In our first Dominion test we played all 52 kingdom cards of the base game and Intrigue against each other. One card stood out: Witch, which beat every other card. But the cards people actually ban mostly come from later expansions. So we taught the simulator five of them, with the new rules they need:
- Wharf (Seaside, $5): +2 Cards and +1 Buy now and at the start of your next turn. It is a Duration card: it stays in play until that second turn is over.
- Goons (Prosperity first edition, $6): +1 Buy, +$2, the other player discards down to 3 cards, and while it is in play every card you buy is worth a 1 VP token.
- King's Court (Prosperity, $7): play an Action card from your hand three times.
- Rebuild (Dark Ages, $5): +1 Action; name a card, then trash the first other Victory card from your deck and gain one costing up to $3 more. Name Province and Estates become Duchies, Duchies become Provinces.
- Cultist (Dark Ages, $5): +2 Cards, the other player gains a Ruins (a weak junk Action), and you may play another Cultist from your hand for free.
Same three questions as before. Does the card win by a mile in a simple Big Money deck? Does it still win against the strongest cards we already know? And can you get it in time? We left out Possession and Stash, which need rules our engine does not have yet.
Five ban-list cards in a money deck
Share of games won by Big Money + this card against Big Money alone. For comparison: Witch wins 96%, the best base-game card after it (Courtyard) 82%.
Test 1: against Big Money
Each card gets its own tuned buy rule, like the base-game cards did: how many copies, and whether it comes before Silver or even before Gold. For Goons we also tried buying Coppers with spare buys (each one is a point while Goons is in play), for Rebuild buying Duchies early. Up to 36 rules per card; the best one then played 20,000 fresh games against Big Money.
The ban list next to the best of the base game
Win rate of Big Money + the card against Big Money. Ban-list cards in orange.
Show the numbers
| Card | Wins vs Big Money | Best buy rule | Copies at end |
|---|---|---|---|
| Goons | 87.8% | Buy one, plus one more per 10 cards in your deck, even over Gold; with Goons in play, spend spare buys on Copper (+1 VP each) all game | 3.9 |
| Wharf | 87.6% | Buy up to 2, even over Gold | 2.0 |
| Cultist | 86.8% | Buy up to 4, even over Gold | 4.0 |
| Rebuild | 80.3% | Buy up to 3, even over Gold; once you own one, Duchy over Silver all game | 3.0 |
| King's Court | 22.1% | Buy one copy, even over Gold | 0.9 |
Three of the five land in the same spot: Goons 87.8%, Wharf 87.6% and Cultist 86.8%. That is clearly better than anything in the base game except Witch (96.2%). Goons gets there with points: our Goons bot collects 17.2 VP in tokens in an average game, from Provinces and Coppers bought while a Goons is in play. Against Cultist, Big Money ends the game with 10.0 of the 10 Ruins on average. Rebuild (80.3%) is at the level of the base game's best.
King's Court is last, by a distance: 22.1%. In a money deck it has nothing to play three times, so it is a $7 card that does nothing, bought instead of a Gold. That is not the whole story, and we come back to it below.
Test 2: against the strongest cards we know
Beating Big Money is easy. So every ban-list bot also played the 12 strongest bots of our first round robin, and each other: 175 pairings of 6,000 games, with both cards in the supply.
Head to head: the ban list and the base game's best
Each cell: how often the row card's bot beats the column card's bot. Blue = row wins, red = row loses. Ban-list cards: Cultist, Wharf, Goons and Rebuild.
Show the numbers
| Witch | Cultist | Wharf | Goons | Rebuild | Torturer | Masquerade | Patrol | Swindler | Courtyard | Courtier | Militia | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Witch | - | 63% | 79% | 76% | 70% | 83% | 52% | 75% | 70% | 84% | 83% | 90% |
| Cultist | 37% | - | 70% | 62% | 50% | 70% | 56% | 76% | 68% | 80% | 66% | 77% |
| Wharf | 21% | 30% | - | 54% | 56% | 60% | 64% | 60% | 55% | 61% | 71% | 74% |
| Goons | 24% | 38% | 46% | - | 69% | 50% | 68% | 58% | 65% | 61% | 66% | 62% |
| Rebuild | 30% | 50% | 44% | 31% | - | 51% | 54% | 53% | 57% | 52% | 66% | 56% |
| Torturer | 17% | 30% | 40% | 50% | 49% | - | 54% | 50% | 49% | 53% | 58% | 69% |
| Masquerade | 48% | 44% | 37% | 32% | 46% | 46% | - | 48% | 69% | 46% | 55% | 43% |
| Patrol | 25% | 24% | 40% | 42% | 48% | 50% | 52% | - | 53% | 49% | 63% | 61% |
| Swindler | 30% | 32% | 45% | 35% | 43% | 51% | 31% | 48% | - | 65% | 53% | 52% |
| Courtyard | 16% | 20% | 39% | 40% | 49% | 47% | 54% | 51% | 35% | - | 62% | 56% |
| Courtier | 17% | 34% | 29% | 34% | 34% | 42% | 46% | 38% | 47% | 38% | - | 54% |
| Militia | 10% | 23% | 26% | 38% | 44% | 31% | 57% | 40% | 48% | 44% | 46% | - |
Witch is still on top: it beats all five ban-list cards. Cultist is a clear second. It beats Torturer 70%, Patrol 76% and Courtyard 80%, the cards right behind Witch in the first test, and Goons 62% and Wharf 70%. Think of it as a milder Witch: a Ruins costs no points, unlike a Curse, but it still clogs a deck, and two Cultists in one hand play each other.
