Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.

176

Dominion General Discussion / $6+ cost cards

« on: January 05, 2015, 04:39:42 pm »

$6+ cost cards

Rank	Card	+/- vs. Qvist	% games gained	# games gained	# games available
1	Border Village	+3	89.3%	6708	7512
2	Goons	0	88.4%	7053	7979
3	King's Court	-2	80.8%	6276	7769
4	Nobles	+2	78.8%	6284	7978
5	Grand Market	-2	75.8%	6179	8156
6	Peddler	+1	72.8%	5649	7755
7	Altar	-2	59.7%	4726	7916
8	Hoard	+1	58.2%	4765	8182
9	Farmland	+6	54.6%	4263	7812
10	Expand	+4	48.4%	3848	7957
11	Fairgrounds	-3	47.5%	3749	7892
12	Harem	+1	46.7%	3687	7902
13	Hunting Grounds	-3	45.0%	3515	7805
14	Forge	-2	43.9%	3496	7970
15	Prince	n/a	43.4%	289	666
16	Bank	-5	36.9%	3011	8149
17	Adventurer	-1	7.3%	684	9278

177

Dominion General Discussion / $5 cost cards

« on: January 05, 2015, 04:38:54 pm »

$5 cost cards

Rank	Card	+/- vs. Qvist	% games gained	# games gained	# games available
1	Governor	+7	93.0%	2417	2598
2	Wharf	+1	89.0%	7092	7965
3	Mountebank	-2	86.9%	6757	7779
4	Hunting Party	+2	81.1%	6246	7705
5	Minion	+4	80.1%	6252	7807
6	Cultist	-2	79.0%	6103	7730
7	Counterfeit	+5	78.2%	6107	7805
8	City	+29	77.0%	6146	7985
9	Butcher	+12	76.4%	5317	6954
10	Witch	-5	76.4%	7123	9323
11	Upgrade	+4	74.9%	6005	8013
12	Rebuild	-10	74.4%	5800	7800
13	Junk Dealer	-2	72.5%	5792	7984
14	Knights	+13	71.8%	5530	7698
15	Stables	+7	71.8%	5668	7896
16	Festival	+22	70.7%	6534	9245
17	Margrave	-3	70.4%	5485	7793
18	Highway	+7	70.0%	5451	7791
19	Haggler	19	69.5%	5382	7744
20	Laboratory	0	69.1%	6234	9018
21	Baker	+2	67.5%	4824	7150
22	Bazaar	+6	67.2%	5326	7930
23	Apprentice	-6	66.8%	5105	7643
24	Tactician	-8	66.2%	5214	7879
25	Bandit Camp	+5	65.2%	5279	8096
26	Soothsayer	-8	65.0%	4617	7100
27	Inn	+16	61.7%	4816	7810
28	Market	+12	61.3%	5720	9327
29	Torturer	-21	59.9%	4663	7782
30	Ill-Gotten Gains	-20	59.9%	4591	7664
31	Count	+1	59.8%	4607	7700
32	Ghost Ship	-20	58.6%	4550	7760
33	Merchant Guild	+8	55.5%	3869	6972
34	Jester	0	52.5%	4023	7658
35	Embassy	-11	48.7%	3734	7669
36	Cartographer	+3	47.9%	3623	7556
37	Duke	-11	47.7%	3731	7823
38	Council Room	+4	47.7%	4444	9326
39	Rabble	-6	47.3%	3701	7832
40	Vault	-11	46.6%	3677	7888
41	Catacombs	-5	46.4%	3568	7685
42	Mint	+11	46.1%	3655	7936
43	Trading Post	+6	45.3%	3585	7907
44	Band of Misfits	0	45.2%	3457	7646
45	Treasury	+3	44.2%	3424	7743
46	Horn of Plenty	-15	44.0%	3409	7750
47	Journeyman	-12	42.2%	3005	7129
48	Mystic	-2	37.5%	2926	7806
49	Library	-4	34.6%	3242	9358
50	Rogue	+4	33.2%	2520	7588
51	Venture	-1	33.2%	2657	8002
52	Pillage	-1	30.7%	2402	7815
53	Graverobber	-1	30.7%	2381	7752
54	Outpost	+2	29.6%	2344	7906
55	Merchant Ship	-8	28.7%	2278	7931
56	Tribute	-1	23.5%	1815	7739
57	Saboteur	+4	20.7%	1605	7772
58	Explorer	0	18.7%	1489	7943
59	Royal Seal	+1	18.7%	1491	7994
60	Stash	+2	16.9%	306	1811
61	Mine	-2	16.7%	1572	9431
62	Mandarin	-5	16.0%	1277	7998
63	Cache	+1	11.2%	854	7627
64	Contraband	-1	10.9%	865	7960
65	Harvest	0	9.7%	759	7859
66	Counting House	0	8.3%	660	7916

