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Dominion Articles / Thoughts on Strategy vs Tactics
« on: May 04, 2012, 10:11:42 pm »
[Thoughts on Strategy vs Tactics]
The aim of this article is to revive a distinction made by a top player a little while ago:
I'll reformulate the two skillsets with my own wording:
Strategy is defined as analyzing the board, and either consciously, or unconsciously, appreciate its richness. It involves planning out not just your opening, or your most likely deck construction path, but also means taking into account other outcomes than the 'typical' one (i.e. so called 'strategy switches').
Tactics is how you execute your plays, and focuses on the actual, every-turn decisions you make. It involves how you play, buy or trash cards and more importantly, in which order. It also crucially involves the greening stage, moneyness and engine-building decisions.
In more mathematical terms, Tactics solely relies on a probability framework, while Strategy includes a dose of uncertainty, due to the inherently complex nature of some boards. The usual approach towards the study of Tactics, brilliantly illustrated by both the Geronimoo and Dominiate simulators, is to simplify the dominion board to the clash between two 1-3 card strategies. This makes the problem of finding the optimal execution policy actually tractable, greatly improving someone's understanding of how a particular strategy works, and how it interacts with a particular competing one. Now, technically, the simulator is also supposed to answer questions of strategic nature. And it does so quite well for certain strategies, but I would like to stress the limits of that approach. My aim is not to diminish the importance of simulation: it is probably one of the biggest achievement in our strategic thinking, having discovered simple and elegant strategies such as Double-jack and Fool's gold. But I do think it pre-conditions us to think of strategies that have a low level of tactics involved... though paradoxically, the people who then use these strategies by default end up with a very high level of tactics.
In order to illustrate my point, let me review what are considered the two most common families of strategies, and how they relate to Tactics and randomness. My claim is that both try to reduce randomness in order to make tactics-related decisions easier... and of course, improve your chances of winning:
I'll start with the more obvious link. Engine building is a difficult but rewarding subgame of Dominion. It often involves more cards than big money, but not necessarily more types of cards. Most of the engines can be summarized by two cards, with often a third card being splashed in practice: Torturer chains,, Hunting Party engines, King's Court/Scheme shenanigans, Scrying pool engines, Hamlet/Menagerie interaction or the brilliant Apothecary/Native village Combo of Mean Mr Mustard. What all of these engines have in common, is that they try to defeat randomness by building a deck that will behave nearly exactly in the same manner every single turn. This often involves either heavy trashing (let's not forget that chapel is still probably the best card in the game) or drawing your whole deck (e.g.: brilliant win by O.G.), but can also involve scheme or hunting party (or both). The point is, you want to be able to play exactly the same set of cards every turn. I cannot end this paragraph without quoting the impressive Marin and his amazing engines.
Big Money is the other grand line of strategy. It comes in various shapes and sizes, often as BM+card. The most elegant version of it is probably double-jack, which not only truly encompasses the core value of 'moneyness' of the archetype, but also single-handedly defends it against pesky attacks such as sea hag or witch. An extensive review of the paradigm behind big money, read WanderingWinder's two articles on the topic. The man is the master of the field, and one of the two most skillful players I have had to chance to play with. Now, after you read about money density, about the relationship between deck size, hand size, and the ratio of green to treasure, I hope you appreciate what truly lies behind the spirit of Big money: the law of large numbers! Indeed, whereas engines try to defeat minimize randomness by building towards a near-deterministic play-mat every turn, big money attempts to minimize randomness by placing itself in the most favorable 'average' scenario. By keeping the strategy nice and simple, it avoids non-linearities, letting its tempo, and the law of large numbers, simply slide itself to victory.
Now you see why these strategies lend themselves to somewhat easier decisions in terms of tactics: they involve a relatively limited amount of cards, and the aim is to reduce the number of encountered scenarios inside a same game. This allows for a more rigorous training in the exact set of tactical skills you need to perfectly execute the strategy: by playing a simple, 1-2 card strategy over and over again, you will learn in which order to buy the cards, when to green and how to best close the game. You can also have a hope of simulating the strategy with a decent bot, greatly bootstrapping your analysis. But this only works for simple strategies. With simple, I don't mean 'simplistic' but rather elegant. And even the simplest of strategies, BM+Envoy, includes a learning curve in terms of greening decisions.
