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[Empathy]

I was wondering if anyone had ideas and thoughts about the natural bias the game has towards the first player. I'm pretty sure it's statistically verified, and it seems to be non negligable. Most players I know have a 0.1-0.2 point difference between their first player and second player game stats.

More importantly than evaluating the statistical advantage of the first player, I was wondering if it had any impact on strategies, in particular openings.

A basic heuristic seems to imply that yes. Assume the optimal strategy is some nearly deterministic chapel strategy that takes exactly 17 turns to grab more than half the points. Then, clearly, if both players play the optimal strategy, the first player will win with probability 1. Any sub-optimal strategy with higher variance is therefore preferable for the second player. Treasure mapping, even if it will on average only win on turn 20, might be preferable because it has a small chance of winning much earlier if lucky.

I think that could be a reasonable rule of thumb: as the first player, go for the best, safest strategy. As a second player, go for one that is just as good/slightly worse, but has higher variance to maximize probability of winning.

Any ideas on the matter? How important do you think it is to adapt your opening strategy to your table position?

[guided]

I do occasionally think about this if I'm playing an evenly matched opponent, or an opponent who clearly knows how to play some scripted strategy well (like Workshop/Gardens). Generally though, rather than taking some clearly sub-optimal opening (like passing up Potion in favor of Treasure Map on a board where Familiar is going to be a key factor, or whatever) I'll note within a few turns that I appear to be behind the curve as 2nd player and take steps to shake things up somehow. But then, this is the same way I approach being behind due to bad shuffling.

[Fangz]

There are cases where there's an advantage in going second: but it's not often. For example, games with a not-overwhelming strategy can allow the second player to read what the first player is aiming at, and play to counter that strategy. On decks with pirate ship, for example, seeing the opponent go pirate ship first means I can then design a strategy tailored to getting money from actions and trashing coppers quickly.

[Geronimoo]

A strategy that will always win by turn 17 doesn't actually exist, so playing some non-optimal strategy will most of the time result in more losses.

Their are some cases where choosing a non-optimal strategy will be better. Take for instance Tournament which is a very swingy card. The player who goes first has a huge advantage because he will most likely get the first Province, possibly countering the second player's Tournaments AND access at the first prize (Followers, which is a broken card). So if your opponent goes first and opens Tournament/Silver, you might want to look in a different direction even if you know Tournament will be part of the optimal strategy for that board.

You can test this yourself with my simulator with 2 of the built-in bots:

BM - Tournament is dominant over BM - Militia (by 1%)

But if we keep player order the same for all games:

Tournament (starting player) 59% - Tournament 39%
Tournament 56% (starting player) - Militia 41%

So by picking the non-optimal strategy the second player increases his win rate.

[guided]

It's my crusade to say it every time the subject comes up, so forgive me the slight derail: I do not find Tournament to be high-variance! I am very good with it, having demonstrated consistent skill in winning Tournament games at a significantly higher rate than my overall average. This is as opposed to, say, Mountebank or Witch, strong cards I know how to play well that I nonetheless have negative "effects with" because they lead to genuinely high-variance games against lower-rated opponents. Having played around with veto mode on an alt, Mountebank is probably my #1 veto priority at this point (even above the hated Swindler!) simply because it's so high-variance. Indeed I've come to the conclusion (in contrast to my earlier position) that Mountebank is a significantly higher-variance card than Swindler. But I will never veto Tournament... unless I see some fun engine I can build that doesn't want Tournament on the board for some reason

[WanderingWinder]

guided, I don't think that's what Geronimoo was saying...

[Thisisnotasmile]

I think guided was responding to this:

Take for instance Tournament which is a very swingy card.

and nothing else.

[DG]

I put a simulation challenge a few days ago and one of the results seen was the strength of first player with tournaments. When two players competed with my optimised simulator strategy the first player was winning games 63%:36%, almost two to one. This was with a 4/3 split and when I played the game on isotropic I went first with 2/5. At the time I judged this to be a poor start as the best start appears to be a 3 or 4 cost card and went for a gambling approach as suggested in the original post. This turned out to be wrong as following optimal 4/3 strategy with the 2/5 split still simulated as a reasonable 45%:55% win ratio in first seat.

As another example, I recently had a 3 player game where first player opened with a sea hag and second player with a cutpurse. I didn't see this as the time to gamble, however it was clearly a time when I needed to re-evaluate what my 3rd and 4th hands would achieve and there was little point planning around a 5 cost card. I'd suggest that re-evaluation is more common than gambling.