178

Dominion General Discussion / $4 cost cards

« on: January 05, 2015, 04:38:07 pm »

$4 cost cards

Rank	Card	+/- vs. Qvist	% games gained	# games gained	# games available
1	Tournament	+1	95.4%	7467	7825
2	Ironmonger	+3	87.2%	6947	7970
3	Plaza	+13	82.7%	5953	7196
4	Wandering Minstrel	+3	79.4%	6215	7828
5	Caravan	+7	78.3%	6029	7698
6	Worker's Village	+8	77.8%	6055	7778
7	Remake	-4	75.2%	5689	7566
8	JackOfAllTrades	-4	74.9%	5929	7911
9	Herald	+9	74.3%	5315	7153
10	Spice Merchant	+5	72.1%	5549	7692
11	Island	+26	70.9%	5594	7891
12	Throne Room	+5	70.5%	6517	9241
13	Conspirator	+7	69.0%	5438	7880
14	Fortress	+16	68.1%	5316	7807
15	Salvager	+6	68.0%	5357	7880
16	Mining Village	+17	66.2%	5264	7952
17	Farming Village	+11	65.8%	5103	7760
18	Marauder	-5	65.7%	5086	7739
19	Bridge	-9	65.5%	5203	7946
20	Sea Hag	-19	64.7%	5068	7829
21	Militia	-11	62.8%	5750	9161
22	Horse Traders	+2	62.7%	4972	7933
23	Monument	-15	62.2%	5001	8044
24	Gardens	+5	60.6%	5620	9271
25	Walled Village	+18	60.6%	797	1315
26	Ironworks	-4	59.9%	4832	8073
27	Bishop	-16	57.9%	4598	7935
28	Quarry	-5	56.8%	4470	7876
29	Remodel	+5	54.2%	5088	9394
30	Silk Road	+1	52.7%	4094	7772
31	Young Witch	-30	52.6%	4029	7666
32	Moneylender	-6	51.9%	4917	9466
33	Advisor	+6	50.7%	3609	7115
34	Smithy	-15	48.1%	4491	9341
35	Scavenger	-10	44.9%	3570	7958
36	Trader	+2	43.7%	3352	7676
37	Envoy	-10	43.1%	795	1843
38	Baron	-2	41.7%	3330	7984
39	Nomad Camp	+7	41.2%	3165	7686
40	Feodum	+2	40.3%	3102	7687
41	Procession	-6	37.7%	2907	7714
42	Cutpurse	-10	34.9%	2719	7791
43	Armory	-2	34.6%	2742	7935
44	Rats	+3	34.4%	2696	7843
45	Feast	+10	29.3%	2683	9159
46	Death Cart	-6	29.2%	2287	7828
47	Talisman	+1	28.8%	2292	7959
48	Spy	+3	28.4%	2621	9243
49	Taxman	-4	25.4%	1808	7114
50	Noble Brigand	-6	24.9%	1939	7784
51	Navigator	+1	19.3%	1484	7692
52	Treasure Map	+1	16.2%	1294	7972
53	Bureaucrat	-3	13.3%	1251	9395
54	Pirate Ship	-5	12.9%	995	7705
55	Scout	+2	11.2%	868	7739
56	Coppersmith	-2	10.2%	786	7734
57	Thief	-1	8.5%	777	9188

179

Dominion General Discussion / $3 cost cards

« on: January 05, 2015, 04:37:35 pm »

