HP formula stored on participant, loads in edit modal

hpFormula field persisted on participant doc (makeParticipant + builder).
Add handler stores formula. Edit modal loads participant.hpFormula, reroll
button sets maxHp field (no save until save). Edit submit persists formula.
Formula only for monster/npc types.

shared/tests/turn.hpformula.test.js

@@ -0,0 +1,60 @@
+// HP formula roll: parse "2d6+9" style, roll, return total.
+const shared = require('@ttrpg/shared');
+const { rollHpFormula } = shared;
+
+describe('rollHpFormula', () => {
+  test('basic NdM', () => {
+    const r = rollHpFormula('2d6');
+    expect(r).toBeGreaterThanOrEqual(2);
+    expect(r).toBeLessThanOrEqual(12);
+  });
+
+  test('NdM+bonus', () => {
+    const r = rollHpFormula('2d6+9');
+    expect(r).toBeGreaterThanOrEqual(11);
+    expect(r).toBeLessThanOrEqual(21);
+  });
+
+  test('NdM-bonus', () => {
+    const r = rollHpFormula('3d8-2');
+    expect(r).toBeGreaterThanOrEqual(1);
+    expect(r).toBeLessThanOrEqual(22);
+  });
+
+  test('single die', () => {
+    const r = rollHpFormula('1d20');
+    expect(r).toBeGreaterThanOrEqual(1);
+    expect(r).toBeLessThanOrEqual(20);
+  });
+
+  test('case insensitive', () => {
+    const r = rollHpFormula('2D6+5');
+    expect(r).toBeGreaterThanOrEqual(7);
+    expect(r).toBeLessThanOrEqual(17);
+  });
+
+  test('whitespace tolerant', () => {
+    const r = rollHpFormula(' 2d6 + 9 ');
+    expect(r).toBeGreaterThanOrEqual(11);
+    expect(r).toBeLessThanOrEqual(21);
+  });
+
+  test('large die', () => {
+    const r = rollHpFormula('4d12+10');
+    expect(r).toBeGreaterThanOrEqual(14);
+    expect(r).toBeLessThanOrEqual(58);
+  });
+
+  test('invalid returns null', () => {
+    expect(rollHpFormula('abc')).toBeNull();
+    expect(rollHpFormula('')).toBeNull();
+    expect(rollHpFormula(null)).toBeNull();
+    expect(rollHpFormula(undefined)).toBeNull();
+    expect(rollHpFormula('2d')).toBeNull();
+    expect(rollHpFormula('d6')).toBeNull();
+  });
+
+  test('zero dice invalid', () => {
+    expect(rollHpFormula('0d6')).toBeNull();
+  });
+});

shared/turn.js

@@ -28,6 +28,22 @@ const generateId = () =>
 
 const rollD20 = () => Math.floor(Math.random() * 20) + 1;
 
+// Parse HP formula like "2d6+9" or "3d8-2" or "1d20". Roll, return total.
+// Returns null on invalid input. Whitespace/case tolerant.
+function rollHpFormula(str) {
+  if (!str || typeof str !== 'string') return null;
+  const m = str.trim().toLowerCase().match(/^(\d+)d(\d+)\s*([+-]\s*\d+)?$/);
+  if (!m) return null;
+  const count = parseInt(m[1], 10);
+  const sides = parseInt(m[2], 10);
+  if (count === 0 || sides === 0) return null;
+  let bonus = 0;
+  if (m[3]) bonus = parseInt(m[3].replace(/\s/g, ''), 10);
+  let total = 0;
+  for (let i = 0; i < count; i++) total += Math.floor(Math.random() * sides) + 1;
+  return total + bonus;
+}
+
 const formatInitMod = (mod) => {
   if (mod === undefined || mod === null) return 'N/A';
   return mod >= 0 ? `+${mod}` : `${mod}`;
@@ -344,6 +360,7 @@ function makeParticipant(opts) {
     status: opts.status || (opts.currentHp === 0 ? 'dying' : 'conscious'),
     deathSaveSuccesses: opts.deathSaveSuccesses || 0,
     deathSaveFailures: opts.deathSaveFailures || 0,
+    hpFormula: opts.hpFormula || null,
   };
 }
 
@@ -365,11 +382,22 @@ function buildCharacterParticipant(character) {
   };
 }
 
-function buildMonsterParticipant({ name, maxHp, initMod, asNpc }) {
+function buildMonsterParticipant({ name, maxHp, initMod, asNpc, hpFormula }) {
   const initiativeRoll = rollD20();
   const modifier = initMod !== undefined ? initMod : MONSTER_DEFAULT_INIT_MOD;
   const finalInitiative = initiativeRoll + modifier;
-  const hp = maxHp || DEFAULT_MAX_HP;
+  // maxHp wins if both set; else roll formula; else default.
+  let hp;
+  let hpRoll = null;
+  if (maxHp) {
+    hp = maxHp;
+  } else if (hpFormula) {
+    const rolled = rollHpFormula(hpFormula);
+    hp = rolled || DEFAULT_MAX_HP;
+    hpRoll = rolled;
+  } else {
+    hp = DEFAULT_MAX_HP;
+  }
   return {
     participant: makeParticipant({
       name,
@@ -377,8 +405,9 @@ function buildMonsterParticipant({ name, maxHp, initMod, asNpc }) {
       initiative: finalInitiative,
       maxHp: hp,
       currentHp: hp,
+      hpFormula: hpFormula || null,
     }),
-    roll: { roll: initiativeRoll, mod: modifier, total: finalInitiative },
+    roll: { roll: initiativeRoll, mod: modifier, total: finalInitiative, hpRoll },
   };
 }
 
@@ -1044,7 +1073,7 @@ async function toggleHidePlayerHp(currentValue, ctx) {
 
 module.exports = {
   DEFAULT_MAX_HP, DEFAULT_INIT_MOD, MONSTER_DEFAULT_INIT_MOD,
-  generateId, rollD20, formatInitMod,
+  generateId, rollD20, rollHpFormula, formatInitMod,
   sortParticipantsByInitiative, syncTurnOrder, computeTurnOrderAfterRemoval,
   snapshotOf, buildEntry, expandUndo,
   makeParticipant, buildCharacterParticipant, buildMonsterParticipant,