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[-Stef-]

Suppose we're playing Borinion, a much more boring game then Dominion. Two players, P1 and P2, take consecutive turns. P1 gets to start, and due to the unfair nature of this game it ends after 9 turns. So P1 always gets to make one extra turn. Both players start at 100 points, and every turn they choose...

option A: 60% chance at +3 points, 40% at -3 points
option B: 50% chance at +5 points, 50% at -5 points
option C: 40% chance at +10 points, 60% at -10 points

If you play this game in isolation, it's easy: always option A is best. In fact, it's the only option with a positive mathematical expectation. Simulation over one million games shows that if both players follow this simple minded strategy, P1 will win approximately 555000 vs 445000 (55.5 win% for P1).

However, this game is not about scoring as many points as you can. It's about scoring more points than your opponent. And thus, plans that might look bad at first glance end up being better after all.

Suppose we leave the game plan of P1 what it was ('always go A'), but experiment a bit with P2. If we change it to 'option A when ahead, option B when behind' the win% for P1 drops to 51%. 'option A when ahead, option C when behind' works even better; now P1 only wins 46% of the games. We can improve P2 further by delaying the risky things, and enforcing option A on his first turn (42.5% for P1) or his first two turns (42.1% for P1).

I'm starting to get convinced the optimal strategy is actually quite complex. I think it uses all 3 options, and also includes the 'turns to go' and 'actual point difference' (not just 'am I behind or ahead'). But I won't go into that - I didn't name it Borinion for nothing.

So what does this game teach us about Dominion? Most of all that the optimal strategy always involves your opponent. Even on kingdoms without any attacks, it matters a lot what he's doing and how well he's doing. If you both start out the same, but he has some shuffle luck and you don’t, it's time for crazy things. I he stumbles where you thrive, try to buy safe cards.

It also suggests it’s good to have options. If you create an option B, C or D for yourself to use later on, that choice itself is already good. Engines give you much more options than BigMoney. So in playing engines right, it's not just about 'how can I effectively build this engine in solo play'. It also requires a good feeling/understanding for taking risks. Simulators we use today don't understand it at all, and that may very well be the reason variants of BigMoney strategies do so well in simulation and so poorly in reality.

Opening two terminals isn't all that bad just because they might collide. P1 has no real reason to take this risk, but P2 is already behind at the start. It of course depends on the questions 'how good is it if they don't collide' and 'how bad is it if they do'.

One of my favorites is double Steward, because if they collide I can still get rid of 2 cards. I wasn't going to do much more on a turn with steward without collision anyway. Don't get me wrong - I'm not happy with the collision at all - but it's not a game losing disaster either. And depending on the kingdom, being able to get rid of 4 cards in the first round may very well be winning. As a rule of thumb, opening with two terminals is too soon to take risks though.

It’s not easy to define risky or safe things in general. A safe choice that happens often midgame is adding a little more +actions to your deck than the bare minimum. Another safe choice is to stop playing your engine where you could draw some more cards, just to prevent a reshuffle. Maybe you can put a good card on top for next turn?

Risky things could include adding more cards that require other cards (Baron, Remodel, Forge) or buying slightly too many terminals in general. Village + smithy is more risky than laboratory + laboratory. Swindler has the risk build-in all by himself. So do treasure map and tournament, but they’re not really an addition to a deck - they require building your entire deck around them.

In the endgame it can get quite complex because of the ending conditions of a Dominion game. The most common risky thing is buying the next-to-last province. There is a rule for not doing it, but even if it made you lose, that doesn't automatically say it was a bad thing to buy it. If your deck is not so good, and you're losing the long run for sure, try to sneak out a victory now.

To summarize: constantly figure out whether you’re ahead or behind. If you’re ahead consolidate, if you’re behind make a plan to get back. As player 2, you’re behind when you start - do something with it.