$3 cost cards

Rank	Card	+/- vs. Qvist	% games gained	# games gained	# games available
1	Fishing Village	+2	89.2%	7006	7854
2	Forager	+5	88.7%	7094	7999
3	Masquerade	-2	87.7%	7031	8015
4	Ambassador	-2	83.6%	6757	8078
5	Warehouse	+5	82.6%	6674	8084
6	Black Market	+12	80.6%	2729	3386
7	Swindler	-2	79.1%	6447	8147
8	Market Square	+5	78.9%	6162	7813
9	Hermit	0	78.3%	6232	7964
10	Steward	-6	77.7%	6282	8083
11	Menagerie	-5	77.7%	6100	7854
12	Urchin	-1	77.1%	6126	7947
13	Scheme	-1	75.6%	6016	7954
14	Shanty Town	+9	73.9%	5996	8118
15	Tunnel	+2	71.3%	5640	7913
16	Great Hall	+16	69.2%	5804	8397
17	Oasis	+2	68.0%	5305	7798
18	Village	-4	67.1%	6354	9464
19	Watchtower	-11	61.5%	4916	7990
20	Sage	+5	56.6%	4517	7987
21	Lookout	0	56.0%	4420	7888
22	Wishing Well	+2	55.4%	4504	8126
23	Doctor	-7	54.6%	3887	7124
24	Trade Route	+3	54.1%	4366	8070
25	Smugglers	+1	51.0%	4066	7965
26	Storeroom	-6	47.8%	3806	7958
27	Oracle	-12	44.9%	3521	7849
28	Loan	0	41.0%	3333	8127
29	Develop	+2	36.4%	2900	7965
30	Workshop	0	35.3%	3286	9319
31	Fortune Teller	-2	29.7%	2354	7919
32	Woodcutter	+1	27.6%	2622	9506
33	Masterpiece	-11	24.6%	1797	7309
34	Chancellor	0	13.7%	1305	9512

180

Dominion General Discussion / $1 and $2 cost cards

« on: January 05, 2015, 04:37:05 pm »

$1 and $2 cost cards

Rank	Card	+/- vs. Qvist	% games gained	# games gained	# games available
1	Chapel	0	87.6%	8408	9596
2	Squire	+3	83.4%	6452	7732
3	Hamlet	+1	83.2%	6564	7892
4	Candlestick Maker	+3	80.9%	5859	7242
5	Crossroads	+4	79.2%	6112	7713
6	Lighthouse	0	74.4%	5877	7898
7	Courtyard	-4	71.7%	5741	8005
8	Fool's Gold	-6	68.2%	5415	7936
9	Cellar	+4	67.3%	6418	9533
10	Stonemason	-2	66.2%	4883	7381
11	Haven	+1	65.8%	5152	7830
12	Vagrant	+4	65.5%	5350	8164
13	Pawn	-5	63.7%	4975	7807
14	Native Village	-4	61.2%	4781	7814
15	Pearl Diver	+5	50.2%	4021	8014
16	Embargo	-2	48.4%	3902	8059
17	Moat	0	43.7%	4160	9516
18	Duchess	+3	40.1%	3117	7773
19	Poor House	-4	32.0%	2521	7871
20	Beggar	-2	29.4%	2306	7840
21	Herbalist	-2	26.2%	2061	7877
22	Secret Chamber	0	25.6%	2105	8235

181

Dominion General Discussion / Dominion Data Mining: Card Rankings

« on: January 05, 2015, 04:35:56 pm »

Everybody loves the card rankings that Qvist puts out, but I've always secretly wondered how these lists compare to the way the top players really play the cards.

So I've collected over 90,000 game logs of the top 100 Dominion players on the Isotrophish rankings (2-player, pro rating, no bots) and analyzed them to determine how the best players in the world approach the cards.  Obviously there are a lot of differing opinions on the best way to determine which of two cards is better.  The method I've chosen is to measure the percentage of kingdoms containing card X where the top-100 player gains card X.  If card X really is one of the best cards, then it should be bought on almost every kingdom where it is available.  The nice thing about measuring cards this way is that it puts cards like Cultist (where you usually want as many as possible) and Chapel (where you usually only want one) on equal footing.

The list below orders the cards by how often they are gained.  In the next couple posts, I'm planning on splitting these by cost and comparing them to Qvist's card lists.

