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[Karhumies]

Thanks RisingJaguar for salvaging a usable point from my post.

I think the theoretical mirror is too unrealistic for whole-game scenarios, but it's useful for modeling two players rushing a single pile, because those fairly often end up in buy-1-per-turn scenarios. I think it's useful to look at bad luck resistance, here. For example, when rushing Duchies (for a Duke strategy), player 1 gets a "free miss"; not making $5 for one turn can still allow an even Duchy split. Player 2 doesn't get this comfort zone.

Now that "free miss" is an actually usable concept / piece of information. Unlike most of my previous off-the-target-by-wide-margin-but-still-gets-the-conversation-started stuff.

[Karhumies]

Anyhow, one of my main points in this thread is to illustrate some key differences between 2p and MP. And only secondarily think about the reasons. I am NOT an expert on 2p (mostly theorizing about it...as in subjectively perceived theoretical differences), and therefore everything I say about 2p should be questioned/tested by readers of the thread. Which I am glad you have done so far.

Therefore, mini-article #1 point:
in 2p, P2 mirroring P1 = advantage to P1
compare to MP, where P2 mirroring P1 = more likely disadvantage to both P1 & P2; more likely advantage to P3, P4, etc.

When analysing potential reasons for this, it was found out that I know very little about 2p and 2p mirroring. Which I am not trying to disprove, since it is true.

[DStu]

Anyhow, one of my main points in this thread is to illustrate some key differences between 2p and MP. And only secondarily think about the reasons. I am NOT an expert on 2p (mostly theorizing about it...as in subjectively perceived theoretical differences), and therefore everything I say about 2p should be questioned/tested by readers of the thread. Which I am glad you have done so far.

Therefore, mini-article #1 point:
in 2p, P2 mirroring P1 = advantage to P1
compare to MP, where P2 mirroring P1 = more likely disadvantage to both P1 & P2; more likely advantage to P3, P4, etc.

When analysing potential reasons for this, it was found out that I know very little about 2p and 2p mirroring. Which I am not trying to disprove, since it is true.

I'm not an expert on the 3++player, but my feeling is that this is true. In 2p, you usually (at least think that you) have a dominant strategy, and maybe some alternatives. But usually the alternatives are weaker. Second player now can decide if to mirror or going alternative, but usually is behind in both cases. In the mirror because of first player advantage, in the alternative because it is weaker.
In multiplayer, mirroring might weaker or strengthen a strategy, so having knowledge on what the other players play might be much more helpfull.

[Karhumies]

Mini-article on Dominion game theory, 2p vs larger amounts of players, #4:

Impressions on MP Big money strategy

Big money goes against much of what has already been said in mini-articles 1-3. Also, it is quite a powerful strategy in MP - at least more powerful than in 2p, given an environment with not a lot of "deck spamming" (curses, coppers) diluting it too much.

What makes Big money so good in MP?
1. In 4p, 5p and 6p, people are racing to 3 provinces/colonies, not 4. This is a significant decrease to engine decks' # of turns to setup before game ends in most settings. This is a very, very good thing for big money.
2. Big money is less dependant on gaining, drawing and recurring multiples of single key cards than most other strategies.
3. Big money essentially can not become contested. This is one key for MP success: avoiding contest.
4. 2+ other people contesting one another slows both of those players down; while big money is (almost always) unaffected. This scenario can never happen in 2p setting. This again improves big money in MP, although it does improve the other uncontested players (regardless of strategy) as well.
5. Big money is one of the very few (the only?) MP first player strategy, which can actually maintain the mirror advantage over late player copycats.
6. Some actions + Big money -combination strategy often makes for an excellent "plan B" when your plan A becomes too heavily contested to make it worth your while.

What are the big problems of Big Money in MP? When to avoid it?

