Who's The Beatdown is one of the most influential Magic: the Gathering strategy articles of all time. Who's The Beatdown was written over 17 years ago, but its core principles are still applicable today, not just in MtG, but in gaming communities the world over. I highly recommend reading it if you're familiar with MtG terminology.
I don't expect to write a good article the first time through, so I'll post a draft now, and edit it when I have time to.
Version history: last updated May 21, 2016
There's a saying in the Dominion community: when in doubt between a money strategy and an engine strategy, build the engine. In practice, players who practice this philosophy have been among the strongest players of the game. Why?
The reason given by SCSN for this philosophy is that engine games are harder to play optimally than money games. Engine games simply have more decisions - what actions to buy, how and when to buy VP, what order to play actions, and so on. In other words, the skill ceiling of engine play is much, much higher than BM games. By trying to go for the engine, you get more experience in engine building, which is key to climbing the ladder. This is a fine argument, but I want to focus on arguments for winning the current game, not meta-arguments about improvement strategies.
My reason for preferring the engine is simple.
Playing an engine gives you more control over the game. When properly built, an engine has more control over when the game ends than a BM deck. The engine dictates which piles get low at what times. The engine can limit the other player's options, by playing an attack every turn. An engine is always, always favored long term. If the Province pile was 16 or 20 Provinces instead of 8, even the most absurd engines would beat a BM strategy.
The reason, then, that BM is still relevant is because engines are not always easy to build. In games with hard engines, a money strategy can often race down enough Provinces to stop the engine from catching up in VP. This is what makes Rebuild-BM so monolithic - it grabs Provinces fairly quickly, while destroying the catch-up mechanism of buying Duchies, and can accelerate the game end by trashing Province -> Province. By itself, Rebuild gives an unprecedented amount of control over the game, and because it does so by itself, it's hard to justify adding too much to Rebuild-BM.
In short, in the classical BM vs engine question, BM is the beatdown player, and the engine is the control player. The BM player wants to end the game as quickly as possible, while the control player wants to prolong the game end to give time to build. This heavily influences how both players should play. When playing against an engine, the BM player buys Gold over Duchy much longer than they would in a BM mirror, because their win condition is emptying Provinces; little else matters. When playing against BM, the engine player can empty action piles much lower than in an engine mirror, because the BM player has fewer buys, and cannot easily contest actions without slowing down their deck.
The key realization here is that the beatdown vs control dichotomy appears in every game. In BM mirrors, in engine mirrors, there is always a player who wants the game to end quickly, and a player who wants the game to end slowly. Furthermore,
a BM player is not always beatdown, and an engine player is not always control.Consider the following scenario: in an engine mirror, the key action split is the Villages, and the split happens 4-6. The player with 6 Villages is now favored long term. If they have time to do so, the max capacity of their deck is bigger. Thus, the player with 4 Villages is now the beatdown, even though they're building an engine. Their goal is to end the game before the 6 Village player has time to build. The beatdown will still buy actions for their Villages, but will buy Treasures and Victory cards sooner. The 6 Village player, in turn, will try to stall the game by buying more actions, because their deck can afford to and will win long term if given the chance.
Here's a generalization of the same scenario: both players are playing an engine mirror. One player is ahead on building. This player is now the beatdown - they want to continue pressing their advantage, eventually buying VP at a time when the other engine both cannot afford to ignore VP and cannot afford to stop building.
What makes Dominion so interesting to me is that unlike MtG, the deck is created during the game itself. This tests your ability to recognize game flow more than any other game. An engine could be the beatdown in an engine mirror, dud for a turn, then have to be the control player.
These beatdown vs control decisions are not always overarching strategy decisions - they are implicitly baked into the cards each player decides to buy. If you open with a trashing card, you're implicitly making the following bet: "the short term economy loss I'll get from trashing cards is worth the long term improvements to my deck". Trashing is fundamentally a control player move, because trashing is only worth it if the game lasts long enough to make the short term loss worth it. This is why Chapel is so strong - it trashes so quickly that the long term is almost
always going to come fast enough.
A single Herald is awful, but many Heralds are amazing. When a player buys a Herald, they're staking a claim. "I believe I can buy enough actions in time to make this cantrip for $4 worth it down the line." If you believe Herald isn't worth it, you're now the beatdown player - you need, absolutely need, to end the game before you die to a Herald stack.
A player who starts playing BM, then tries to switch to engine is going to lose, because they started out with a beatdown strategy, and tried switching to a control strategy. If you plan to take short term losses for long term gains, you should do so as early as possible, to make sure there's enough game left to reap your reward. Similarly, an engine player that tries switching to BM will often fizzle out, because they didn't finish their plan of buying enough actions to make their short term losses pay off. It can be scary, and it's not always right, but sometimes you have to have faith that your engine will come together in time, and not be intimidated when the BM player has 4 Provinces before you've bought one.
If you're playing engine or BM against a Gardens rush, you are the control player. The BM deck should not contest many Gardens, and neither should the engine, because it forces the game to end sooner. It is only worth doing so if you believe you can both deny enough VP and gain enough catchup VP to have more by the game end, while the Gardens player is ending the game ASAP. This is usually not true.
The greatest position you can be in is forcing the beatdown player to play like a control player, or vice versa. Gain enough VP to make the Gardens rush forced to stall and try to buy Duchies. Get action piles low enough to force the other engine player to buy VP for fear of a 3-pile. If you can get in a scenario where your opponent has to play against type, they'll do a bad job at it, because everything about their deck is pulling them the other way.
And, in turn, the greatest mistake you can make is playing against your role. Picking up VP when your engine has control and still has time to build. Contesting Duchies against Duchy-Duke as an engine player, instead of trying to rush down Provinces before the Duke player can buy 6 VP Dukes for $5.
If you do not identify whether you want the game to go long or short, and play against your best interests,
you will lose, unless you have a big enough advantage to cover for your mistakes.