Rank	Card	% games gained	# games gained	# games available
1	Tournament	95.4%	7467	7825
2	Governor	93.0%	2417	2598
3	Border Village	89.3%	6708	7512
4	Fishing Village	89.2%	7006	7854
5	Wharf	89.0%	7092	7965
6	Forager	88.7%	7094	7999
7	Goons	88.4%	7053	7979
8	Masquerade	87.7%	7031	8015
9	Chapel	87.6%	8408	9596
10	Ironmonger	87.2%	6947	7970
11	Mountebank	86.9%	6757	7779
12	Ambassador	83.6%	6757	8078
13	Squire	83.4%	6452	7732
14	Hamlet	83.2%	6564	7892
15	Plaza	82.7%	5953	7196
16	Warehouse	82.6%	6674	8084
17	Hunting Party	81.1%	6246	7705
18	Candlestick Maker	80.9%	5859	7242
19	King's Court	80.8%	6276	7769
20	Black Market	80.6%	2729	3386
21	Minion	80.1%	6252	7807
22	Wandering Minstrel	79.4%	6215	7828
23	Crossroads	79.2%	6112	7713
24	Swindler	79.1%	6447	8147
25	Cultist	79.0%	6103	7730
26	Market Square	78.9%	6162	7813
27	Nobles	78.8%	6284	7978
28	Caravan	78.3%	6029	7698
29	Hermit	78.3%	6232	7964
30	Counterfeit	78.2%	6107	7805
31	Worker's Village	77.8%	6055	7778
32	Steward	77.7%	6282	8083
33	Menagerie	77.7%	6100	7854
34	Urchin	77.1%	6126	7947
35	City	77.0%	6146	7985
36	Butcher	76.5%	5317	6954
37	Witch	76.4%	7123	9323
38	Grand Market	75.8%	6179	8156
39	Scheme	75.6%	6016	7954
40	Remake	75.2%	5689	7566
41	JackOfAllTrades	74.9%	5929	7911
42	Upgrade	74.9%	6005	8013
43	Lighthouse	74.4%	5877	7898
44	Rebuild	74.4%	5800	7800
45	Herald	74.3%	5315	7153
46	Shanty Town	73.9%	5996	8118
47	Peddler	72.8%	5649	7755
48	Junk Dealer	72.5%	5792	7984
49	Spice Merchant	72.1%	5549	7692
50	Knights	71.8%	5530	7698
51	Stables	71.8%	5668	7896
52	Courtyard	71.7%	5741	8005
53	Tunnel	71.3%	5640	7913
54	Island	70.9%	5594	7891
55	Festival	70.7%	6534	9245
56	Throne Room	70.5%	6517	9241
57	Margrave	70.4%	5485	7793
58	Highway	70.0%	5451	7791
59	Haggler	69.5%	5382	7744
60	Laboratory	69.1%	6234	9018
61	Great Hall	69.1%	5804	8397
62	Conspirator	69.0%	5438	7880
63	Fool's Gold	68.2%	5415	7936
64	Fortress	68.1%	5316	7807
65	Oasis	68.0%	5305	7798
66	Salvager	68.0%	5357	7880
67	Baker	67.5%	4824	7150
68	Scrying Pool	67.4%	5142	7634
69	Cellar	67.3%	6418	9533
70	Bazaar	67.2%	5326	7930
71	Village	67.1%	6354	9464
72	Apprentice	66.8%	5105	7643
73	Mining Village	66.2%	5264	7952
74	Tactician	66.2%	5214	7879
75	Stonemason	66.2%	4883	7381
76	Haven	65.8%	5152	7830
77	Farming Village	65.8%	5103	7760
78	Marauder	65.7%	5086	7739
79	Vagrant	65.5%	5350	8164
80	Bridge	65.5%	5203	7946
81	Bandit Camp	65.2%	5279	8096
82	Soothsayer	65.0%	4617	7100
83	University	64.9%	4919	7574
84	Sea Hag	64.7%	5068	7829
85	Pawn	63.7%	4975	7807
86	Militia	62.8%	5750	9161
87	Horse Traders	62.7%	4972	7933
88	Monument	62.2%	5001	8044
89	Inn	61.7%	4816	7810
90	Watchtower	61.5%	4916	7990
91	Market	61.3%	5720	9327
92	Native Village	61.2%	4781	7814
93	Gardens	60.6%	5620	9271
94	Walled Village	60.6%	797	1315
95	Familiar	60.0%	4553	7592
96	Torturer	59.9%	4663	7782
97	Ill-Gotten Gains	59.9%	4591	7664
98	Ironworks	59.9%	4832	8073
99	Count	59.8%	4607	7700
100	Altar	59.7%	4726	7916
101	Ghost Ship	58.6%	4550	7760
102	Hoard	58.2%	4765	8182
103	Bishop	57.9%	4598	7935