[WanderingWinder]

Your game is actually not so hard to 'solve'. You just have to work from the end. And take some time. Probably a couple hour or so and you're done. Faster if you can program the thing.
i.e. if coming into the ninth turn, P1 is...:
more than 3 points ahead, he takes option a and wins 100% of the time. (100%)
exactly 3 points ahead, he takes option a and wins 60% of the time, ties 40% of the time. (80%)
from two points ahead through two points behind, he takes option a and wins 60% of the time (60%)
three to four points behind: he takes option b and wins 50% of the time (50%)
five to nine points behind: he takes option c and wins 40% of the time (40%)
ten points behind: he takes option c and ties 40% of the time (20%)
more than ten points behind: he always loses (0%).

To find out what P2 should do on turn 8, you look at the different starting values, and what each thing gets you, except now, instead of having 100% win, 100% tie, 60s and 50s and 40s, you have to look at how much of a lead/deficit that eighth turn gets you, and then use the probabilities from the ninth turn to get your win percentage. Every extra step adds many more possibilities, so it grows pretty quickly in the number of computations. But it took me longer to type this than it did to calculate.

[WanderingWinder]

Dominion-wise, this has a nice point, that you need to adjust to your opponent, but... there really isn't any advice here as to how to do that. 'When you're ahead, consolidate.' Well, sort of. But mostly how? What do you mean by ahead? What do you mean by consolidate? You have to know what you mean by this in order to put your advice into any kind of good use. Because a lot of people will read this and think 'oh, I have more points than him right now, playing my BM deck, I need to absolutely buy green every step of the way so that I have a big lead before his engine roars into life'. Which is basically wrong - you want to build more in this situation, generally, as the money player, with a number of exceptions of course.
'When you're behind, take risks'. Well, again, what do you mean? What does behind mean? Does it mean points, deck quality, both? How do I know when I'm behind?
Finally, there's also some kind of inherent strength of the strategies. What do I mean? To use your example, if you extend it past 9 turns to like 40 turns (more like a typical game of dominion...), then there's going to be no circumstance where before, I dunno, turn 8 (I don't know when it is exactly, without calculating), you should play anything other than option A. Because it's just stronger. In Dominion terms, two strategies have to be very very close for you to take a different road just because of seat. Now, later in the game, you need to make different plays more often, because the situations change a lot more. But the idea that I should play some strategy other than the optimal one that player 1 just took, just because I'm player 2, is generally a losing proposition.

Finally finally (yeah, I know I said finally earlier...), the one really concrete thing. Double steward. It's generally a really bad opening, unless you have a $2 you really want to buy early on (lighthouse, hamlet, crossroads). In those cases, it can be pretty darn strong. Otherwise, in your best case scenario, all you're doing is trash 4 cards all reshuffle long, and buying nothing. Which is almost never better than, say, opening steward/silver (or some other 3 or 4 you want) and then picking up your second steward on the reshuffle.
Having said that, I think people are way too scared of things like terminal collision. Thing is, if you're going to have that bad luck, like the 20% of the time worst luck, you're probably going to lose on any strategy (if you're opponent is much good). So go for the risks anyway. Indeed, I think people don't take risks nearly enough, and this is true in the P1 or P2 seat.

[-Stef-]

I know I didn't include any real practical advice. I'm just trying to point out that 'best in quarantine' and 'best in an actual game' can be very different things.

--

For a set where I actually would open steward/steward as P2 I refer to a post of Jeebus (http://forum.dominionstrategy.com/index.php?topic=2469.0) where he references this game http://councilroom.com/game?game_id=game-20120430-220116-745a70e9.html

I want to draw my deck with highways/markets ASAP, and I'm not that interested in anything else. No good draw available, so getting rid of 4 cards is really good. As P1, or against an opponent going for the alchemists, fishing/steward feels better & safer.

[Obi Wan Bonogi]

Great article Stef.  This is how I think about risk every single game.  It feels the most rewarding when it leads to successful lines which in isolation would look very curious or downright terrible.  You have enough bewildered opponents that I'm sure you can attest to that. 