The prime situation for gambling would be in the mid game where it will be difficult to simply out-purchase the first player and the first player will control the endgame purchasing strategy. In this situation you might want to gamble by perhaps not trashing the last estate with a masquerade just so you keep an extra victory point when province buying starts. This might still be a calculated risk rather than a gamble. Calculated risks seem well worth taking in Dominion.

[DG]

Guided, if you could see my simulator results for tournament challenge I posted then you would believe it was a very swingy card. Even in a set with a variety of interesting continuations based on the prizes taken, 75% of the games were seemingly decided by the tournament draws, the winning margins varied massively, and first player advantage was massive.

[guided]

I believe Tournament to be a high-skill card, and I generally play it in decks involving complex interactions with other Kingdom cards. I am not sanguine about the possibility of being persuaded otherwise by simulator results based on a comparatively simple set of buy/play rules. If I find some time I'll give that thread at least a brief look though.

I could believe that among equally-skilled opponents it exhibits an unusually large first-player advantage. Not to say I'm granting that's true, but it's certainly within the realm of possibility, and I have no specific evidence to offer up one way or the other.

WW: TINAS has the right of it. I didn't (and still don't) intend to make this an extended derail, but I try to fight the notion (wherever I may find it) that Tournament is some luck-based circus card, since I'm just about the only person who seems to disagree.


late edit: I will say that if "swingy" was meant to indicate large score differences created by small changes in shuffle luck, I don't disagree, and I apologize for misunderstanding. Tournament is a lot like Possession (another high-skill card) in that way. I just don't find score differences interesting to talk about. When I speak of variance in Dominion, I mean the effect of luck (as opposed to skill) upon the trinary W/L/T outcome, without regard to score differences. I consider a card to be high-variance if it offers a bad player an unusually good chance to beat a good player. To my mind, King's Court for example offers much more of that sort of variance than Tournament (in addition to the score-difference sort of variance).

[Empathy]

First, to give my opinion on tournament. I think on complex boards, it is a low variance card, because as one of the older blog articles argued well, the point is to get a province fast and to match it to a tournament. Just loading on tournaments is not the best way of doing it, and going for some money or trashing engine can be a much better plan to start off with (you can always buy the tournaments on the way). This means that the actual "problem", if there is any, is about the randomness of the engine you are using.

Now I'm pretty sure that is not big news, and that most people here seem to agree on that anyway. Saying that for two players of equal level, tournament is a high variance card does not tell us anything: it is true of any game. If no player has a big edge over the other, the outcome of any game like dominion/poker/chess will exhibit high variance. I do think however, that tournament is a high variance card when there are no other strong options on the table. This is the case whenever the optimal strategy is tournament-BM. I don't think that is often the case however, and people rush into tournament-BM far too often. I might be wrong.


Back to my initial topic. It does depend on the board, and I agree that in some "rock-paper-scizzors" kind of boards, being second actually helps.

But the statistical bias is there, and I'm sure I can fetch an example using chapel that nearly deterministically finishes the game at a certain turn N. I can then probably chose the other cards such that that strategy is optimal  (in the sense of minimimizing average turn to a winning score).

I still think there are boards where you will opt for the higher variance strategy due to going second. That is, maybe you have two strategies that are, on average, equally good (or at least, close enough as that you can't distinguish the statistical winner), but with one being higher variance than the other. Most people being risk-averse, will go for the safer strategy. This also usually corresponds to the one they know best how to play, because learning all the tricks of a deterministic strategy goes faster than learning all the outcomes of a highly stochastic one. I am arguing that knowing how to execute more high variance strategies (treasure map being the prime example) in an optimal way might improve your second player scores.

I think Geronimoo's result with tournament can probably be reproduced in other contexts.

[DStu]

I think Geronimoo's result with tournament can probably be reproduced in other contexts.

Chapel->Quarry->GM

[Mean Mr Mustard]

It sure is nice to be second position when you are leading Provinces 4-3.

[Empathy]

It sure is nice to be second position when you are leading Provinces 4-3.

Table position 1   1476-714-50   1.342
Table position 2   1546-969-45   1.227

I'm still convinced there is potential for a deeper discussion than this. Maybe I'll try to find examples of games related to the topic.

[Mean Mr Mustard]

Yes, on some boards against competent opponents it is nigh impossible to win from the second seat without some good luck.  That is a part of the game that we just have to accept.  I guess my point is, on boards that allow for more skill-based games, it can actually mitigate the disadvantage for the more experienced or skilled player in the second seat, as it is the onus of the first player to not end the game with even scores.

[ackack]

Yes, on some boards against competent opponents it is nigh impossible to win from the second seat without some good luck.

