We’re waiting to see how US Masters shakes out, but in the meantime, a recent Facebook post lit up my feed:
“Why were three armies not taken to Masters? Are things less balanced now?”
“If factions were equal you’d see two or three of each army.”
I love a good hot-take–but I love numbers more. So let’s test those claims instead of guessing.
Setting the scene
Masters uses a 64-player invite. Third-edition KoW has 28 legal factions. If every player picked at random with no bias whatsoever, what distribution should we expect?
Randomness 101: 64 darts at 28 targets
| Value | |
| Players (darts) | 64 |
| Factions (targets) | 28 |
| Average per faction | 64 ÷ 28 ≈ 2.29 |
How often does a faction get zero lists?
P(zero) = (1− 1/28)^64 ≈ 10.1%
Multiply by 28 factions and you get an expected 2.8 empty armies–call it three. In fact, a quick Monte-Carlo (code below) puts the chance of three or more no-shows at 52 %. That’s randomness, not imbalance.
“But surely we should see 2–3 of every faction!”
For that to happen every bucket needs at least two darts. The probability clocks in at ≈ 0.000001—one in a hundred-thousand events. Hitting the oft-cited “8 factions with three lists, 20 with two” is even wilder: 1-in-185 billion.
Translation: A few blank factions is the rule, not the exception.
Run it yourself
# 100k-trial Monte-Carlo: 64 lists, 28 factions
import random, collections
TRIALS = 100_000
empty = collections.Counter()
for _ in range(TRIALS):
picks = [random.randrange(28) for _ in range(64)]
missing = 28 - len(set(picks))
empty[missing] += 1
for k in sorted(empty):
print(f"{k} factions missing: {empty[k]/TRIALS:.1%}")
Typical output:
0 → 5.6% 1 → 17.1% 2 → 24.9% ≥3 → 52.3%
Feel free to bump TRIALS or swap 28/64 to test other event sizes.
Reality check: what US Masters actually showed
| Metric | 2025 US Masters |
| Factions represented | 25 / 28 |
| Lists in top-3 factions | 28 % |
| HHI (concentration) | 581 |
The Herfindahl–Hirschman Index sums the squares of each faction’s share—zero means everyone plays something different; 10 000 means a mono-faction event. Antitrust regulators consider markets un-concentrated when HHI < 1 000 (see the DOJ primer below). Masters sits at 581, well inside the “healthy mix” zone.
• Three no-shows? Exactly on-par with random expectation.
• 28 % of lists in the top three armies? Leaves 72 % spread across everything else.
• HHI = 581? A competitive field by any economic standard.
Sidebar: “It looks clumpy at the table!”
People are great at spotting patterns and terrible at estimating their likelihood. For a quick illustration, simulate a five-player card game: each player gets five cards (25 total). What’s the chance somebody holds a three-card straight (e.g., 7-8-9)?
Short answer: ≈ 72 %—randomness produces “suspicious” runs all the time. (Code in the appendix if you’re curious.)
Zooming out—11 GTs from 2024-25
| GT | Players | Top-3 share | HHI |
| UK Clash of Kings | 195 | 23.6 % | 525 |
| Adepticon | 51 | 25.5 % | 550 |
| US Masters | 64 | 28.1 % | 581 |
| Northern Kings | 34 | 29.4 % | 623 |
| Briscon | 19 | 31.6 % | 914 |
I pulled together quick data from 11 GTs across the world over 24-25 to test the HHI. Some notes:
- Take-overs usually show up as Top-3 share › 35 % and HHI › 1,000.
- Even the smallest GT (Briscon) stays below the 1,000 threshold.
- Every large event (50-plus players) includes 22-28 factions.
What should we actually worry about?
| Watch-item | Why it matters |
| Top-3 share creeping past 35 % | Early signal a new book is crowding out choice. |
| HHI above 1,000 at ≥ 50-player GTs | Field starting to compress; time for CoK tweaks. |
| The same fringe factions missing everywhere | Could hint at genuine under-power. |
Right now? None of those alarms are flashing.
Take-aways
- Three empty factions is normal, not proof of imbalance.
- HHI scores across the season are comfortably “un-concentrated.”
- Player choice looks broad and healthy. If the data shift, we’ll know.
In short: roll dice, not eyes: the meta’s fine.
Appendix A HHI primer
A friendly overview lives on Wikipedia: https://en.wikipedia.org/wiki/Herfindahl%E2%80%93Hirschman_index
US DOJ & FTC merger guidelines (scroll to “Concentration thresholds”): https://www.justice.gov/atr/hmerger-guidelines
Appendix B Card-straight simulation (optional)
import random
def has_small_straight(hand):
ranks = sorted({r % 13 for r in hand})
return any(b == a + 1 and c == b + 1
for a, b, c in zip(ranks, ranks[1:], ranks[2:]))
TRIALS = 50_000
hits = 0
for _ in range(TRIALS):
deck = list(range(52))
random.shuffle(deck)
groups = [deck[i*5:(i+1)*5] for i in range(5)]
if any(has_small_straight(g) for g in groups):
hits += 1
print(f"Chance ≥ 1 player has a 3-card straight: {hits/TRIALS:.1%}")