I am going to propose a third group of strategies, one that is in my opinion somewhat under-evaluated. It might also often be confused, or maybe just mixed, with engine strategies. I will dub them messy strategies, in the sense that they often are played less tactically skillful than the previous two, maybe because they are undervalued, but mostly because they have an inherently higher learning curve. This is because they often involve either cards that are less powerful (and with which players have therefore less experience), or just a greater number of different cards (and the combination therefore appears less often, leading to less experience as well). The essence of these strategies is to embrace, rather than fight, randomness or uncertainty. They reward risk, although in a measured manner. Probably the most known example are treasure map based strategies. I in particular believe those strategies to be well adapted to a player who faces a severe bias against him, due to for example to First player bias. Here are two examples of such plays: One successful noble brigand gamble, and another not immediately successful treasuremap/black market gamble. Of course, the first game is biased by the sheer fact that I hit Wanderingwinder's silver, but regardless, it added a fair amount of variance to a game that would otherwise have been dominated by a BM-variant. The second game is really just me attempting two initial gambles (black market and treasure map), but transitioning to a menagerie engine powered by exactly that variance in card types (crossroads,treasure mapand black market all work well with menagerie). The opponent's strategy was a standard pirateship/crossroad engine that would have perfectly messed up a BM in position 2. Messy strategies often also rely on one particular 'non-linear' event to happen, which of course strongly increases their variance. This awesome play michaeljb needs him to buy exactly one province (but not more, lest I finish the pile!), a few tournaments (without overcomiting, as I will have more provinces) all this to get the one princess that will allow the mega-turn. Of course, it's embedded in a more standard wharf engine, but that is secondary. A card I really enjoy using for messy strategies is navigator. Now in that particular example, the non-linear event is tactician with several banks (with some wharf help). It's not really an engine, as I do not pull of the thing with anywhere near enough regularity. Nor is it big money, given how I do not rely on the law of large numbers. It truly means I set up one or two very big turns to swing the game in my favor, often forcing my opponent into plays he did not foresee having to do (like getting duchies early). Navigator helps a lot in this situation, because it allows you to virtually hit more hands, increasing your odds of getting that magical non-linear one. KC-Navigator in particular I would rank as a full combo, probably very typical of the messy strategy: first, similarly to warehouse a lonely navigator increases your odds of having a KC paired up with an important target (like another KC), but more importantly, KC on navigator nets you 6$, and often guarantees you that your next hand will have KC+target. Of course, sometimes the wanted non-linear event just happens too late (I still think it was the correct play on that board, at least as p2).
Messy strategies face a big hurdle, however. Because they often rely on a mix of variance, non-linear effects and more than 2-3 types of cards, they are very hard to re-encounter, simulate and evaluate. This makes it very hard to anakyze certain weird strategies (like this talisman=>feast=>city idea) and leads to discussions where it is unclear whether the elegant strategy is necessarily the best one (I much prefer the ironworks/smuggler opening, which also grabs a ton of silvers, but obviously does not have the spy effect. On the up side, it can grab islands as well as lucky golds and duchies. But while I prefer it (because more decisions are involved), I am not convinced it is the better move).
To summarize, I tried to reintroduce an old concept, Strategy versus Tactics, illustrating it on the two dominant classes of strategies. Then I argue that a third class of strategies exists (and maybe more?), which is in a weird sense more tactics intensive (because it is intrinsically harder to be experienced in it) and paradoxically played by less tactically skilled players (because tactics-players tend to hone their strategies by repeating them). This presents an interesting conundrum to players that are willing to push their strategic thinking a bit further, at the expense of losing their tactical edge. I hope you enjoyed the read.
Edit: replaced "Skill" by "Tactics". Thanks for the feedback!