Because a lot of people will read this and think 'oh, I have more points than him right now, playing my BM deck, I need to absolutely buy green every step of the way so that I have a big lead before his engine roars into life'.

The amount of people who read Stef's article and somehow conjure up this nugget should not be classified as "a lot," perhaps "a few people will read this and think ..." or "one person will read this and think..."   

The article is about risk-taking in engine builds and how to think about risk-taking strategically.  I don't see how anyone could distort his points into BM green buying gibberish.

the one really concrete thing. Double steward. It's generally a really bad opening

He gives MANY concrete examples of risky options that take into account how he thinks about risk-taking.  (Baron, Forge, Swindler, +terminals, treasure map, etc) 

Don't mind WW.  This is the best article I have come across on here.

[WanderingWinder]

Great article Stef.  This is how I think about risk every single game.  It feels the most rewarding when it leads to successful lines which in isolation would look very curious or downright terrible.  You have enough bewildered opponents that I'm sure you can attest to that. 

Because a lot of people will read this and think 'oh, I have more points than him right now, playing my BM deck, I need to absolutely buy green every step of the way so that I have a big lead before his engine roars into life'.

The amount of people who read Stef's article and somehow conjure up this nugget should not be classified as "a lot," perhaps "a few people will read this and think ..." or "one person will read this and think..."   

The article is about risk-taking in engine builds and how to think about risk-taking strategically.  I don't see how anyone could distort his points into BM green buying gibberish.

Obviously hyperbole. But not really that far off the mark. And if you think people won't read this as needing to green faster... you don't know what you're talking about.

the one really concrete thing. Double steward. It's generally a really bad opening

He gives MANY concrete examples of risky options that take into account how he thinks about risk-taking.  (Baron, Forge, Swindler, +terminals, treasure map, etc) 

No, he gives many vague examples. Baron is not a concrete example, because it's a single card, which is clearly not always the risky option. You can see this about any of the other things as well, except the extra terminals, which, while a very good tip (the best thing in the article, perhaps), is definitely not a concrete example.

Don't mind WW.  This is the best article I have come across on here.

I'm not trying to say that it's a bad article. If he can't take some criticism, he really ought not to be writing. There hasn't been a single article on here that hasn't gotten some, and there are several articles better than this one, despite this being one of the better articles. The points that -Stef- is trying to make are absolutely critical, but I think they can be made more clearly.

[WanderingWinder]

I know I didn't include any real practical advice. I'm just trying to point out that 'best in quarantine' and 'best in an actual game' can be very different things.

--

For a set where I actually would open steward/steward as P2 I refer to a post of Jeebus (http://forum.dominionstrategy.com/index.php?topic=2469.0) where he references this game http://councilroom.com/game?game_id=game-20120430-220116-745a70e9.html

I want to draw my deck with highways/markets ASAP, and I'm not that interested in anything else. No good draw available, so getting rid of 4 cards is really good. As P1, or against an opponent going for the alchemists, fishing/steward feels better & safer.

How is fishing village/steward, picking up a second steward on the reshuffle, not better in either case? Seriously, this is one of the things I'm talking about: if this is the right play as second player, I really don't know how it's not the right play as first player, too. If taking the risks are worth it, it's going to be worth it either way.

[DG]

I'd agree with the philosophy of Stef's article but I'd give some caution as to how players should let it affect their play. Unless you're really on top of your game and can see entirely how a kingdom will play out, you can lose games by pursuing a riskier strategy that doesn't work. For example, if you can see a flaw in the risky strategy then sometimes that minor flaw is actually a misjudgement of a major flaw. Perhaps your opponent isn't going to play as well as you're giving them credit for. Perhaps your opponent will draw badly enough for a safe strategy to beat them, and that happens quite often. I know that some of my worst self-inflicted losses have come through overestimating an opponent's advantage and using that as an excuse to play some desperately poor (risky) Dominion.

