Dominion Strategy Forum

Please login or register.

Login with username, password and session length
Pages: [1]

Author Topic: Player 1 advantage, quantified  (Read 3490 times)

0 Members and 1 Guest are viewing this topic.

theory

  • Administrator
  • *****
  • Offline Offline
  • Posts: 3594
  • Respect: +6035
    • View Profile
    • Dominion Strategy
Player 1 advantage, quantified
« on: December 19, 2011, 10:50:24 am »
0

I want to know what cards affect the P1 advantage.  Does DoubleJack advantage P1?  How about SeaHag/BM or Envoy/BM or Mint/FG?

This experiment can also be run on CouncilRoom data, and would have the added advantage of identifying which cards most help P1 and which most help P2.  I think rspeer was working on this a while ago?  This could lead to quite a bit of veto strategy.
Logged

rod-

  • Conspirator
  • ****
  • Offline Offline
  • Posts: 213
  • Respect: +49
    • View Profile
Re: Player 1 advantage, quantified
« Reply #1 on: December 19, 2011, 01:01:57 pm »
+2

What little work i did with the councilroom data indicated that there wasn't an appreciable difference in 1p advantage with any individual cards.  The advantage varied by about +/- 2% maximum around the initial 10%, regardless of the cards present. 

However, there was a suggestion that was beyond my ability test: The implication was that councilroom logs as a whole are biased towards a 2nd player advantage (or at least away from 1st player advantage) due to the fact that the good players play from 2nd position more frequently.  The idea being that in a series of games between player A and player B of equal caliber, The 1st player advantage is greater than 10% and may vary more considerably due to cards.  However, I did not attempt to cull the datasets to include only equally-matched opponents or equal numbers of games from position A + B for each player.  That might be interesting, but i am skeptical that there is sufficient raw data to draw any conclusions.
Logged

DG

  • Governor
  • *****
  • Offline Offline
  • Posts: 4071
  • Respect: +2611
    • View Profile
Re: Player 1 advantage, quantified
« Reply #2 on: December 19, 2011, 02:26:21 pm »
0

As far as I can remember from the first time this was analysed, the first player advantage cards fell into three camps

(1) Cards that attack the opponent's first shuffle (ambassador, cursing), sometimes letting the first player reshuffle unscathed.
(2) Big engine cards turns or quick accelerator cards that often gave the second player has no vp purchasing strategy to offset first player advantage (wharf, chapel). 
(3) Key cards where the second player has great difficulty buying a majority (minions).

Of the cards released since then tournament stands out since the shuffle sequence is very important and it also provides unique key cards.

The second player advantage cards were a peculiar mix. The bishop was almost even and there could be any number of reasons for that. Secret chambers and moats probably offered robust defence to a second player who was aware of the first player's purchases. Some other cards like a navigator were again a mystery, but perhaps indicated defensive qualities that a first player might not see a need for.
Logged

theory

  • Administrator
  • *****
  • Offline Offline
  • Posts: 3594
  • Respect: +6035
    • View Profile
    • Dominion Strategy
Re: Player 1 advantage, quantified
« Reply #3 on: December 20, 2011, 10:47:11 am »
0

Do you have a link to that analysis?
Logged

DG

  • Governor
  • *****
  • Offline Offline
  • Posts: 4071
  • Respect: +2611
    • View Profile
Re: Player 1 advantage, quantified
« Reply #4 on: December 20, 2011, 12:04:31 pm »
0

It was an old BBG thread perhaps from over six months ago. Unfortunately there are a lot of old BGG threads to look through. If I remember correctly, and I might not be, it may have been about the time that Renaud first collected the council room 'best and worst openings'. Perhaps he collected a bit more data on first and second seat wins as well.
Logged

DG

  • Governor
  • *****
  • Offline Offline
  • Posts: 4071
  • Respect: +2611
    • View Profile
Re: Player 1 advantage, quantified
« Reply #5 on: December 20, 2011, 01:50:04 pm »
0

Here it is. It was Guided who collected the data. http://www.boardgamegeek.com/thread/597851/opening-card-strength/page/1. You've no excuses for forgetting it since you posted on it!

There are actually some very good quotes from Donald X. in there too.

Quote
"Well I don't want to get involved in discussing strategy. I have seen all of the varying numbers of Pirate Ships lose, sometimes to treasureless decks and sometimes not.
In the very first game with Pirate Ship, it was a 3-player game, and we all bought it. It necessarily won. At the end of the game, someone said, "well that was obv. broken." We debated this for a few minutes, then played again with the same set of cards. I didn't buy Pirate Ships, and won. So this has been the story from the beginning."

Quote
Oh here's something. If you play multiple games in a session with the same players, the winner goes last each time after the first. Isotropic implements this. I don't know how often people on isotropic play multiple games, but it must happen sometimes. So P2 is more often the better player.
Logged

theory

  • Administrator
  • *****
  • Offline Offline
  • Posts: 3594
  • Respect: +6035
    • View Profile
    • Dominion Strategy
Re: Player 1 advantage, quantified
« Reply #6 on: December 20, 2011, 01:57:13 pm »
0

Oh god, I used to think Pirate Ship was good?

I should edit your post and hide all such evidence.

(Though the shame of leaving Masquerade off the first Best $3 Cards list will live on forever.)