The aim of this article is to revive a distinction made by a top player a little while ago:
At its very core, I think Dominion only tests two skillsets; to identify the strongest strategy, and to execute that strategy optimally. Is there a difference between very strong players and exceptionally strong players in these areas, you think?
I'll reformulate the two skillsets with my own wording:
Strategy is defined as analyzing the board, and either consciously, or unconsciously, appreciate its richness. It involves planning out not just your opening, or your most likely deck construction path, but also means taking into account other outcomes than the 'typical' one (i.e. so called 'strategy switches').
Tactics is how you execute your plays, and focuses on the actual, every-turn decisions you make. It involves how you play, buy or trash cards and more importantly, in which order. It also crucially involves the greening stage, moneyness and engine-building decisions.
In more mathematical terms, Tactics solely relies on a probability framework, while Strategy includes a dose of uncertainty, due to the inherently complex nature of some boards. The usual approach towards the study of Tactics, brilliantly illustrated by both the Geronimoo and Dominiate simulators, is to simplify the dominion board to the clash between two 1-3 card strategies. This makes the problem of finding the optimal execution policy actually tractable, greatly improving someone's understanding of how a particular strategy works, and how it interacts with a particular competing one. Now, technically, the simulator is also supposed to answer questions of strategic nature. And it does so quite well for certain strategies, but I would like to stress the limits of that approach. My aim is not to diminish the importance of simulation: it is probably one of the biggest achievement in our strategic thinking, having discovered simple and elegant strategies such as Double-jack and Fool's gold. But I do think it pre-conditions us to think of strategies that have a low level of tactics involved... though paradoxically, the people who then use these strategies by default end up with a very high level of tactics.
In order to illustrate my point, let me review what are considered the two most common families of strategies, and how they relate to Tactics and randomness. My claim is that both try to reduce randomness in order to make tactics-related decisions easier... and of course, improve your chances of winning:
I'll start with the more obvious link. Engine building is a difficult but rewarding subgame of Dominion. It often involves more cards than big money, but not necessarily more types of cards. Most of the engines can be summarized by two cards, with often a third card being splashed in practice: Torturer chains,, Hunting Party engines, King's Court/Scheme shenanigans, Scrying pool engines, Hamlet/Menagerie interaction or the brilliant Apothecary/Native village Combo of Mean Mr Mustard. What all of these engines have in common, is that they try to defeat randomness by building a deck that will behave nearly exactly in the same manner every single turn. This often involves either heavy trashing (let's not forget that chapel is still probably the best card in the game) or drawing your whole deck (e.g.: brilliant win by O.G.), but can also involve scheme or hunting party (or both). The point is, you want to be able to play exactly the same set of cards every turn. I cannot end this paragraph without quoting the impressive Marin and his amazing engines.
Big Money is the other grand line of strategy. It comes in various shapes and sizes, often as BM+card. The most elegant version of it is probably double-jack, which not only truly encompasses the core value of 'moneyness' of the archetype, but also single-handedly defends it against pesky attacks such as sea hag or witch. An extensive review of the paradigm behind big money, read WanderingWinder's two articles on the topic. The man is the master of the field, and one of the two most skillful players I have had to chance to play with. Now, after you read about money density, about the relationship between deck size, hand size, and the ratio of green to treasure, I hope you appreciate what truly lies behind the spirit of Big money: the law of large numbers! Indeed, whereas engines try to defeat minimize randomness by building towards a near-deterministic play-mat every turn, big money attempts to minimize randomness by placing itself in the most favorable 'average' scenario. By keeping the strategy nice and simple, it avoids non-linearities, letting its tempo, and the law of large numbers, simply slide itself to victory.
Now you see why these strategies lend themselves to somewhat easier decisions in terms of tactics: they involve a relatively limited amount of cards, and the aim is to reduce the number of encountered scenarios inside a same game. This allows for a more rigorous training in the exact set of tactical skills you need to perfectly execute the strategy: by playing a simple, 1-2 card strategy over and over again, you will learn in which order to buy the cards, when to green and how to best close the game. You can also have a hope of simulating the strategy with a decent bot, greatly bootstrapping your analysis. But this only works for simple strategies. With simple, I don't mean 'simplistic' but rather elegant. And even the simplest of strategies, BM+Envoy, includes a learning curve in terms of greening decisions.