As a game progresses though I'd certainly agree that you should evaluate your strategies on the chance of winning rather than points per turn. The PPR is the best example of that but it goes a lot further. Always prepare your deck so that it has a chance to win on best draws.

Long games tend to reduce the chance of the first player winning through the extra turn so that's the simplest thing the second player can try as metagame. This would mean avoiding game accelerators (governor, vault, council room, embassy) but using more attacks and variable vp cards.

the one really concrete thing. Double steward. It's generally a really bad opening

Not for players who realise that the village is a good card.


edit- thanks for pointing out the error

[Obi Wan Bonogi]

 
Stef used Baron as a passing example.  I don't think Stef should be required to teach everyone how to build with Baron in order to use the concept in high-level article about risk-taking. 

Seriously, this is one of the things I'm talking about: if this is the right play as second player, I really don't know how it's not the right play as first player, too. If taking the risks are worth it, it's going to be worth it either way.

You literally don't know what he is talking about.  Regardless of any specific example the whole point is precisely "how to think about when the right play is not always the right play and if the risks are worth it."

[Grujah]

I actually liked the article quite a bit.
Stuff like this always impress me, especially the sim. Though, I expect quite a different result with larger number of turns (as a lucky C wouldn't cause such a big spike).

Long games tend to reduce the chance of the second player winning through the extra turn so that's the simplest thing the second player can try as metagame. This would mean avoiding game accelerators (governor, vault, council room, embassy) but using more attacks and variable vp cards.

You mean "the first player winning through the extra turn".

[Empathy]

Liked the article.

My preferred example for the "p2 likes variance, p1 likes certainty" is the following game:

First to 43 points wins. Each player has two available strategies:

-Safe: 43 points in 20 turns, no matter what
-Risky: 10% chance of getting 43 points in 15 turns, 90% chance of self-destructing and never getting 43 points.

p1 will always play the safe strategy, and p2 the risky one.

As for the domi example:

Governor (5/2 as p1) vs Smuggler (3/4 as p2)?

I'm not sure to what extent this proves the point, or just my failure at using the simulator, but I hope it makes sense.

[O]

This is pretty true for two player dominion but even more applicable for 4-player dominion. Your odds of winning as P4 with equally skilled opponents are so slim that the stupidly luck-dependent treasure map strategy starts to look pretty good...

Actually, in four-player dominion even P1 has more incentive to pick the more luck dependent strategy, though I'm not sure its proportionately so.

[Geronimoo]

Very interesting article, Stef, but add a few example games, please.

[ARTjoMS]

Some good strategies.

Here are some examples.

Strategy: open 2 stewards, play steward  6 turns in a row, buy gold, mining village, goons etc and dont forget to gg.

Another really good strategy: get 5-2 split on trating-post governor deck.

Open silver potion - buy familiars and make them not miss shuffle.

Want more? Ask -Stef- .

[WanderingWinder]

 
Stef used Baron as a passing example.  I don't think Stef should be required to teach everyone how to build with Baron in order to use the concept in high-level article about risk-taking. 

So first it's a concrete example, now it's a passing example? I agree, it's a passing example. I don't think he needs to explain every card in this article. But I would like some examples of 'I played this risky strategy here, here's why I did it.' If it had that, it could be one of the finest articles I've read (since it's already pretty good).

Seriously, this is one of the things I'm talking about: if this is the right play as second player, I really don't know how it's not the right play as first player, too. If taking the risks are worth it, it's going to be worth it either way.

You literally don't know what he is talking about.  Regardless of any specific example the whole point is precisely "how to think about when the right play is not always the right play and if the risks are worth it."

