Say who can win each pot in the fewest names that answer it

The pot breakdown listed every eligible player for every pot. Pot
eligibility is nested — the main pot is everyone still live and each side
pot above it drops whoever was all-in below — so the main pot's line was
every name at the table and each side pot repeated it minus one.

The lines too long to fit were exactly the ones nobody needed spelled
out, and the short ones at the bottom were the side pots a dealer
actually announces by name. Measured on an iPhone 14: a single all-in
five-handed already clipped the main pot, and twelve-handed the first row
wanted 521px of a 254px slot. There was no count and no title, so a
dealer reading "Alexandra…" could not tell whether three people or eleven
were eligible — the number the showdown turns on.

Each line now names whichever of "who is in" and "who is out" is shorter,
which nesting guarantees is never more than half the table, and leads
with the count because the line is right-aligned and it is the tail that
gets cut off. "all 9", "8 in, not Mike from work". On a phone this takes
one, two and three all-ins from every main-pot line clipped to nothing
clipped at all; twelve-handed goes 6 clipped rows to 5, and even a cut
row still opens with "9 in".

The wizard's copy of the same announcement wraps instead — it is a dialog
that scrolls, and it is what the dealer reads out before anybody shows a
hand — so nothing there is ever cut off. The full list is also on the
title for anyone with a pointer, which is the extra rather than the
answer, since a tooltip is not a mechanism a keyboard reaches.

potCalculator.test.js now proves the nesting across 20,000 random tables
and asserts on its own generator, so the loop cannot go vacuous. Audit
unchanged at 2 failing configurations and 3 offenders, both pre-existing.
787 unit tests pass.

Co-Authored-By: Claude Opus 5 <[email protected]>
Claude-Session: https://claude.ai/code/session_015bnp7xKUPFFSpwkYNFaPgb

tests/holdem/potCalculator.test.js

@@ -122,3 +122,63 @@ describe("PotCalculator.resolveRound", () => {
         assert.throws(() => PotCalculator.resolveRound(entries, ["ghost"]), /No valid winners/);
     });
 });
+
+// The pots come out of layers() in one order and with one relationship between them,
+// and the action bar's wording now depends on both. If eligibility were not nested,
+// "8 in, not Mike and Bob" would be a lie — there would be someone eligible for a side
+// pot who was never eligible for the main one, and naming the complement would hide
+// them. It is a property of how the layers are built rather than an accident of the
+// examples above, so it is checked as one.
+describe("pot eligibility is nested", () => {
+    function rng(seed) {
+        let s = seed >>> 0;
+        return () => {
+            s = (s * 1664525 + 1013904223) >>> 0;
+            return s / 4294967296;
+        };
+    }
+
+    test("every side pot's players are a strict subset of the pot below it", () => {
+        const random = rng(20260905);
+        let multiPotTables = 0;
+        let pairs = 0;
+
+        for (let table = 0; table < 20000; table++) {
+            const n = 2 + Math.floor(random() * 11);
+            const players = Array.from({ length: n }, (_, i) => p(
+                `p${i}`,
+                // A sixth of the table never puts anything in, which is a table mid-deal.
+                random() < 1 / 6 ? 0 : (1 + Math.floor(random() * 8)) * 25,
+                random() < 0.2));
+
+            const layers = PotCalculator.layers(players);
+            if (layers.length > 1) multiPotTables++;
+
+            for (let i = 1; i < layers.length; i++) {
+                const below = layers[i - 1].eligible;
+                const belowSet = new Set(below);
+                const here = layers[i].eligible;
+                pairs++;
+                assert.ok(here.every(id => belowSet.has(id)),
+                    `table ${table}: ${layers[i].label} has a player ${layers[i - 1].label} does not\n` +
+                    JSON.stringify(players));
+                assert.ok(here.length < below.length,
+                    `table ${table}: ${layers[i].label} is no smaller than ${layers[i - 1].label} — ` +
+                    `layers with the same eligibility are supposed to be merged into one pot\n` +
+                    JSON.stringify(players));
+            }
+        }
+
+        // Guards the generator rather than the code: a shape that stopped producing side
+        // pots would make every assertion above vacuous and the test would still pass.
+        assert.ok(multiPotTables > 10000, `only ${multiPotTables} tables had a side pot`);
+        assert.ok(pairs > 20000, `only ${pairs} adjacent pairs to check`);
+    });
+
+    test("so the main pot is everyone still live, and it is the widest", () => {
+        const layers = PotCalculator.layers([p("a", 100), p("b", 40), p("c", 100), p("d", 25)]);
+        assert.deepEqual(layers[0].eligible.sort(), ["a", "b", "c", "d"]);
+        layers.slice(1).forEach(layer =>
+            assert.ok(layer.eligible.length < layers[0].eligible.length));
+    });
+});