104	Quarry	56.8%	4470	7876
105	Sage	56.6%	4517	7987
106	Lookout	56.0%	4420	7888
107	Merchant Guild	55.5%	3869	6972
108	Wishing Well	55.4%	4504	8126
109	Farmland	54.6%	4263	7812
110	Doctor	54.6%	3887	7124
111	Remodel	54.2%	5088	9394
112	Trade Route	54.1%	4366	8070
113	Alchemist	52.9%	3986	7534
114	Silk Road	52.7%	4094	7772
115	Young Witch	52.6%	4029	7666
116	Jester	52.5%	4023	7658
117	Moneylender	51.9%	4917	9466
118	Smugglers	51.0%	4066	7965
119	Advisor	50.7%	3609	7115
120	Pearl Diver	50.2%	4021	8014
121	Embassy	48.7%	3734	7669
122	Embargo	48.4%	3902	8059
123	Expand	48.4%	3848	7957
124	Smithy	48.1%	4491	9341
125	Cartographer	47.9%	3623	7556
126	Storeroom	47.8%	3806	7958
127	Duke	47.7%	3731	7823
128	Council Room	47.7%	4444	9326
129	Fairgrounds	47.5%	3749	7892
130	Rabble	47.3%	3701	7832
131	Vineyard	47.2%	3578	7588
132	Apothecary	47.1%	3570	7575
133	Harem	46.7%	3687	7902
134	Vault	46.6%	3677	7888
135	Catacombs	46.4%	3568	7685
136	Mint	46.1%	3655	7936
137	Trading Post	45.3%	3585	7907
138	Band of Misfits	45.2%	3457	7646
139	Hunting Grounds	45.0%	3515	7805
140	Scavenger	44.9%	3570	7958
141	Oracle	44.9%	3521	7849
142	Treasury	44.2%	3424	7743
143	Horn of Plenty	44.0%	3409	7750
144	Forge	43.9%	3496	7970
145	Moat	43.7%	4160	9516
146	Trader	43.7%	3352	7676
147	Prince	43.4%	289	666
148	Envoy	43.1%	795	1843
149	Journeyman	42.2%	3005	7129
150	Baron	41.7%	3330	7984
151	Nomad Camp	41.2%	3165	7686
152	Loan	41.0%	3333	8127
153	Golem	40.4%	3032	7503
154	Feodum	40.4%	3102	7687
155	Duchess	40.1%	3117	7773
156	Possession	37.8%	2815	7452
157	Procession	37.7%	2907	7714
158	Mystic	37.5%	2926	7806
159	Bank	36.9%	3011	8149
160	Develop	36.4%	2900	7965
161	Workshop	35.3%	3286	9319
162	Cutpurse	34.9%	2719	7791
163	Library	34.6%	3242	9358
164	Armory	34.6%	2742	7935
165	Rats	34.4%	2696	7843
166	Rogue	33.2%	2520	7588
167	Venture	33.2%	2657	8002
168	Poor House	32.0%	2521	7871
169	Pillage	30.7%	2402	7815
170	Graverobber	30.7%	2381	7752
171	Fortune Teller	29.7%	2354	7919
172	Outpost	29.6%	2344	7906
173	Beggar	29.4%	2306	7840
174	Feast	29.3%	2683	9159
175	Death Cart	29.2%	2287	7828
176	Talisman	28.8%	2292	7959
177	Merchant Ship	28.7%	2278	7931
178	Spy	28.4%	2621	9243
179	Woodcutter	27.6%	2622	9506
180	Herbalist	26.2%	2061	7877
181	Secret Chamber	25.6%	2105	8235
182	Taxman	25.4%	1808	7114
183	Noble Brigand	24.9%	1939	7784
184	Masterpiece	24.6%	1797	7309
185	Tribute	23.5%	1815	7739
186	Saboteur	20.7%	1605	7772
187	Navigator	19.3%	1484	7692
188	Explorer	18.7%	1489	7943
189	Royal Seal	18.7%	1491	7994
190	Stash	16.9%	306	1811
191	Mine	16.7%	1572	9431
192	Treasure Map	16.2%	1294	7972
193	Mandarin	16.0%	1277	7998
194	Chancellor	13.7%	1305	9512
195	Bureaucrat	13.3%	1251	9395
196	Pirate Ship	12.9%	995	7705
197	Philosopher's Stone	12.1%	907	7518
198	Scout	11.2%	868	7739
199	Cache	11.2%	854	7627
200	Contraband	10.9%	865	7960
201	Coppersmith	10.2%	786	7734
202	Harvest	9.7%	759	7859
203	Thief	8.5%	777	9188
204	Counting House	8.3%	660	7916
205	Transmute	7.6%	584	7661
206	Adventurer	7.4%	684	9278

