wound from a Devastating Wounds weapon ends that attack's sequence and inflicts mortal wounds equal to the weapon's Damage — no save of any kind, though Feel No Pain still applies. Those mortal wounds can damage only one model per critical wound, and they are resolved after the normal damage.

Not always. An auto-wound is never a critical wound, so it can never become Devastating Wounds. Hitting on a 3+ with Strength 4 against Toughness 4 and a 2+ save, taking the auto-wound gives 0.139 damaging wounds per attack on average, and rolling to wound gives 0.148.

No. Each unsaved attack damages one model; if it has more Damage than that model has wounds left, the rest is lost. The calculator shows that loss as "wasted to overkill".

Feel No Pain is rolled for each wound that would be lost, not once per attack. So a Damage 3 attack into a one-wound model with Feel No Pain 5+ still kills 26 times in 27: all three rolls have to succeed to save it.

Mathhammer is the hobby's name for working out the odds of an attack. This calculator computes the exact probabilities, outcome by outcome, rather than averaging thousands of simulated rolls, so the same inputs always give the same answer.