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Author Topic: More data mining: Answering Dominion questions with data  (Read 10679 times)

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WanderingWinder

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Re: More data mining: Card "strength"
« Reply #50 on: February 01, 2015, 09:59:16 am »
0

Quote from: Wandering Winder
The thing about SR in high-level games is, it's a card you often go to if you're way behind. "I'm very far behind - if I'm going to win, it will have to go long enough for SR to be good (better than duchy anyway), so SR it is". Desperation moves are going to look bad, even if they may up your winrate in the situation you get them.

Yes, this. I've been trying to think up a way to account for this. Something I'm considering is establishing an arbitrary turn limit, like, only counting cardS purchased before turn 10 or something. I *think* this should sufficiently account for deliberate strategies, and weed out ad hoc desperation tactics. Thoughts?

My thoughts are that you really can't come up with a solution to do it based on a scripted kind of numerical analysis. Only counting the first X turns will sometimes include desperation plays and sometimes not include real strategic decisions. Essentially, things are on far too much of a case-by-case basis to 'correct for' everything - you won't get there, and you lose the simplicity of a nice little metric. I mean, you can do whatever you want, but after very far at all, I don't see what the point is, personally.

Throwaway_bicycling

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Re: More data mining: Card "strength"
« Reply #51 on: February 01, 2015, 10:01:08 am »
0

SilkRoad             0.402 0.433 0.031

I think this will be because if Silk Road is good it can be mirrored.
Or at least a few will be denied.
So a lot of the time if you are the only player to buy one, it was a late game $4 hand that you wish was a duchy.

That sounds right to me. Do you have a Pirate Ship theory that fits the data? Only thing I can think of without combing through lots of actual games is when a Top 20 player buys it, he or she buys it relatively late and has a way to play it 2 or 3 times per turn in an engine, uses it to "mast" an opponent by taking down the money then grabs $2-3 every turn (maybe times 2 or 3) and is immune to the mirror because their deck has no money.

Meanwhile, there are some cards where Top 20 players actually outperform their overall win rate (given as 65% here) when they alone gain, although the caveat here is that for some of these cards, overall win rate on the board that contains them could be overall higher or lower than 65%.
Card                 All   Top20 Diff

Swindler             0.474 0.652 0.178
Bank                 0.463 0.653 0.190
Duchess              0.494 0.653 0.159
PearlDiver           0.498 0.654 0.156
Remodel              0.472 0.654 0.182
Mystic               0.509 0.655 0.146
BandofMisfits        0.478 0.658 0.180
Woodcutter           0.474 0.661 0.187
CandlestickMaker     0.519 0.662 0.143
Haggler              0.478 0.662 0.184
Ill-GottenGains      0.545 0.663 0.118
Smithy               0.461 0.664 0.203
BanditCamp           0.512 0.667 0.155
Fortress             0.483 0.667 0.184
JunkDealer           0.497 0.667 0.170
Moat                 0.435 0.667 0.232
Scavenger            0.506 0.667 0.161
Trader               0.410 0.667 0.257
WanderingMinstrel    0.516 0.667 0.151
Worker'sVillage      0.498 0.667 0.169
Gold                 0.468 0.669 0.201
Harem                0.499 0.671 0.172
Quarry               0.505 0.674 0.169
Masterpiece          0.606 0.676 0.070
Venture              0.487 0.677 0.190
Copper               0.520 0.678 0.158
Torturer             0.484 0.679 0.195
Altar                0.513 0.680 0.167
Mandarin             0.455 0.680 0.225
Cellar               0.441 0.681 0.240
FishingVillage       0.495 0.681 0.186
Watchtower           0.493 0.681 0.188
Highway              0.505 0.683 0.178
Marauder             0.445 0.683 0.238
Embassy              0.517 0.685 0.168
TradingPost          0.497 0.687 0.190
Crossroads           0.523 0.688 0.165
Embargo              0.466 0.689 0.223
WishingWell          0.575 0.690 0.115

So some of these cards are ones that lower-rated players (that is, players overall) do well with when they are the sole gainers as well (e.g., Wishing Well, Crossroads, Highway, Altar, Copper (?), Quarry, Embassy, Scavenger and Mystic). Except for Copper, all of those basically make sense to me since they can work well with building up engines, so any time you are building one and opponent isn't or you are building a better one...makes sense. And gaining Embassy curses your opponent. :-)

But others of these cards seem to be just more magic in the deck of a Top 20 player, the top ten of those in sorted order:
Card                 All   Top20 Diff
Trader               0.410 0.667 0.257
Cellar               0.441 0.681 0.240
Marauder             0.445 0.683 0.238
Moat                 0.435 0.667 0.232
Mandarin             0.455 0.680 0.225
Embargo              0.466 0.689 0.223
Smithy               0.461 0.664 0.203
Gold                 0.468 0.669 0.201
Torturer             0.484 0.679 0.195
Venture              0.487 0.677 0.190