And my whole point is that he isn't explaining how to think quite right. Because you shouldn't be taking more risks as p2 than p1. Okay, you should, but it's a really really small difference. You'll notice the difference once every hundred games, at most. Probably once every few hundred games. Does this make it un-important? In the scheme of things, yeah. I'm fine talking about it, because it's not nothing. But I think way too much emphasis is being put here on the p1 vs p2 thing. I think prima facie that the difference in positions at the start of a game p1 to p2 is being blown out of proportion here. The larger points that he's trying to make about taking risks, particularly when behind (though I think here only later in the game, where you actually are significantly behind!) are absolutely important, and sort of getting lost with this p1 vs p2 thing.

[RisingJaguar]

Disclaimer, I didn't read the full article but tried to find a game that followed Player 1: safe - Player 2: Risky (or at least unfamiliar)

http://councilroom.com/game?game_id=game-20120102-125145-aeff94ae.html
Player 1: Wharf-BM on 5/2
Player 2: Wharf -> highways. 
I'm not sure if I just had the superior strategy or just superior luck here (I do get great draws... or at least make great use of my draws? No I definitely got good draws), but the idea is that going different as second player gave me a better chance than the mirror would.  Or at least that's how I feel.  The player going as engine can make a lot of mistakes with their purchases and its 'best' to take the BM approach with player 1. 

I hope this is along the right track of the article. 

PS. It is REALLY hard to try and find games like this, looking at logs takes so much time. 

[WanderingWinder]

I'm not sure if I just had the superior strategy or just superior luck here (I do get great draws... or at least make great use of my draws? No I definitely got good draws), but the idea is that going different as second player gave me a better chance than the mirror would.  Or at least that's how I feel.  The player going as engine can make a lot of mistakes with their purchases and its 'best' to take the BM approach with player 1. 

An excellent example of what I'm disagreeing with. Pretty sure that the highway route is just better here. But my larger point is... like, if it increases your win% as player two to play the 'riskier' strategy, then it probably also increases your chances as player 1 to play the 'riskier' strategy, at least just looking from the outset. At some point in the games, you do go to playing riskier. But you don't want to plan that from the beginning. Again, 'I can't play the mirror, because that gives me a disadvantage as p2' is wrong thinking. You ALREADY HAVE the disadvantage as player two; playing a worse strategy is generally going to compound that.

[Empathy]

 
Stef used Baron as a passing example.  I don't think Stef should be required to teach everyone how to build with Baron in order to use the concept in high-level article about risk-taking. 

So first it's a concrete example, now it's a passing example? I agree, it's a passing example. I don't think he needs to explain every card in this article. But I would like some examples of 'I played this risky strategy here, here's why I did it.' If it had that, it could be one of the finest articles I've read (since it's already pretty good).

Seriously, this is one of the things I'm talking about: if this is the right play as second player, I really don't know how it's not the right play as first player, too. If taking the risks are worth it, it's going to be worth it either way.

You literally don't know what he is talking about.  Regardless of any specific example the whole point is precisely "how to think about when the right play is not always the right play and if the risks are worth it."

And my whole point is that he isn't explaining how to think quite right. Because you shouldn't be taking more risks as p2 than p1. Okay, you should, but it's a really really small difference. You'll notice the difference once every hundred games, at most. Probably once every few hundred games. Does this make it un-important? In the scheme of things, yeah. I'm fine talking about it, because it's not nothing. But I think way too much emphasis is being put here on the p1 vs p2 thing. I think prima facie that the difference in positions at the start of a game p1 to p2 is being blown out of proportion here. The larger points that he's trying to make about taking risks, particularly when behind (though I think here only later in the game, where you actually are significantly behind!) are absolutely important, and sort of getting lost with this p1 vs p2 thing.