Goons and Wharf each beat 11 of the 12 base-game cards, all but Witch, and lose to Witch (24% and 21%) and to Cultist. They are strong cards, not a ban case: if Witch or Cultist is on the table, that is what you buy.
The best answers to Cultist
Win rate of each bot against Big Money + Cultist. A Cultist mirror would be 50%.
Show the numbers
| Bot | Wins vs Cultist |
|---|---|
| Witch | 63.3% |
| King's Court/Witch | 56.1% |
| Rebuild | 50.4% |
| Masquerade | 43.7% |
| Goons | 37.9% |
| Courtier | 33.6% |
| Swindler | 31.6% |
| Wharf | 30.3% |
| Torturer | 29.8% |
| Bandit | 26.1% |
| Council Room | 25.3% |
| King's Court/Goons | 24.9% |
| Patrol | 23.8% |
| Militia | 23.4% |
| Smithy | 21.9% |
| Courtyard | 19.7% |
| King's Court/Wharf | 19.3% |
| Throne Room/Wharf | 12.8% |
| Mill | 10.3% |
| King's Court/Smithy | 7.9% |
| King's Court | 4.2% |
The answer to Cultist is Witch (63%). Without Witch, the best we found was Rebuild, at a coin flip (50.4%). Our guess why: Rebuild turns Estates into Duchies and Duchies into Provinces, so it scores fast and cares less about a clogged deck. The best base-game card against Cultist is Masquerade (44%), which can pass the Ruins back. So with Cultist on the table and no Witch, buy Cultist.
King's Court: worse with a partner
King's Court is the odd one out: Big Money with one King's Court lost 78% of its games. That is not a fair test: it needs an Action to play. So we gave it partners (Wharf, Goons, Smithy, Witch) and tuned how many of each to buy, then compared each pair with the partner alone.
What King's Court adds to its partner
Win rate against Big Money of the partner alone, with King's Court, and (for Wharf) with Throne Room. 20,000 games per bar.
- Partner alone
- With King's Court
- With Throne Room
Show the numbers
| Partner | Alone | With King's Court | Best King's Court rule |
|---|---|---|---|
| Wharf | 87.6% | 84.1% | Buy one King's Court once you own a Wharf, and up to 3 Wharfs even over Gold; Provinces once your deck holds more than $18 |
| Goons | 87.8% | 82.7% | Buy one King's Court once you own a Goons, and up to 6 Goons even over Gold; Provinces once your deck holds more than $18; spare buys on Copper once 5 or fewer gains end the game |
| Smithy | 73.3% | 49.1% | Buy one King's Court once you own a Smithy, and up to 2 Smithies instead of Silver; Provinces once your deck holds more than $15 |
| Witch | 96.2% | 93.8% | Buy one King's Court once you own a Witch, and up to 3 Witches even over Gold; Provinces once your deck holds more than $15 |
| Wharf (with Throne Room) | 87.6% | 78.6% | Buy one Throne Room once you own a Wharf, and up to 3 Wharfs even over Gold; Provinces once your deck holds more than $18 |
| Nothing (King's Court alone) | - | 22.1% | Buy one copy, even over Gold |
Every partner did worse with King's Court. Smithy drops the most, from 73% to 49%: King's Court on a Smithy draws nine cards, but with one buy most of that money is wasted. Head to head, King's Court/Wharf wins 49% against plain Wharf and King's Court/Witch 42% against plain Witch.
The clearest sign is the late-start test. When we banned the bot from buying its King's Court before turn 13, King's Court/Smithy went from 49% to 72%. The less King's Court, the better. In a money deck it often turns up without its partner, and then it is a dead card.
So why do people ban it? Because of engines: decks with villages, draw and extra buys that play King's Court every turn, often on another King's Court. Our bots play engines poorly (see the first article), so this test cannot clear King's Court there. What it does show: King's Court is not a card you can just add to any deck.