Moat does not top this list, but would have been a good guess. :-)

Finally, there are cards that the Top20 just crush with if they are the only ones to gain them:
Card                 All   Top20 Diff
Colony               0.786 0.935 0.149
Goons                0.682 0.875 0.193
Province             0.667 0.853 0.186
Butcher              0.674 0.853 0.179
Platinum             0.593 0.818 0.225
City                 0.495 0.809 0.314
Mountebank           0.602 0.807 0.205
BorderVillage        0.581 0.804 0.223
Vineyard             0.653 0.802 0.149
Tournament           0.485 0.800 0.315

I think most of these are pretty obvious. The relative top player advantage with City and Tournament is pretty striking, though.

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Rabid

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Re: More data mining: Card "strength"
« Reply #52 on: February 01, 2015, 10:22:33 am »
+1

That sounds right to me. Do you have a Pirate Ship theory that fits the data?

My guesses for this are: small sample size, fun, testing or learning.

Copper (?)
I guess this would be mostly Goons, and also people buying random copper on the winning turn.
The all data will also be dragged down by new players using up all the buys.
« Last Edit: February 01, 2015, 10:28:28 am by Rabid »
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Throwaway_bicycling

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Re: More data mining: Card "strength"
« Reply #53 on: February 01, 2015, 10:41:38 am »
0

That sounds right to me. Do you have a Pirate Ship theory that fits the data?
My guesses for this are: small sample size, fun, testing or learning.
Good point; it still is below .500, so the "F it, I'm going Pirate Ship, Arrr!" Theory is good. Less good players are probably acquiring it for very different reasons.

Copper (?)
I guess this would be mostly Goons, and also people buying random copper on the winning turn.
The all data will also be dragged down by new players using up all the buys.
Goons was my best guess, too, except I would have thought most Top20 games would have been Goons mirrors, where copper buying is not unheard of. But you're right that these could be last turn buys of (say) 11 Coppers to gain 44 VP or something.

Would have been cooler if it were due to some trippy Coppersmith megaturn engine, but speaking of small sample sizes...

Expressicist: what are the sample sizes of the game base you are working with?
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WanderingWinder

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Re: More data mining: Card "strength"
« Reply #54 on: February 01, 2015, 10:48:03 am »
0

That sounds right to me. Do you have a Pirate Ship theory that fits the data?
My guesses for this are: small sample size, fun, testing or learning.
Good point; it still is below .500, so the "F it, I'm going Pirate Ship, Arrr!" Theory is good. Less good players are probably acquiring it for very different reasons.

Copper (?)
I guess this would be mostly Goons, and also people buying random copper on the winning turn.
The all data will also be dragged down by new players using up all the buys.
Goons was my best guess, too, except I would have thought most Top20 games would have been Goons mirrors, where copper buying is not unheard of. But you're right that these could be last turn buys of (say) 11 Coppers to gain 44 VP or something.

Would have been cooler if it were due to some trippy Coppersmith megaturn engine, but speaking of small sample sizes...

Expressicist: what are the sample sizes of the game base you are working with?

The other thing for coppers, more than goons, is going to be mountebank. You also sometimes get them in slogs and for Apothecary or counting house or as additional fuel for trashers. But the biggest thing is, good players know that buying copper is awful, so when they do it, they are probably doing really well, whereas their opponents can often write it off entirely.

TheExpressicist

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Re: More data mining: Card "strength"
« Reply #55 on: February 01, 2015, 02:52:51 pm »
+4

I'm gonna update the thread title from being just about card strength to the general subject of trying to answer Dominion questions using game data. I have some more data but I don't really want to start yet another thread.

Impact of First-Shuffle Luck on Win %
In other words, how big of an impact does missing one or both of your T1/T2 purchases before the second reshuffle have on the Win % of the Top-20 players? Measured in "Adjusted Win %", see first post for explanation.

When opening Action/Action (63.5% of the time):
Hit Both Actions: +4%
Hit One Action: -3%
Hit Neither Action: -11%

When opening Action/Treasure (32% of the time):
Hit Action + Treasure: +1.5%
Hit Treasure Only: -11%
Hit Action Only: -0.5%
Hit Neither: -11%

When opening Treasure/Treasure (4.5% of the time):
Hit Both Treasures: +2%
Hit 1 Treasure: -12%
Hit Neither Treasure: -40%
« Last Edit: February 01, 2015, 02:58:55 pm by TheExpressicist »
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JW

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Re: More data mining: Answering Dominion questions with data
« Reply #56 on: February 01, 2015, 04:28:10 pm »
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Do those stats take into account that the number of cards you draw depends on how you open? So Silver-Silver is drawn less than Silver-smithy because your smithy might help draw your silver?
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TheExpressicist

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Re: More data mining: Answering Dominion questions with data
« Reply #57 on: February 01, 2015, 05:47:40 pm »
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Do those stats take into account that the number of cards you draw depends on how you open? So Silver-Silver is drawn less than Silver-smithy because your smithy might help draw your silver?

