diff --git a/app/features/tournament-bracket/core/Swiss.test.ts b/app/features/tournament-bracket/core/Swiss.test.ts
index dfc07e236..536a85751 100644
--- a/app/features/tournament-bracket/core/Swiss.test.ts
+++ b/app/features/tournament-bracket/core/Swiss.test.ts
@@ -3,6 +3,7 @@ import type { TournamentStageSettings } from "~/db/tables-json";
 import { Tournament } from "~/features/tournament-bracket/core/Tournament";
 import {
 	LOW_INK_AUGUST_2025,
+	LOW_INK_AUGUST_2026_ROUND_3,
 	RUSH_WEEKEND_3,
 } from "~/features/tournament-bracket/core/tests/mocks-swiss";
 import { ZONES_WEEKLY_38 } from "~/features/tournament-bracket/core/tests/mocks-zones-weekly";
@@ -232,7 +233,11 @@ describe("Swiss", () => {
 		});
 	});
 
-	const PAIR_UP_TEST_CASES = [RUSH_WEEKEND_3, LOW_INK_AUGUST_2025];
+	const PAIR_UP_TEST_CASES = [
+		RUSH_WEEKEND_3,
+		LOW_INK_AUGUST_2025,
+		LOW_INK_AUGUST_2026_ROUND_3,
+	];
 
 	describe("pairUp()", () => {
 		test.for(PAIR_UP_TEST_CASES)(
@@ -376,6 +381,23 @@ describe("Swiss", () => {
 
 			expect(bye?.opponentOne).toBe(2);
 		});
+
+		test("gives the bye to the lowest score group even when byeing a top group team would keep every pairing within its score group", () => {
+			// real state where the top score group had an odd size (7) while the
+			// lower groups were even (16 and 6): byeing an undefeated team lets
+			// every match stay within its score group, which the weights preferred:
+			// live this gave the free win to the 2-0 top seed instead of a 0-2 team
+			const result = Swiss.pairUp(LOW_INK_AUGUST_2026_ROUND_3);
+
+			const bye = result.find((match) => match.opponentTwo === null);
+			invariant(bye, "bye not found");
+
+			const byeTeam = LOW_INK_AUGUST_2026_ROUND_3.find(
+				(team) => team.id === bye.opponentOne,
+			);
+
+			expect(byeTeam?.score).toBe(0);
+		});
 	});
 
 	describe("calculateTeamStatus()", () => {
diff --git a/app/features/tournament-bracket/core/engine/swiss/pairing.ts b/app/features/tournament-bracket/core/engine/swiss/pairing.ts
index d9e18e268..99c30b708 100644
--- a/app/features/tournament-bracket/core/engine/swiss/pairing.ts
+++ b/app/features/tournament-bracket/core/engine/swiss/pairing.ts
@@ -16,7 +16,7 @@ import { calculateTeamStatus } from "./team-status";
  * to dwarf every other weight of the whole round, meaning rematches only happen when
  * unavoidable and then as few of them as possible.
  */
-const REMATCH_PENALTY = 1_000_000;
+const REMATCH_PENALTY = 1_000_000_000;
 
 /**
  * Weight added for each team of a pair that has already received a bye, making
@@ -24,9 +24,21 @@ const REMATCH_PENALTY = 1_000_000;
  * so that a matching leaving a bye-less team unpaired always beats one giving a team
  * a second bye: with an odd team count exactly one team is left unpaired, so the
  * matchings differ by exactly one bonus, which is set to dwarf every score-based
- * weight while staying far below REMATCH_PENALTY.
+ * weight (including HIGH_SCORE_PAIRING_BONUS) while staying far below
+ * REMATCH_PENALTY.
  */
-const PRIOR_BYE_PAIRING_BONUS = 10_000;
+const PRIOR_BYE_PAIRING_BONUS = 10_000_000;
+
+/**
+ * Weight added per score point of both teams of a pair. Summed over a full matching
+ * this contributes the bonus times the total score of all paired teams, so with an
+ * odd team count the matching maximizes it by leaving a lowest-score team unpaired —
+ * that team receives the bye. Without this term the bye can drift to a top score
+ * group team whenever the score group size parities make all-within-group pairings
+ * possible only that way. Sized to dwarf the pairing quality weights (< ~100 per
+ * pair) while a full round's worth stays far below PRIOR_BYE_PAIRING_BONUS.
+ */
+const HIGH_SCORE_PAIRING_BONUS = 10_000;
 
 interface GroupArgs {
 	groupId: number;
@@ -295,6 +307,8 @@ function generateWeightedPairs({
 				wt -= 10;
 			}
 