Example:
Consider two strategies: Geronimoo's optimized tournie bot, and a tournie/baron bot I quickly scrambled together.

p1/p2 (both with 4/3)

tournie/tournie: 58/39
tournie/baron: 57/41
baron/tournie: 55/43

Code: [Select]

<player name="Baron/tournie"
 author="Empathy"
 description="Baron trying to race an early province to block the tournie p1.">
 <type name="Generated"/>
 <type name="Province"/>
 <type name="BigMoney"/>
 <type name="Bot"/>
 <type name="TwoPlayer"/>
 <type name="UserCreated"/>
 <type name="SingleCard"/>
   <buy name="Followers"/>
   <buy name="Trusty_Steed"/>
   <buy name="Princess"/>
   <buy name="Bag_of_Gold"/>
   <buy name="Province"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Baron">
      <condition>
         <left type="countCardsInDeck" attribute="Baron"/>
         <operator type="smallerThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Tournament"/>
   <buy name="Silver"/>
</player>

Agreed, it's a small effect. But I think veto allows you to create (or remove) a lot of such scenarios: therefore, you should be thinking about it while vetoing (I think).

[WanderingWinder]

 
Stef used Baron as a passing example.  I don't think Stef should be required to teach everyone how to build with Baron in order to use the concept in high-level article about risk-taking. 

So first it's a concrete example, now it's a passing example? I agree, it's a passing example. I don't think he needs to explain every card in this article. But I would like some examples of 'I played this risky strategy here, here's why I did it.' If it had that, it could be one of the finest articles I've read (since it's already pretty good).

Seriously, this is one of the things I'm talking about: if this is the right play as second player, I really don't know how it's not the right play as first player, too. If taking the risks are worth it, it's going to be worth it either way.

You literally don't know what he is talking about.  Regardless of any specific example the whole point is precisely "how to think about when the right play is not always the right play and if the risks are worth it."

And my whole point is that he isn't explaining how to think quite right. Because you shouldn't be taking more risks as p2 than p1. Okay, you should, but it's a really really small difference. You'll notice the difference once every hundred games, at most. Probably once every few hundred games. Does this make it un-important? In the scheme of things, yeah. I'm fine talking about it, because it's not nothing. But I think way too much emphasis is being put here on the p1 vs p2 thing. I think prima facie that the difference in positions at the start of a game p1 to p2 is being blown out of proportion here. The larger points that he's trying to make about taking risks, particularly when behind (though I think here only later in the game, where you actually are significantly behind!) are absolutely important, and sort of getting lost with this p1 vs p2 thing.

Example:
Consider two strategies: Geronimoo's optimized tournie bot, and a tournie/baron bot I quickly scrambled together.

p1/p2 (both with 4/3)

tournie/tournie: 58/39
tournie/baron: 57/41
baron/tournie: 55/43

Code: [Select]

<player name="Baron/tournie"
 author="Empathy"
 description="Baron trying to race an early province to block the tournie p1.">
 <type name="Generated"/>
 <type name="Province"/>
 <type name="BigMoney"/>
 <type name="Bot"/>
 <type name="TwoPlayer"/>
 <type name="UserCreated"/>
 <type name="SingleCard"/>
   <buy name="Followers"/>
   <buy name="Trusty_Steed"/>
   <buy name="Princess"/>
   <buy name="Bag_of_Gold"/>
   <buy name="Province"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="4.0"/>
      </condition>
   </buy>
   <buy name="Estate">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Gold"/>
   <buy name="Duchy">
      <condition>
         <left type="countCardsInSupply" attribute="Province"/>
         <operator type="smallerOrEqualThan" />
         <right type="constant" attribute="6.0"/>
      </condition>
   </buy>
   <buy name="Baron">
      <condition>
         <left type="countCardsInDeck" attribute="Baron"/>
         <operator type="smallerThan" />
         <right type="constant" attribute="2.0"/>
      </condition>
   </buy>
   <buy name="Tournament"/>
   <buy name="Silver"/>
</player>

Agreed, it's a small effect. But I think veto allows you to create (or remove) a lot of such scenarios: therefore, you should be thinking about it while vetoing (I think).

I find it ironic that you come with simulator bots. The whole point of the article is that you have to adjust to your opponent, something you  can barely take a stab at with simulators, surely without spending LOTS of time at it.