I think that's a very important point. Thinking about things in terms of generic first player advantage is probably wrong, since it varies hugely from board to board. I think the place where first player is strongest is in games where the primary strategy involves an engine that is building toward one or two powerful game-ending turns. And in those spots, there's not really much to be done other than try to get the engine up a little faster.

[guided]

Quite a small sample size so far, but I'm finding a massive spread between 1st and 2nd player win rates when playing with veto mode. My veto strategy is focused on reducing variance, so it's plausible that could have a noticeable effect by making it more difficult for 2nd player to catch up through luck to 1st player's tempo advantage.

http://councilroom.com/player?player=led - 1.778 AWP in 1st seat vs. 1.393 in 2nd seat, a spread of almost four tenths.

as opposed to http://councilroom.com/player?player=guided - 1.416 in 1st seat, 1.298 in 2nd seat, a spread of just over a tenth.

I guess time will tell whether this is a real effect or just a statistical anomaly.

[WanderingWinder]

Quite a small sample size so far, but I'm finding a massive spread between 1st and 2nd player win rates when playing with veto mode. My veto strategy is focused on reducing variance, so it's plausible that could have a noticeable effect by making it more difficult for 2nd player to catch up through luck to 1st player's tempo advantage.

http://councilroom.com/player?player=led - 1.778 AWP in 1st seat vs. 1.393 in 2nd seat, a spread of almost four tenths.

as opposed to http://councilroom.com/player?player=guided - 1.416 in 1st seat, 1.298 in 2nd seat, a spread of just over a tenth.

I guess time will tell whether this is a real effect or just a statistical anomaly.

Interesting. My hypothesis is that veto mode should generally reduce first player variance, since second player has much more control over what the feel of the game is by vetoing second (well, last). It'd be interesting to know how many of those guided games came in the same time as the led ones (and the stats for that subset) as well as whether the class of opposition between the two nicknames is similar or not.

[guided]

Not a lot of overlap. The aggregate strength of opposition is probably higher for "guided" since I switched to mostly automatch a month or two ago. "guided" also has a significant history of games where I was still learning high level play. These are also effects that matter.

2nd player can steer the game in a certain direction a little bit more than 1st player, but if 1st player is skilled they're not at any significant disadvantage in strategizing for the final board. I would think one player vetoing with the explicit goal of reducing variance (by getting rid of things like Mountebank and Treasure Map) is going to be a much larger effect than whatever playstyle advantage 2nd player gets from vetoing last.

[Empathy]

Two questions now:

a) How is turn order determined on isotropic? I would assume it's random, but in my case there is an awkward tilt towards second position (which is why I notice this sort of thing a lot) despite mostly playing 2p games and having a fair number of them (so statistical fluctuation is slightly less likely).

b) As discussed above with the veto mode, some cards seem to be better for the second player, and some for the first one. Examples given are pretty intuitive: KC, mountebank, treasure map for 2p, chapel, ambassador for 1p. First, would it be possible to think of more examples (which could turn into an article of some sort)? Second, is there a statistical test we could do on the council room data to find examples and confirm them?

[guided]

Anybody who has just lost a game will go after anyone who has not just lost a game. If you win a lot, you disproportionately go 2nd.

[guided]

I guess time will tell whether this is a real effect or just a statistical anomaly.

Looks like the smart money was on "statistical anomaly". The effect has mostly disappeared from my stats already.

[Mean Mr Mustard]

I have been taking into account position while playing in veto made this week, and I have made a few observations that may not apply to all players.  It seems for my playstyle, vetoing the strongest card or the key of a powerful but obvious combo helps me more than when I veto the commonly understood variance cards.  Many of my losses from second position come from boards with cards like wharf/village or FV/torturer; easily mirrored and with a strong advantage for the first player.

I think that slowing the speed of the Kingdom may be an advantage to the better player regardless of position;  I feel more confident slogging out games as Player 2 than playing very fast boards.  I have noticed that a card like Apprentice may actually be "bad" for playing second because it is easily mirrored and is extremely fast in the endgame.  On a board full of cards like Warehouse and Explorer it seems that the player with the deeper insight had a severe advantage.

[rrenaud]

A new reason for first player advantage:  Pile limits on avalanche cards, especially peddler.

It's not hard for the peddler split to go 6-4 (or even 7-3) just because of the extra turn.

[fellowmartian]

Anybody who has just lost a game will go after anyone who has not just lost a game. If you win a lot, you disproportionately go 2nd.

I knew this, but I only just thought (which probably makes me slow): surely this means that stats drawn from isotropic will under-rate the value of going first? If player one is on average worse skill-wise than player two, this seems unavoidable. I wonder if there's any way to work out by how much it undervalues it?