Multiplayer series, part 2: Card Strength

This is the second part in a series of articles written by Polk5440. The series studies games of Dominion with three or more players and how they differ from games with just two players.

More Players, More Chances

Some cards get better with more players because their effects have more chances to hit. For example, gaining potentially 2, 3, 4, or 5 excellent cards with Jester or multiple Treasures with Noble Brigand can accelerate your deck quickly. In the other direction, Tournament actually becomes weaker with more players because there are more opponents who may reveal a Province (blocking Tournament’s on-play effect) and more competition for Prizes.

 

Stacked Attacks

Most attack cards’ effects get better with more players because they stack and potentially more copies of the card can be played per turn. For example, with 4 players, if every player has one Witch, you could get up to 3 Curses instead of one by the end of the turn. Discard attacks like Militia don’t truly stack because once you discard down to 3 cards in hand, the damage is done; however, they are more likely to be played consistently if everyone buys a copy, which can make them feel more oppressive. Pirate Ship powers up more consistently with more players, and the increased frequency of attacking can make treasure-based decks completely infeasible. Torturer, Ambassador, Mountebank, and their relatives (while certainly powerful cards in two player Dominion) can turn a multiplayer game into a slog even if there are strong anti-junking cards in the kingdom.

There are two ways of handling that incoming junk: deal with it once it’s in your deck or prevent it from entering your deck in the first place. While trashing is an effective way of dealing with the incoming junk no matter the number of players, with more players most trashing cards are less effective at preventing your deck from being bogged down early in the game, and thus are a little weaker. Lookout can still only trash one card a turn; Trade Route can only trash one card a turn; Sentry can only trash up to two cards a turn.

This may be fast enough in a lot of two-player kingdoms where you are only getting one piece of junk a turn early on, but it can be too slow with several players dishing them out each turn. You can buy more copies of trashing cards to provide your deck with more trashing capacity, but that comes at the expense of attacking others or building your deck’s draw capacity or economy.

 

Defense

Because many attacks’ effects stack, defensive cards like Moat, Watchtower, and Guardian are much better with more players because they provide defense against any number of attacks. While the number of cards Sentry can trash per turn is capped, the reaction on Moat doesn’t wear out — its reaction prevents you from suffering the effect of any number of attacks on a given turn as long as you have it in hand.

Additionally, with more opponents you are probably going to be attacked more consistently; this also makes defensive cards better. For example, with four players, you have three opponents who might play a Witch when you have a Moat in hand instead of just one opponent who might play a Witch in a two player game.

 

Example: Moat and Witch

 

To see how cards’ relative power levels depend on the number of players, consider Moat and Witch. They both draw two cards, so that ability is a wash. The real comparison is between the ability to dole out a Curse to an ability to block incoming Curses.

In two player games, Witch is an absolute powerhouse and Moat is a weak card; often, Witch is a must-buy and Moat is ignored.

Let’s put a little evidence toward this claim with a simple simulation of the head-to-head match up of a player who only buys Witches versus a player who only buys Moats.

The strategies simulated are as follows: The Witch-only player buys two Witches; the first one as soon as possible, the second one on the next $5. The Moat-only player opens Moat-Silver, buys a second Moat on $2 or when there are 10 Treasures in the deck (otherwise buys Silver), and continues to buy Moat on $2 up to 5 total Moats in the deck.

2pgraph

Buying only Witch absolutely smokes buying only Moat. Moat’s defense is not a guarantee against infiltration; those 10 Curses will find their way into the Moat player’s deck eventually, ruining the deck’s potential to score.

Tweaking the buy rules doesn’t change the simulation very much, though you can play around with these strategies yourself“It’s OK to ignore Moat” is an early lesson learned when becoming more competitive at two-player Dominion.

This may surprise some players, though. Blocking all incoming attacks seems so powerful. How could it not be good? That intuition does not come from nothing; Moat’s defense CAN BE strong… in games with four players.

4pgraph

Using the exact same buy rules as before, but just adding two more players playing the Witch only strategy results in the Moat only player winning nearly half of the games.

The Moat player can actually improve to better than 50% win rate versus three Witch only players by opening Moat-Moat instead of Moat-Silver, and there are probably tweaks to when additional Moats are purchased that can be made to improve the Moat only strategy even more. Conversely, there is not much the Witch only players can do to improve their win rate, except give up playing a Witch only strategy and buy Moat, as well.

What is going on here? Moat is at its best when it’s able to block multiple stacking attacks at once. As mentioned in the previous section, multiplayer games with junking attacks like Witch are basically exactly this scenario.

There are a couple of other things going on, as well. Players playing only Witch are ALSO playing against players playing only Witch, so they are also being slowed down by gaining Curses. This doesn’t happen with two players. This means the Witch players are slowed down and the Moat player is not destined to get all of the Curses. While Moat may not create an impermeable defense, Curses now go to other players, too. The players playing only Witch may even get MORE Curses than if the Moat player wasn’t even in the game. (Remember, more players means more Curses are available per person.)

While this is not a recommendation to buy only Witch or only Moat in any game (just to be clear: it’s definitely not), this is an illustration of how the relative power levels of cards do depend on the number of players, and intuition built in one context (two players) may not carry over into another (four or more players).

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2 Responses to Multiplayer series, part 2: Card Strength

  1. Jomini says:

    It is worth mentioning that cards that have benefits to other players (e.g. Council room, Gov, Bishop, Embassy) also become relatively worse. Take a BM/Cr option. In single player odds of you getting the other guy up to some really big humps is just not that high; sure some percentage of the time he goes $6 -> $8, but there are going to be more times where he will go from $8 -> $10 without a +buy (if he skips Cr). In 4er, you both stack the draw effect (starting hand of 7 is huge) and you increase the number of people who might be tipped into province territory.

    Often this effect embodies the opposite of both Jester (more targets who might benefit, e.g. getting Bishop in a junking game) and Witch (the one guy who doesn’t opener Messenger/Silver can get a huge benefit by doing something that takes advantage of his high cash density like opening Trade Route).

    Gov is particularly dangerous as at game end pile control utterly breaks down. You will have somebody who can make a prov or duchy if there are viable $7 or $4 cards to have in hand and you want to remodel golds. If you need to the duchy pile or the provs to stay topped off, it is far more risky to remodel for points (e.g. Silver -> Duchy when you have $18 and 3 buys).

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