[Empathy]

Simulation is good at answering *very targeted* questions. Here the question was: give an example where there is a mean-variance trade-off happening from a baron opening where p2 and p1 have differing strategies.

Any other comment?

[WanderingWinder]

Simulation is good at answering *very targeted* questions. Here the question was: give an example where there is a mean-variance trade-off happening from a baron opening where p2 and p1 have differing strategies.

Any other comment?

Well, the point is that this is a useless question. There's obviously some cards that benefit a little more than others from being p2 in pre-set simulated strategies. This fails to prove anything meaningful for the game. I should change my behaviour off of the 'optimized' bot (BTW, this tournament bot is NOT optimized) based on whether I'm p1 or p2, more importantly based on where the game stands, and also very importantly based on what you do. Sure, you can get some benefit if they put their heads down and only play some pre-written strategy like a simulator would. The whole point of this article is that you should NOT do that - you have to react to them, meaning that you should stray from your script.
The simulator does NOT answer this question. And while it can sort of be made to, it will take you way way way way too long to do that - you need to program decisions for at least tens of thousands of different circumstances, and probably meaningful differences on hundreds.

[RisingJaguar]

I'm not sure if I just had the superior strategy or just superior luck here (I do get great draws... or at least make great use of my draws? No I definitely got good draws), but the idea is that going different as second player gave me a better chance than the mirror would.  Or at least that's how I feel.  The player going as engine can make a lot of mistakes with their purchases and its 'best' to take the BM approach with player 1. 

An excellent example of what I'm disagreeing with. Pretty sure that the highway route is just better here. But my larger point is... like, if it increases your win% as player two to play the 'riskier' strategy, then it probably also increases your chances as player 1 to play the 'riskier' strategy, at least just looking from the outset. At some point in the games, you do go to playing riskier. But you don't want to plan that from the beginning. Again, 'I can't play the mirror, because that gives me a disadvantage as p2' is wrong thinking. You ALREADY HAVE the disadvantage as player two; playing a worse strategy is generally going to compound that.

This was the first example I thought of and I personally agree that highway on average will probably beat out Wharf BM.  Maybe a little different if its 4/3 as the engine player would need to obtain actual silvers which I think really hurts here but not the point.  This game was 5/2.  I would say this is a good example that $3 leads you to wharf-BM and $4 leads you to my strategy (having options with your opening).  Quasi was probably thinking this after getting $3/$6 with his draws and I suspect I was too. 

I pretty much agree with what you are saying that this was a bad example.  Although I wouldn't say Stef (or people supporting Stef) is to play the out-right worse strategy because that would be stupid.  By riskier, it is to play something  has more variance in the outcome, which often looks much worse than it is.  My intention was to show that higher-variance has its place as 2P (or by 2P, Stef is essentially saying when you are behind and 2P is the most common time you are behind).  I just sucked at it. 

I think that the higher-variance we are trying to find (myself included) is more subtle than we expect.  This could be a difference of a single purchase that turns an engine from low-variance to high-variance.  Something like double terminal vs. terminal and non-terminal (including silver).  Or a mid-to late game purchase. 

With that said, I am curious how often 2P wins mirrors in BM+X games as well as engine games.  I just assumed it was worse than the 55% - 45% of first turn advantage.

[Obi Wan Bonogi]

So first it's a concrete example, now it's a passing example? I agree, it's a passing example.
......
And my whole point is that he isn't explaining how to think quite right. Because you shouldn't be taking more risks as p2 than p1...
.. like, if it increases your win% as player two to play the 'riskier' strategy, then it probably also increases your chances as player 1 to play the 'riskier' strategy,

Yes...it's a concrete example that is mentioned in passing.  As opposed to a vague or unclear example mentioned in passing.  You argue about the most pointless shit I swear.  I'm not sure what makes you come here and try to take an article by the best dominion player we have seen(in my opinion) and turn it on it's head.   It's clear that you are thinking about the cards and their effects in relation to the state of the game very differently.  However I have no doubt that this thinking occurs in your play somewhere on some semantically pleasing level and that you could add to the topic if you wanted to...