182

Dominion General Discussion / Re: Openings that are better for P1 or P2

« on: January 02, 2015, 11:37:13 am »

I'm surprised bishop/silver doesn't show up for P2, and surprised militia/silver doesn't show up for P1. My nonsense theory for hermit-silver: these game tend towards fast three piles, which has more ties than average, which favors P2.

I'm really surprised that there are mirror openings where P1 has a 70% winrate... that means there are kingdoms where P1 is heavily favored.

Bishop-Silver is up there for P2 with a P2 win % of 47% (the overall expected win percentage for P2 is 43%), but I don't have enough data to say for sure that this is a real effect.  Surprisingly, Militia-Silver seems pretty close to average with a P2 win % of 44%.

There are actually several openings that have a much higher P1 % than 70% in the mirror, but I don't have enough data to be totally confident about them. 

• Haggler-<nothing> (81%)
• Wharf-Silver (80%)
• Monument-Forager (79%)
• Horse Traders-Chapel (77%)
• Salvager-Market Square (76%)

183

Dominion General Discussion / Re: Openings that are better for P1 or P2

« on: January 02, 2015, 12:36:16 am »

It's kind of surprising that with this many games, it's still possible to lack statistical significance, but there are so many possible openings that most of the openings don't have enough data to really be sure.  Even so, I took the data and looked at wins/losses using the binomial test for p-value with 0.57 and 0.43 the expected values for wins and losses for P1 (and vice-versa for P2).  Here are some things that we have enough data to say with 95% confidence (p < 0.05):

Here P<0.05 only means that if the true expected rate were 0.57/0.43, that you would get a result "this extreme" less than 0.05 of the time. Since you presumably tested many hundreds of different hypotheses (the win rates for each opening, both overall and for Player 1/player 2 separately), we would expect about 1/20th of them to fall outside those bounds even if all openings had a 0.57/0.43 expected win rate. 

This isn't to say that I think Mountebank isn't a good opening . But when testing many hundreds of hypotheses, p<0.05 isn't strict enough to avoid many false positives.

One correction (the Bonferroni correction) that minimizes the chance that multiple comparisons lead to false positives is that if you apply a 0.05 threshold for the p-value a single comparison, for N comparisons apply a 0.05/N threshold.

Totally agree.  Unfortunately, I don't have close to enough data to establish significance even with the Bonferroni correction.  Even so, here are some results from analyzing mirror openings.  I suspect that these are real effects, the significance of which could be established with enough data.

Mirror openings that are better for P1 than P2

Opening	Number of occurences	P1 win%	Why this might be a real effect
Oracle-Silver	112	73%	Since Oracle messes with the top of the opponent's deck, playing it right after the 1st shuffle can keep an opponent from hitting 5
Swindler-Silver	133	68%	P1's Swindler might hit P2's Swindler and keep him from ever getting to play it
Tournament-Ambassador	52	71%	Tournament is a race, and winning simultaneously gets you a good prize and denies that prize to your opponent

There's only one opening favoring P2 that seems to be a real effect.  But I don't have a good explanation for why it would be better for P2.
Mirror openings that are better for P2 than P1

Opening	Number of occurences	P1 win%	Why this might be a real effect
Hermit-Silver	157	43%	(Remember that 57% is the baseline win percentage for P1, so this is way below that)

It does seem to me (though it's not backed up by the data) that there could be some cards like Trade Route, Forager, or Graverobber that could legitimately be better cards for P2 to open in a mirror since he could get P1 to help activate it for him.

184

Dominion General Discussion / Re: Openings that are better for P1 or P2

« on: December 24, 2014, 12:07:51 am »

Only the original poster could answer this question exactly because no one else knows the details of the pool of openings he has analyzed.

But here's a sample calculation that is much simpler: if there are 400 openings that have 50 games each, and in actuality P1 wins 57% for every opening (with no ties), the chance that at least one of those 400 openings would have >=60% win rate for P2 is about 95%.

Details: The standard deviation of P1's win rate for each opening is about 7%, so (by the central limit theorem for simplicity) the chance that each of the 400 openings has a <=40% win chance for P1 is about 0.76%. So the chance that at least one of the openings has a <=40% win chance for P1 is 1-(the chance that none of the openings have this). Assume that the results of games with one opening doesn't depend on results from other openings (not quite true, because each game will be counted twice since each player has an opening) and you get to 95%.