I am going to propose a third group of strategies, one that is in my opinion somewhat under-evaluated. It might also often be confused, or maybe just mixed, with engine strategies. I will dub them messy strategies, in the sense that they often are played less tactically skillful than the previous two, maybe because they are undervalued, but mostly because they have an inherently higher learning curve. This is because they often involve either cards that are less powerful (and with which players have therefore less experience), or just a greater number of different cards (and the combination therefore appears less often, leading to less experience as well). The essence of these strategies is to embrace, rather than fight, randomness or uncertainty. They reward risk, although in a measured manner. Probably the most known example are treasure map based strategies. I in particular believe those strategies to be well adapted to a player who faces a severe bias against him, due to for example to First player bias. Here are two examples of such plays: One successful noble brigand gamble, and another not immediately successful treasuremap/black market gamble. Of course, the first game is biased by the sheer fact that I hit Wanderingwinder's silver, but regardless, it added a fair amount of variance to a game that would otherwise have been dominated by a BM-variant. The second game is really just me attempting two initial gambles (black market and treasure map), but transitioning to a menagerie engine powered by exactly that variance in card types (crossroads,treasure mapand black market all work well with menagerie). The opponent's strategy was a standard pirateship/crossroad engine that would have perfectly messed up a BM in position 2. Messy strategies often also rely on one particular 'non-linear' event to happen, which of course strongly increases their variance. This awesome play michaeljb needs him to buy exactly one province (but not more, lest I finish the pile!), a few tournaments (without overcomiting, as I will have more provinces) all this to get the one princess that will allow the mega-turn. Of course, it's embedded in a more standard wharf engine, but that is secondary. A card I really enjoy using for messy strategies is navigator. Now in that particular example, the non-linear event is tactician with several banks (with some wharf help). It's not really an engine, as I do not pull of the thing with anywhere near enough regularity. Nor is it big money, given how I do not rely on the law of large numbers. It truly means I set up one or two very big turns to swing the game in my favor, often forcing my opponent into plays he did not foresee having to do (like getting duchies early). Navigator helps a lot in this situation, because it allows you to virtually hit more hands, increasing your odds of getting that magical non-linear one. KC-Navigator in particular I would rank as a full combo, probably very typical of the messy strategy: first, similarly to warehouse a lonely navigator increases your odds of having a KC paired up with an important target (like another KC), but more importantly, KC on navigator nets you 6$, and often guarantees you that your next hand will have KC+target. Of course, sometimes the wanted non-linear event just happens too late (I still think it was the correct play on that board, at least as p2).
Messy strategies face a big hurdle, however. Because they often rely on a mix of variance, non-linear effects and more than 2-3 types of cards, they are very hard to re-encounter, simulate and evaluate. This makes it very hard to anakyze certain weird strategies (like this talisman=>feast=>city idea) and leads to discussions where it is unclear whether the elegant strategy is necessarily the best one (I much prefer the ironworks/smuggler opening, which also grabs a ton of silvers, but obviously does not have the spy effect. On the up side, it can grab islands as well as lucky golds and duchies. But while I prefer it (because more decisions are involved), I am not convinced it is the better move).
To summarize, I tried to reintroduce an old concept, Strategy versus Tactics, illustrating it on the two dominant classes of strategies. Then I argue that a third class of strategies exists (and maybe more?), which is in a weird sense more tactics intensive (because it is intrinsically harder to be experienced in it) and paradoxically played by less tactically skilled players (because tactics-players tend to hone their strategies by repeating them). This presents an interesting conundrum to players that are willing to push their strategic thinking a bit further, at the expense of losing their tactical edge. I hope you enjoyed the read.
Edit: replaced "Skill" by "Tactics". Thanks for the feedback!
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