Every choice within a line doesn't have a linear flat impact.  Each option will produce results on a spectrum of worst case to best case. His point with Borinion is that the results of these options will be polarized.   The notion of "risk" comes both from how polarized those results are and where their balance lies on this spectrum.  Sometimes your evaluation of state of the the game will lead you to conclude that the choice giving you the best chance to win is to take the option with the most polarized results aka the "riskier" (even though this new "best" chance of winning may still be well below 50%).

He perhaps overemphasizes P1 vs P2 in terms of "ahead vs behind." But he also talks about how important shuffle luck can be in terms of risk-taking and the need for constant reevaluation. 

Finally, in passing I will leave a concrete example of a cute risk-taking option.  This is card's text might as well just say "polarized results."  I don't buy it often but when I do I am almost surely WAY behind.  It is the: Scout.

[Empathy]

But my larger point is... like, if it increases your win% as player two to play the 'riskier' strategy, then it probably also increases your chances as player 1 to play the 'riskier' strategy, at least just looking from the outset.

Well, the point is that this is a useless question.

Maybe, but a question was raised, so I try to answer.

I think way too much emphasis is being put here on the p1 vs p2 thing.

There's obviously some cards that benefit a little more than others from being p2 in pre-set simulated strategies. This fails to prove anything meaningful for the game.

So, would you open tournament or baron? It would be consistent if you were not allowed to make that depend on being p1/p2.

I should change my behaviour off of the 'optimized' bot (BTW, this tournament bot is NOT optimized) based on whether I'm p1 or p2, more importantly based on where the game stands, and also very importantly based on what you do.

Agreed, which is why I only reasoned in terms of openings. The simulation is just a crude measure of the quality of the two openings with respect to p1/p2 position. I am sure that methodology has been used in the past.

Sure, you can get some benefit if they put their heads down and only play some pre-written strategy like a simulator would. The whole point of this article is that you should NOT do that - you have to react to them, meaning that you should stray from your script.
The simulator does NOT answer this question. And while it can sort of be made to, it will take you way way way way too long to do that - you need to program decisions for at least tens of thousands of different circumstances, and probably meaningful differences on hundreds.

A sub-part of the article which you vehemently disagreed with was the impact of the p1/p2 bias on openings (regardless of reactions later in the game). Which is why my two examples are basically purely reactions on opening luck: how to react to a 5/2 vs 3/4 or a p1/p2 position. Reading anything beyond that is a waste of time.

Sorry if this sounds negative, I usually really like what you do WW: but it really feels like you are the one being somewhat vague in this topic. Sorry if we are slow and force you to double-post and expand on your posts a bit.

[ftl]

So I like the article and it makes sense. But on second thought, doesn't it only apply to the very very highest levels, where you can basically be assured that your opponent will play optimally?

Like, at my level (25-30 when I played regularly), I think that either as p1 or p2, I would take whatever strategy I thought had the lowest median number of turns to half the VP (or to the mega-turn, or to the pin, or to the golden deck, or whatever). Like, in the example of the 90/10 game from post http://forum.dominionstrategy.com/index.php?topic=2711.msg43622#msg43622, if I was p2, I'd probably still take the the safe strategy, because I'd expect there's a more than 10% chance that my opponent would just mess something up, or pick a 'safe' strategy that was actually slower than the optimal safe strategy, or something.

I would guess that if I'm not a priori giving the opponent the benefit of the doubt and assuming they'll play optimally, this would still be very applicable to mid-game responses to luck, though. Once I've seen my opponent's strategy and thus can tell whether they're doing and thus respond accordingly. Or am I underestimating p1/p2 disparity?

By the way, I really appreciate Obi Wan and Stef's contributions here. You guys think (or, at least, talk) about this game quite differently than some of the other top players here, and it's very interesting and informative to hear from you guys.