It's kind of surprising that with this many games, it's still possible to lack statistical significance, but there are so many possible openings that most of the openings don't have enough data to really be sure.  Even so, I took the data and looked at wins/losses using the binomial test for p-value with 0.57 and 0.43 the expected values for wins and losses for P1 (and vice-versa for P2).  Here are some things that we have enough data to say with 95% confidence (p < 0.05):

Either player

• Opening Mountebank-<nothing> is significantly better than average (winning percentage of 58.0% averaged over P1 and P2)
• Opening Junk Dealer-<nothing> is significantly better than average (winning percentage of 63.2%)
• Opening Potion-Silver is significantly worse than average (winning percentage of 45.9%)
• Opening Potion-Shanty Town is significantly worse than average (winning percentage of 34.9%)
• Opening Smugglers-Silver is significantly worse than average (winning percentage of 40.4%)
• Opening Plaza-Silver is significantly worse than average (winning percentage of 40.9%)

P1 openings

• Opening Salvager-Silver is significantly better than average (P1 winning percentage of 68.3%)
• Opening Oracle-Silver is significantly better than average (P1 winning percentage of 72.5%)
• Opening Potion-Storeroom is significantly better than average (P1 winning percentage of 70.3%)
• Opening Sea Hag-Silver is signicantly better than average (P1 winning percentage of 64.1%)
• Opening Swindler-Silver is significantly better than average (P1 winning percentage of 68.4%)
• Opening Hermit-Silver is significantly worse than average (P1 winning percentage of 43.0%)
• Opening Wharf-<nothing> is significantly worse than average (P1 winning percentage of 44.2%)

P2 openings

• Opening Upgrade-<nothing> is significantly better than average (P2 winning percentage of 58.8%)
• Opening Potion-Sage is significantly worse than average (P2 winning percentage of 22.2%)
• Opening Fishing Village-Fishing Village is significantly worse than average (P2 winning percentage of 26.9%)
• Opening Lookout-Silver is significantly worse than average (P2 winning percentage 27.0%)

There's not a whole lot here that's surprising, except maybe that Wharf-<nothing> is actually a bad opening for P1 (and not that great for P2 either).  One other interesting thing that the lists above don't show is that while Swindler-Silver is a good opening for P1, it just missed the significance cutoff for being listed as worse than average for P2.

Edit: a note about Rebuild-Silver, which featured prominently in the first post.  The tables in the first post used all 90,000 games, while this analysis used only games between two top-100 players (about 17,000 games).  In the smaller dataset, Rebuild-Silver was opened less than 50 times, and didn't make it into this analysis.

185

Dominion General Discussion / Re: Openings that are better for P1 or P2

« on: December 23, 2014, 04:35:51 pm »

This is exactly what I am saying. I would expect it to be on the order of maybe 10 times less frequent, so I am surprised that it is almost half as common.

Tournament/Ambassador is a stronger opening than Oracle/Silver or Swindler/Silver, so usually people go for it on Tournament/Ambassador boards while there are plenty of alternatives to Swindler/Silver and Oracle/Silver.

This presumably would be an interesting calculation from this top 100 players vs. each other data set: on Tournament/Ambassador (and probably exclude Baker) boards, what % of the time do players with a 4/3 split go for Tournament/Ambassador. And then the same calculation for Oracle/Silver on boards with Oracle (but not Baker), and so on. That would tell you how frequently top players go for each opening when it is available.

I actually already have this data calculated as well, but I was going to make a separate topic for it, because there's just a lot of data.  But just as a teaser, if we order openings according to the ratio of # of times bought to number of times available, here's where openings that you mentioned fall in the ranking:

Rank	Opening	Type	# times bought	# times available	Ratio
...
13	Tournament-Ambassador	4/3	126	194	0.649
...
1563	Swindler-Silver	3/3	369	4266	0.086
...
1816	Oracle-Silver	3/3	287	4074	0.070

My script for calculating these correctly handles coin-token openings (e.g. a Gold-Chapel opening is only counted as available if Baker is on the board and the player gets a 5-2 split).  It currently doesn't handle Nomad Camp openings correctly, which I'm going to try to fix before I post the full list.