1. When there are cumulative (out-of-turn) trashing, filtering, gaining (or even discarding) effects.
1.1 Attacks can be spammed in MP. In 2p, 1 opponent playing a trashing attack like Thief, Pirate Ship or Noble Brigand is not necessarily that much of a deal. In 4p, when all 3 opponents can play 1+ copy each before your next turn, your whole money supply can become screwed way, way faster than you can (re)stock it on your turns. This is essentially a losing battle. Meaning that with certain kingdom cards on the board in MP (given that multiple players buy at least 1 each), big money just is not a feasible strategy in that game. The same goes for spamming curse and copper-giving attacks: big money's draws become diluted and the deck has to slow down to get filter cards, or reaction cards. In which case the strategy is not really big money any more, it's something else. Rabble and similar non-trashing treasure dilution spamming can also be problematic for big money if the beginning estates stay in the deck if there is no filtering included.
1.2 Trader, Watch tower, etc. (especially anti-spam cards) can be insanely powerful cards in 4+ player games, making them single "must buys" even in an otherwise big money deck.
1.3. Utilizing engines based on out-of-turn spamming or filtering effects the other players are using can gain the edge over big money (e.g. Counting House, Bishop)

2. Although complex engines are typically way too slow to compete with big money in MP, uncomplicated engines based around only 1-2 key cards (typically only few copies as well) can still be faster than big money in MP.
2.1 Trashing-based making deck smaller strategy (e.g. Chapel)
2.2 Recursion combo engines (e.g. Scheme)
2.3 Filtering combos (e.g. Golem)

The main point in this post: keep your strategy simple and the game end in sight in MP.

[igelkott]

"1. In 4p, 5p and 6p, people are racing to 3 provinces/colonies, not 4."

This is often not sufficient. In theory, yes, but in practice, no. Often 1 or 2 players fall behind in the beginning of the game, either due to poor purchase decisions or poor draw luck. This means that the leader might need to contend for colonies/provinces with 1 or 2 other players only. This means to win he must strive for at least 4-5 of the cards in order to beat the 2nd place player.  A deck that stalls after only 3 may not cut it.

Your general gist though is correct. It does seem to be the case that BM wins quite often with multiplayer.

[RisingJaguar]

"1. In 4p, 5p and 6p, people are racing to 3 provinces/colonies, not 4."

This is often not sufficient. In theory, yes, but in practice, no. Often 1 or 2 players fall behind in the beginning of the game, either due to poor purchase decisions or poor draw luck. This means that the leader might need to contend for colonies/provinces with 1 or 2 other players only. This means to win he must strive for at least 4-5 of the cards in order to beat the 2nd place player.  A deck that stalls after only 3 may not cut it.

Your general gist though is correct. It does seem to be the case that BM wins quite often with multiplayer.

I think this is slightly out of context, he refers to this only in terms of game speed, and how the increased game speed helps Big Money.  Averaging 3 provinces a player compared to 4 a player leads to inevitably shorter games barring interactions in cards. 

On the flip side, say in 3 players, 1 of them is slow, then the other 2 players may have to get to 5 provinces. 

Now you can say, what if everyone went engine? Then there's the whole scarce resources problem, and kinda leads back to Big money anyways as an often dominant strategy.  There's an equilibrium somewhere, but I'm not sure where in Game theory, which leads to his mini-article #3. 

[DG]

I haven't looked at this thread much but I have to say that the ideas around mirroring are little unsophisticated. There are many very complex issues in multi player games regarding the supply, the pace of the game, and the accumulated impact of different strategies upon play. It is much more difficult for a player in third seat to ignore the pace of the game set by the first two players, just to pursue anything that might be different. There are certainly far fewer options to control the endgame or recover from an early deficit since two opponents can force the game to finish much more easily than one can. My advice would be to always watch the actually game being played and make minor adjustments to strategy in response to the opponents' decks.

For example, if your two opponents in three player game start buying minions then there's no use thinking about mirroring at all ... as a concept. You need independent thought about how the minions will split, how many minions you should compete for, whether your opponents will compete for minions, how the decks will work with various numbers of potential minions, whether trashing will be more valuable than accumulating treasures, and how to win with frequent 4 card hands. This is all far more advanced than mirroring.