Test 3: can you get them in time?
All five cost $5 or more, and the strong ones are early-game cards. Here is the same late-start test as in the first article: the bot may not gain its card before turn 5, 9 or 13.
What a late start costs
Win rate against Big Money when the card can't be gained before a given turn. Witch from the first article for comparison.
- Cultist
- Goons
- Wharf
- Rebuild
- Witch
Show the numbers
| Bot | From turn 1 | Turn 5 | Turn 9 | Turn 13 |
|---|---|---|---|---|
| Wharf | 88% | 79% | 69% | 52% |
| Goons | 88% | 86% | 72% | 53% |
| King's Court | 22% | 23% | 37% | 49% |
| Rebuild | 80% | 71% | 53% | 48% |
| Cultist | 87% | 71% | 50% | 48% |
| King's Court/Wharf | 84% | 84% | 84% | 85% |
| King's Court/Goons | 83% | 82% | 84% | 84% |
| King's Court/Smithy | 49% | 51% | 65% | 72% |
| King's Court/Witch | 94% | 93% | 94% | 96% |
| Throne Room/Wharf | 79% | 79% | 81% | 85% |
| Witch | 96% | 87% | 65% | 51% |
Cultist fades fastest: from turn 9 it wins 50%, a coin flip. Ruins hurt most when they sit in a deck all game, like Curses. Goons drops to 72% and Wharf drops to 69% from turn 9, Rebuild to 53%. None of this saves you in practice: $5 shows up by turn 3 or 4 in almost every game, and our Cultist bot had its first copy on turn 3.2 on average. King's Court runs the other way: every King's Court pair did better when its King's Court could not come before turn 13 than when it could come at once.
So, what should you ban?
If your group bans one card, the numbers still say Witch. If it bans two, Cultist is the second: of everything we tested, only Witch beats it, and only Rebuild holds it to a coin flip. So when it is on the table, both players end up buying it. Wharf and Goons are strong but beatable, Rebuild is fine, and King's Court is a trap for money players. If your group bans King's Court because of engines, that is a question our bots can't answer yet.
At the table
- Cultist out? Buy one with every $5 hand, even over Gold, up to 4, and chain them: a second Cultist in hand is a free play.
- Goons in play? Every card you buy is a point, so a spare buy on a Copper is worth it.
- Wharf in a money deck: 2 copies is the sweet spot for our bots.
- King's Court in a money deck: skip it. Buy it only if your deck has the Actions to play it every turn.
Not sure which box to get? We ranked every Dominion expansion, and the strongest box is not the best one.
How we tested
We extended the rules engine of the first article with the rules these cards need, and wrote checks for the odd cases: a Wharf stays in play through cleanup and is not shuffled into a new deck; a Throne Room or King's Court that plays a Wharf stays in play with it, and the next-turn bonus comes two or three times; Goons gives one VP token per buy for each Goons in play, but a Goons played three times by King's Court is still one Goons; tokens come from buying, not gaining. The Ruins pile holds 10 cards dealt from a shuffled set of all five kinds, and counts as a pile for ending the game. A trashed Cultist draws its owner 3 cards, also when the other player's Swindler trashes it. Rebuild names Province and sets revealed cards aside, so a reshuffle halfway through does not include them.
Bots and Big Money are the same as in the first article. Each card's buy rules were tuned in 2,000-game runs, the best four replayed with 8,000 fresh games each, and the winner measured with 20,000 more. The King's Court pairs were tuned over 48 to 96 rules each, in 4,000-game runs. The head-to-head grid mixes two runs: cells with a ban-list card come from 6,000 games each, cells between two base-game cards from the first article's 2,000. Every number comes from fixed random seeds.
Limits. Two players, and only the tested cards in the supply. Our bots play money decks, not engines, which matters most for King's Court and Goons. The classic nightmare is an engine that plays King's Court on Goons every turn and spends a pile of buys on Coppers for points; our King's Court/Goons bot is a money deck and never gets there. We did not test Possession or Stash. More on how we test.
Image credits
- Photo: Matěj "Dědek" Baťha, via Wikimedia Commons (CC BY-SA 4.0, Matěj "Dědek" Baťha (resized)): Four players in a game of Dominion at the Hry a hlavolamy games fair, 2009
- Box art: Rio Grande Games (publisher box art via retailer product image (philibertnet.com), shown to identify the product): Box of Dominion: Prosperity (2nd edition): a couple picnicking under trees in front of a manor house, Box of Dominion: Seaside (2nd edition): a sailing ship moored at a harbour town with a tall tower, Box of Dominion: Dark Ages: a warrior with an axe in front of ruined columns