186

Dominion General Discussion / Re: Openings that are better for P1 or P2

« on: December 23, 2014, 03:15:57 pm »

The original post included only Pro, 2-player games with no bots.  Over all the games, the average win percentage for P1 was 57% and for P2 was 43%.

I took your recommendation and restricted it to only games between top-100 players.  This leaves us with only ~17,000 openings to analyze.  Here are the same results for the more restricted dataset:

Top openings that are better for P1 than P2

Opening	Type	Number of occurences	P1 win %	P2 win %
Potion-Sage	4/3	53	62%	22%
Fishing Village-Fishing Village	3/3	73	65%	27%
Oracle-Silver	3/3	112	73%	34%
Swindler-Silver	3/3	133	68%	32%
Tournament-Ambassador	4/3	52	71%	38%

Top openings that are better for P2 than P1

Opening	Type	Number of occurences	P1 win %	P2 win %
Hermit-Silver	3/3	157	43%	52%
Upgrade-<nothing>	5/2	67	51%	58%
Chancellor-Silver	3/3	60	43%	50%
Storeroom-Silver	4/3	63	50%	52%
Bishop-Silver	4/3	77	52%	54%

So in this restricted set, any advantage for P2 is much less pronounced.  It seems very possible, as JW was saying, that the top P2 openings from the original post were simply statistical anomalies.  Maybe I'll try to look at mirrors next.

187

Dominion General Discussion / Openings that are better for P1 or P2

« on: December 23, 2014, 01:23:15 pm »

Recently, I collected logs for about 90,000 games involving the top 50 players on the Isotropish ranking, and one thing I've been analyzing is openings.  I noticed something unexpected: there are certain openings that are much better for either P1 or P2.  If I take the openings and exclude everything that's been opened less than 50 times, here's what falls out.

Top openings that are much better for P1 than P2

Opening	Type	Number of occurences	P1 win %	P2 win %
Moneylender-Fishing Village	4/3	124	76%	29%
Soothsayer-Chapel	5/2	64	80%	32%
Soothsayer-Silver	5/3	72	81%	34%
Remake-Swindler	4/3	82	77%	30%
Salvager-Market Square	4/3	87	72%	28%

Of course, Dominion has a strong first-player advantage built in, so those results aren't especially interesting.  What I find much more interesting is that there are openings that are substantially stronger for P2 than for P1.

Top openings that are much better for P2 than P1

Opening	Type	Number of occurences	P1 win %	P2 win %
Rebuild-Silver	5/3	90	36%	67%
Spice Merchant-Lookout	4/3	51	33%	60%
Caravan-Workshop	4/3	59	39%	64%
Quarry-Trade Route	4/3	64	35%	57%
Quarry-Lookout	4/3	77	35%	57%

My first impression here is that the openings in the second table look like higher risk/higher reward openings, which would lend some evidence to the recent discussion about changing strategy/tactics when you're ahead or behind in the game.

Any other thoughts?

188

Variants and Fan Cards / Re: Dominion Progress (my main fan set)

« on: December 16, 2014, 03:44:59 pm »

Superstitious Village – Action – $3
+1 Card
+2 Actions
Each other player may trash a card from his hand. If he doesn't, he gains a curse.

What if you had the other player gain the curse in hand?  That way, it's harder to use this card for a pin, since they could discard the curse the second time.

189

Dominion: Adventures Previews / Re: Groundless speculation about the 2015 expansion

« on: December 15, 2014, 01:48:47 pm »

That's stash, not stache. Stache is this:

I like the potential for a Pearl Diver-Stache combo.

190

Dominion General Discussion / Re: Tortoise vs. Hare (low/high risk play)

« on: December 05, 2014, 03:39:23 pm »

I remember some article somewhere saying that the less likely you are to win, the more you should take risks.

Edit: here.

Yes, it depends on the opponent and how you're doing in the game.  There's a great article about this topic here (it's about basketball, but it applies equally well to any zero-sum game like Dominion): https://gravityandlevity.wordpress.com/2010/12/21/risk-is-the-ally-of-the-underdog/

If you think you're better than your opponent or ahead in the game, then adopting a low-risk strategy is best.  If you're way overmatched by your opponent or way behind, then you might want to think about Treasure Map or Black Market even if there's something safer and less swingy on the board.  If you both play it safe, you'll probably lose.  If you roll the dice, there's a chance you hit the jackpot and win when you didn't really "deserve" it.