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Author Topic: First player advantage  (Read 5003 times)

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rrenaud

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Re: First player advantage
« Reply #25 on: June 16, 2011, 09:06:39 am »
0

It's like trying to extract useful information from experiments conducted in randomly-varying conditions, with each experiment itself producing random data.

FWIW, I think scientists call the process of learning from experiments with randomly varying conditions with each experiment producing random data "science."

Of course, they try to control for important factors, and then run what they intend as the same experiment over and over to get rid of that noise.
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guided

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Re: First player advantage
« Reply #26 on: June 16, 2011, 09:15:04 am »
0

Player 1: normal starting deck
Player 2: puts one Estate in his discard pile, then shuffles deck and draws 5
Player 3: puts two Estates in his discard pile, then shuffles deck and draws 5
Player 4: puts three Estates in his discard pile, then shuffles deck (no need really :) ) and draws 5

If this variant is interesting and fun for you, more power to you. But I wouldn't play it, myself, because I am not so bothered by the seating order asymmetry in Dominion that I would want to throw the game out and play the very different game described here instead ;)
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Mean Mr Mustard

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Re: First player advantage
« Reply #27 on: June 16, 2011, 09:21:38 am »
0

In chess, the first player has an advantage.  Same in Magic, billiards, horse racing and Dominion.  In poker the person who goes last has a distinct advantage.  I don't think it is an innate problem in any of these because in the long run, over many trials, the player with more skill will win more often in whichever position they begin in.
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rrenaud

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Re: First player advantage
« Reply #28 on: June 16, 2011, 09:25:33 am »
+1

Don't trust me! Get the data and do your own analysis, http://councilroom.com/margin.txt.gz
Or find bugs in the code! https://github.com/rrenaud/dominionstats/blob/master/oneoff/process_margin_advantage.py

The second column is the marginal difference between the first player and the second player in the median game when sorted by the score difference across all games on isotropic.
The third column is the marginal difference between first and second player with the first player skill bias removed (eg, pair up two players, only take the same number of games from when player A was first as when player B was first, if they only played one game, it will be thrown out, if A was first once, and B was first 10 times, take the 1 game from A, and 1 game at random from B).

The first player loses a half point for having more turns than player two.

You can view the third column as a reasonable upper bound on what a player should willing to bid.  The games are played on iso with no bidding, so if there was bidding, the second player could use his point advantage to close games that he actually lost and turn them into wins (they whole point).  Thankfully, the third column is quite a bit higher than my heuristic estimate of 1.5 points ;).