It simply looks for if you played one or both of the cards you opened with on or before T4. So, for example if you open Smithy-Silver, you're guaranteed to play both this is wrong. 
« Last Edit: February 01, 2015, 08:20:25 pm by TheExpressicist »
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JW

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Re: More data mining: Answering Dominion questions with data
« Reply #58 on: February 01, 2015, 07:12:14 pm »
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Do those stats take into account that the number of cards you draw depends on how you open? So Silver-Silver is drawn less than Silver-smithy because your smithy might help draw your silver?

It simply looks for if you played one or both of the cards you opened with on or before T4. So, for example if you open Smithy-Silver, you're guaranteed to play both.

If you open double terminal and they collide, that's not the same luck of the draw as having one miss the shuffle. And another factor is that you might choose not to play a drawing action you opened with so that it doesn't trigger a bad shuffle.

Side note, you aren't guaranteed to see both Silver and Smithy if smithy is at the bottom of your deck.
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TheExpressicist

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Re: More data mining: Answering Dominion questions with data
« Reply #59 on: February 01, 2015, 08:23:31 pm »
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Do those stats take into account that the number of cards you draw depends on how you open? So Silver-Silver is drawn less than Silver-smithy because your smithy might help draw your silver?

It simply looks for if you played one or both of the cards you opened with on or before T4. So, for example if you open Smithy-Silver, you're guaranteed to play both.

If you open double terminal and they collide, that's not the same luck of the draw as having one miss the shuffle. And another factor is that you might choose not to play a drawing action you opened with so that it doesn't trigger a bad shuffle.

Side note, you aren't guaranteed to see both Silver and Smithy if smithy is at the bottom of your deck.

Yup, good catch. I edited my post re: silver/smithy.

Re: double terminals, it's not the same luck of the draw, but, regardless there's a luck component. You've got about a 33% chance of two non-drawing terminals colliding. (55% if you have a 2-draw, and 66% if you have a 3-draw). The player who doesn't collide those terminals is going to have an advantage over the player who does, which is what I was trying to quantify.
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TheExpressicist

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Re: More data mining: Answering Dominion questions with data
« Reply #60 on: February 01, 2015, 08:31:06 pm »
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Along the same lines of how much luck plays an impact, I also analyzed Top-20 players' "adjusted win rate" compared to when they played their first $5 card.

T3/T4/T5: +4%
T6/T7: +0%
T8/T9 +0%
T10+: -3%

Of course, this is across the board and doesn't target specific high-value $5 cards like Witch or Mountebank.
 
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liopoil

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Re: More data mining: Answering Dominion questions with data
« Reply #61 on: February 01, 2015, 09:47:35 pm »
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You know, I'm not really sure which is better on average, 5/2 or 4/3. What you just posted suggests 5/2, and I guess that's about right. Can you just look at which opening split is better?
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TheExpressicist

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Re: More data mining: Answering Dominion questions with data
« Reply #62 on: February 02, 2015, 07:05:05 am »
+4

You know, I'm not really sure which is better on average, 5/2 or 4/3. What you just posted suggests 5/2, and I guess that's about right. Can you just look at which opening split is better?

Adjusted Win Rate of 5/2 vs. 4/3:
5/2: + 3.5%
4/3:  - 1%
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Merudo

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Re: More data mining: Answering Dominion questions with data
« Reply #63 on: February 07, 2015, 12:35:03 am »
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Update:
There have been a few requests for additional data and I've done some more research that I wanted to share but I don't want to create yet another thread. I'll update this first post with additional data as I collect it.

It would be wonderful if you could post the win rates of 1st vs 2nd player. I'm especially curious about the importance of player order in games with expert players, as well as games with powerful cards (militia, sea hag, cutpurse) that are even better for player 1.

It may be selective retention, but I feel that against players of comparable skills, most of my wins occur when I have 1 extra turn, while most of my loses happen when I had one less turn.
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JW

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Re: More data mining: Answering Dominion questions with data
« Reply #64 on: February 07, 2015, 02:03:07 am »
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In his data set as a whole, which I believe was games involving top 100 players, P1 won 57-43.
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