+			wt += (curr.score + opp.score) * HIGH_SCORE_PAIRING_BONUS;
+
 			if (curr.receivedBye) {
 				wt += PRIOR_BYE_PAIRING_BONUS;
 			}
diff --git a/app/features/tournament-bracket/core/tests/mocks-swiss.ts b/app/features/tournament-bracket/core/tests/mocks-swiss.ts
index 47117ae24..2046dae8e 100644
--- a/app/features/tournament-bracket/core/tests/mocks-swiss.ts
+++ b/app/features/tournament-bracket/core/tests/mocks-swiss.ts
@@ -19,6 +19,39 @@ export const RUSH_WEEKEND_3 = [
 	{ id: 39814, score: 0, receivedBye: false, avoid: [38337, 39850] },
 ];
 
+// tournament 4224 group A entering round 3: 7 teams at score 2, 16 at score 1, 6 at score 0
+export const LOW_INK_AUGUST_2026_ROUND_3 = [
+	{ id: 83693, score: 2, receivedBye: false, avoid: [85574, 84491] },
+	{ id: 84224, score: 2, receivedBye: false, avoid: [86019, 85541] },
+	{ id: 84735, score: 2, receivedBye: false, avoid: [84239, 83733] },
+	{ id: 85791, score: 2, receivedBye: false, avoid: [85868, 85393] },
+	{ id: 85832, score: 2, receivedBye: false, avoid: [83873, 84857] },
+	{ id: 85909, score: 2, receivedBye: false, avoid: [86038, 86046] },
+	{ id: 85970, score: 2, receivedBye: false, avoid: [85408, 85347] },
+	{ id: 83619, score: 1, receivedBye: false, avoid: [83733, 85775] },
+	{ id: 83733, score: 1, receivedBye: false, avoid: [83619, 84735] },
+	{ id: 84491, score: 1, receivedBye: false, avoid: [84553, 83693] },
+	{ id: 84553, score: 1, receivedBye: false, avoid: [84491, 86019] },
+	{ id: 84857, score: 1, receivedBye: false, avoid: [86067, 85832] },
+	{ id: 85347, score: 1, receivedBye: false, avoid: [85504, 85970] },
+	{ id: 85393, score: 1, receivedBye: false, avoid: [85860, 85791] },
+	{ id: 85408, score: 1, receivedBye: false, avoid: [85970, 85697] },
+	{ id: 85536, score: 1, receivedBye: true, avoid: [86067] },
+	{ id: 85541, score: 1, receivedBye: false, avoid: [85697, 84224] },
+	{ id: 85574, score: 1, receivedBye: false, avoid: [83693, 84239] },
+	{ id: 85860, score: 1, receivedBye: true, avoid: [85393] },
+	{ id: 85868, score: 1, receivedBye: false, avoid: [85791, 85504] },
+	{ id: 86038, score: 1, receivedBye: false, avoid: [85909, 83873] },
+	{ id: 86046, score: 1, receivedBye: false, avoid: [85775, 85909] },
+	{ id: 86067, score: 1, receivedBye: false, avoid: [84857, 85536] },
+	{ id: 83873, score: 0, receivedBye: false, avoid: [85832, 86038] },
+	{ id: 84239, score: 0, receivedBye: false, avoid: [84735, 85574] },
+	{ id: 85504, score: 0, receivedBye: false, avoid: [85347, 85868] },
+	{ id: 85697, score: 0, receivedBye: false, avoid: [85541, 85408] },
+	{ id: 85775, score: 0, receivedBye: false, avoid: [86046, 83619] },
+	{ id: 86019, score: 0, receivedBye: false, avoid: [84224, 84553] },
+];
+
 export const LOW_INK_AUGUST_2025 = [
 	{ id: 40878, score: 2, receivedBye: false, avoid: [39949, 41092] },
 	{ id: 40986, score: 2, receivedBye: false, avoid: [41308, 40796] },