rrenaud@kingscourt:~/dominionstats/oneoff$ python process_margin_advantage.py
from 1122324 sampled down to 329378
*all                           1.0     2.5
Adventurer                     0.5     2.5
Alchemist                      1.0     3.0
Ambassador                     1.0     3.5
Apothecary                     1.0     3.0
Apprentice                     1.0     2.5
Bank                           1.0     3.0
Baron                          0.5     2.5
Bazaar                         1.0     2.5
Bishop                         1.0     3.0
Black Market                   1.0     3.0
Bridge                         1.0     2.5
Bureaucrat                     1.0     2.5
Caravan                        1.0     2.5
Cellar                         1.0     2.5
Chancellor                     1.0     2.5
Chapel                         0.5     3.0
City                           0.5     3.0
Colony                         1.0     4.0
Conspirator                    0.5     2.5
Contraband                     1.0     3.0
Coppersmith                    1.0     2.5
Council Room                   1.0     2.5
Counting House                 1.0     3.0
Courtyard                      1.0     2.5
Cutpurse                       0.5     2.5
Duke                           1.0     2.5
Embargo                        1.0     2.5
Envoy                          1.0     2.5
Expand                         1.0     2.5
Explorer                       1.0     2.5
Fairgrounds                    1.0     3.5
Familiar                       1.5     4.0
Farming Village                1.0     3.0
Feast                          1.0     2.5
Festival                       0.5     2.5
Fishing Village                1.0     3.0
Forge                          1.0     3.0
Fortune Teller                 1.0     2.5
Gardens                        1.0     2.5
Ghost Ship                     1.0     2.5
Golem                          1.0     3.0
Goons                          1.5     4.0
Grand Market                   1.0     3.0
Great Hall                     1.0     2.5
Hamlet                         1.0     3.0
Harem                          1.0     2.5
Harvest                        1.0     3.0
Haven                          1.0     2.5
Herbalist                      1.0     3.0
Hoard                          1.0     3.0
Horn of Plenty                 1.0     3.0
Horse Traders                  1.0     2.5
Hunting Party                  1.0     3.0
Ironworks                      0.5     2.5
Island                         1.0     2.5
Jester                         1.0     3.0
King's Court                   1.0     3.5
Laboratory                     1.0     2.5
Library                        1.0     2.5
Lighthouse                     1.0     2.5
Loan                           0.5     3.0
Lookout                        1.0     2.5
Market                         1.0     2.5
Masquerade                     0.5     2.5
Menagerie                      1.0     3.0
Merchant Ship                  1.0     2.5
Militia                        1.0     2.5
Mine                           1.0     2.5
Mining Village                 1.0     2.5
Minion                         1.0     2.5
Mint                           1.0     3.0
Moat                           0.5     2.5
Moneylender                    1.0     2.5
Monument                       1.0     3.0
Mountebank                     1.0     3.5
Native Village                 1.0     2.5
Navigator                      1.0     2.5
Nobles                         1.0     3.0
Outpost                        1.0     2.5
Pawn                           0.5     2.5
Pearl Diver                    1.0     2.5
Peddler                        1.0     3.0
Philosopher's Stone            1.0     2.5
Pirate Ship                    0.5     2.5
Platinum                       1.0     4.0
Possession                     0.5     3.0
Potion                         1.0     3.0
Quarry                         1.0     2.5
Rabble                         1.0     2.5
Remake                         1.0     3.0
Remodel                        0.5     2.5
Royal Seal                     1.0     3.0
Saboteur                       1.0     2.5
Salvager                       1.0     2.5
Scout                          0.5     2.5
Scrying Pool                   1.0     3.0
Sea Hag                        1.0     3.0
Secret Chamber                 1.0     2.5
Shanty Town                    1.0     2.5
Smithy                         1.0     2.5
Smugglers                      0.5     2.5
Spy                            1.0     2.5
Stash                          1.0     2.5
Steward                        1.0     3.0
Swindler                       1.0     3.0
Tactician                      1.0     2.5
Talisman                       1.0     3.0
Thief                          0.5     2.5
Throne Room                    1.0     2.5
Torturer                       1.0     3.0
Tournament                     1.5     4.0
Trade Route                    0.5     2.5
Trading Post                   1.0     2.5
Transmute                      1.0     3.0
Treasure Map                   1.0     3.0
Treasury                       1.0     2.5
Tribute                        0.5     2.5
University                     1.0     2.5
Upgrade                        1.0     2.5
Vault                          1.0     3.0
Venture                        1.0     3.0
Village                        1.0     2.5
Vineyard                       1.0     3.0
Warehouse                      1.0     2.5
Watchtower                     1.0     2.5
Wharf                          1.0     3.0
Wishing Well                   0.5     2.5
Witch                          1.5     3.5
Woodcutter                     1.0     2.5
Worker's Village               1.0     3.0
Workshop                       1.0     2.5
Young Witch                    1.5     3.5
« Last Edit: June 16, 2011, 09:29:23 am by rrenaud »
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Kuildeous

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Re: First player advantage
« Reply #29 on: June 16, 2011, 11:51:37 am »
0

In my casual games, we sped things up by having each player reveal his hand and buy his first two cards. It saved a little time at the beginning of the game. I hadn't really considered the effect of watching a person's strategy, though recent expansions are really revealing how important that is.

Being able to see what your predecessors buy for their first two turns before making your purchase would actually give a pretty handy advantage to the last player. Is it enough to offset first-player advantage? Probably not, but it would help mitigate it.

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rrenaud

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Re: First player advantage
« Reply #30 on: June 16, 2011, 11:53:28 am »
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Also, I agree that averages are prettty dumb with respect to dominion scores. But median score differences on the other hand are pretty reasonable/robust.
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WanderingWinder

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Re: First player advantage
« Reply #31 on: June 16, 2011, 01:08:15 pm »
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I don't think medians are so hot either for something like this, at least if we're trying to talk about what the advantage SHOULD be, at high levels of play. The vast majority of Isotropic-ers are really really bad at endgames, have no sense of the PPR, and are going to thus skew the results.

theory

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Re: First player advantage
« Reply #32 on: June 16, 2011, 01:27:39 pm »
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I don't understand
Quote
The first player loses a half point for having more turns than player two.

Shouldn't the stats separate out games where first player actually took an extra turn?  E.g., you have the global stats, and then you have games where P1 and P2 took the same number of turns, and then you have games where P1 took an extra turn.  You'd probably want to split the games where P1 took an extra turn into those where P1 won and where P1 lost, and then you could look at how much P1 usually wins by when the extra turn matters.

Because otherwise, what I think ends up happening is, you have the global median, and you say, let's bid this amount.  But in reality, it just favors P2 whenever P1's extra turn doesn't matter, and it isn't enough for P2 when P1's extra turn does actually matter.
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WanderingWinder

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Re: First player advantage
« Reply #33 on: June 16, 2011, 02:06:49 pm »
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I just thought of another factor. Better players tend to win more often, which leads them to be second player more often which will skew positive results to the second player.
I believe rrenaud controlled for this, but other people doing analyses should be wary.

Randal FTW

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Re: First player advantage
« Reply #34 on: June 16, 2011, 02:30:37 pm »
0

In chess, the first player has an advantage.  Same in Magic, billiards, horse racing and Dominion.  In poker the person who goes last has a distinct advantage.  I don't think it is an innate problem in any of these because in the long run, over many trials, the player with more skill will win more often in whichever position they begin in.

this


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