Guided's list is interesting but slightly different from what I was thinking, which is how certain cards, by their very presence, affect P1 vs P2.  Though I suppose choice-of-opening is close enough.
Logged

DG

  • Governor
  • *****
  • Offline Offline
  • Posts: 4071
  • Respect: +2611
    • View Profile
Re: Player 1 advantage, quantified
« Reply #7 on: December 20, 2011, 02:15:06 pm »
0

You can get your techies to collect similar data I'm sure. My guess would be fairgrounds as a good second player card, the bishop (still), farmland, and reactions.
Logged

tlloyd

  • Tactician
  • *****
  • Offline Offline
  • Posts: 404
  • Respect: +82
    • View Profile
Re: Player 1 advantage, quantified
« Reply #8 on: December 20, 2011, 02:18:20 pm »
0

I know this is a data post and not a theory post, but it just occurred to me that some cards should inherently favor P2. The best example I can think of is Smugglers, since P1 will smuggle P2's card from T(n-1) while P2 smuggles P1's card from T(n). And unlike Jester it can't cause the other guy's card to get skipped. So I was wondering if the data backs this up.
Logged

Kirian

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 7092
  • Shuffle iT Username: Kirian
  • An Unbalanced Equation
  • Respect: +9371
    • View Profile
Re: Player 1 advantage, quantified
« Reply #9 on: December 20, 2011, 10:15:05 pm »
0

I think, tlloyd, that this ought to be a theory rather than a data post, mainly for the reason rod- mentions:  better players are more likely to start in position 2.  This means data are most definitely skewed in favor of P2.  This doesn't make the data meaningless--but it does make it less meaningful.

Also, we need a starting point, which can only be determined theoretically I think.  In the BGG post linked above, the P1 advantage is given as 52-48, but with guided counting ties as "win for P2," which I think is a patently bad way of looking at things; no matter how you slice it, a tie is not the same as a win, even if, as he suggests, a tie is better than a loss.  I think Dominiate's method (tie = 0.5 to both players) makes better sense.  One could also, I think, argue that ties should be removed from the count when calculating advantages, though the final ratios aren't much different from what I discuss below.

Here are a few of the more standard "basic" strategies, counting ties as 0.5, using Geronimoo's simulator @100k games:

BMU:  55-45
Optimized BMU:  55.5-44.5
BM-Smithy:  55.5-44.5
BM-Envoy:  55.9-44.1
BMU+Colony:  57-43
BM-Laboratory:  56.8-43.2

Using these, P1 should win about 25% more often than P2.  (55.5/44.5 = 1.247).  This is quite different from the previously mentioned 52-48 split (8.3% advantage to P1).  I think this 25% advantage is a reasonable starting point when we consider these sorts of things.  Questions like the one posed here are better answered relative to this baseline.

For instance, Militia in Geronimoo's simulator gives a 55-45 split.  Militia therefore has no inherent P1 advantage--surprising to me given the strength of Militia.
Double Jack, OTOH, gives a 58.5-41.5 split--that's a 41% advantage to P1 as opposed to 25%.  Jack has an inherent P1 advantage.
Mountebank, not suprisingly, gives a 58-42 split, or a 38% advantage for P1.
Witch gives a staggering 59.7-40.3 split, a 48% advantage.
Double Ambassador: 59-41.
Ghost Ship:  56.8-43.2, oddly not that high.

OK, enough simulating for now.
Logged
Kirian's Law of f.DS jokes:  Any sufficiently unexplained joke is indistinguishable from serious conversation.

tlloyd

  • Tactician
  • *****
  • Offline Offline
  • Posts: 404
  • Respect: +82
    • View Profile
Re: Player 1 advantage, quantified
« Reply #10 on: December 21, 2011, 02:01:57 am »
0

All very interesting. What about Smugglers?  :P
Logged

Kirian

  • Adventurer
  • ******
  • Offline Offline
  • Posts: 7092
  • Shuffle iT Username: Kirian
  • An Unbalanced Equation
  • Respect: +9371
    • View Profile
Re: Player 1 advantage, quantified
« Reply #11 on: December 21, 2011, 02:57:20 am »
0

All very interesting. What about Smugglers?  :P

53.4-46.6 for a single Smuggler
Opening Double-Smuggler is 48.8-51.2 in favor of P2.

A single Smuggler just barely favors P2 vs. normal P1 advantage; two of 'em favor P2. But... P1 with one Smuggler beats P2 with two Smugglers, 56.8-43.2.  Ignoring P1 advantage, taking two Smugglers is worse than taking one.
Logged
Kirian's Law of f.DS jokes:  Any sufficiently unexplained joke is indistinguishable from serious conversation.

mnavratil

  • Conspirator
  • ****
  • Offline Offline
  • Posts: 216
  • Respect: +83
    • View Profile
Re: Player 1 advantage, quantified
« Reply #12 on: December 21, 2011, 11:21:36 am »
0

I wouldn't trust the simulator for ambassador. I tried running a bunch of numbers to quantify this once before (I think there may actually be a full thread dedicated to P1 advantage with ambassador).

Long story short: Geronimoo's simulator plays this suboptimally.

EDIT: Did a quick search but didn't find a thread with that topic, but did find the folloiwng related threads (for reference, if anybody cares):
http://forum.dominionstrategy.com/index.php?topic=946
http://forum.dominionstrategy.com/index.php?topic=712.0
http://forum.dominionstrategy.com/index.php?topic=665
« Last Edit: December 21, 2011, 11:26:29 am by mnavratil »
Logged

DG

  • Governor
  • *****
  • Offline Offline
  • Posts: 4071
  • Respect: +2611
    • View Profile
Re: Player 1 advantage, quantified
« Reply #13 on: December 21, 2011, 01:32:24 pm »
0

I suspect that if you simulate an ambassador/silver opening moving onto a treasure strategy then the Geronimoo ambassador will give reasonable results and have limited decision making.
Logged
Pages: [1]
 

Page created in 0.111 seconds with 20 queries.