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Author Topic: Patterns in Game Length  (Read 2141 times)

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samath

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Patterns in Game Length
« on: September 03, 2018, 11:00:46 pm »
+12

I've been recording myself while playing online Dominion for the last couple of months. I've played 462 ladder games so far in that time against 96 different opponents, not counting League matches, other tournaments, or games where I accidentally didn't press "Start Recording." There's enough information there that I thought I'd share some observations.

I'll be focusing in this post on how long the games take. This counts all games, whether one of the players resigns or not. For what it's worth, I'm generally seen as somewhat on the slow side, and I resign later than most of my opponents if I do at all, both tendencies which would likely skew these numbers to the high end.

Average: 18:24
Median: 16:54
Minimum: 2:07 (a turn 4 frustration resign)
20th Percentile: 11:07
40th Percentile: 14:56
60th Percentile: 18:49
80th Percentile: 24:54
Maximum: 53:23 (this game against Dingan)

So if I were describing how long a game takes to a friend, I'd say "15-20 minutes." If they really needed to know how long the game would last, I might give a wider range, like 10-25 minutes. Only about 10% of games lasted longer than 30 minutes, although those games tend to be the more interesting ones.

We can actually quantify that. I give a completely subjective 1-5 score to every game in terms of interestingness. It's not the most discriminating metric; almost half of all games get a 3. I only give 5 games each week a 5, and those get featured in my Interesting Games of the Week series. As expected, they're a bit longer on average:
InterestingnessCountAverage Length
12812:57
29815:47
321418:44
48320:51
53821:56

Finally, you might be wondering which cards contribute to a game being longer or shorter. I have that data too, although the sample size for each card is much smaller. That said, you might be able to guess some of the top 5 in either direction:

CardGamesMedian Length
Inheritance810:01
Windfall1410:13
King's Court1310:15
Embassy1710:20
Navigator1311:12
.........
Overlord1024:06
Library1524:08
Venture1324:22
Ghost Ship2024:33
Black Market1726:48
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crj

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Re: Patterns in Game Length
« Reply #1 on: September 04, 2018, 09:30:17 am »
+2

The table of contributions of individual "cards" surprises me in several respects. My intuition would have been that:
  • Epic trashers like Chapel and Donate would cause the shortest games
  • For expensive stuff like Inheritance and King's Court, the acceleration they give would be offset by greater game complexity and people deferring their first Province purchase to afford them. Plus, Colony games will be longer, and King's Court correlates with Colony.
  • Ghost Ship is no surprise to me at the long end, but I'd have expected the entire leaderboard to consist of slog-provoking attacks.
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Awaclus

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Re: Patterns in Game Length
« Reply #2 on: September 04, 2018, 09:57:58 am »
+3

The table of contributions of individual "cards" surprises me in several respects. My intuition would have been that:
  • Epic trashers like Chapel and Donate would cause the shortest games
  • For expensive stuff like Inheritance and King's Court, the acceleration they give would be offset by greater game complexity and people deferring their first Province purchase to afford them. Plus, Colony games will be longer, and King's Court correlates with Colony.
  • Ghost Ship is no surprise to me at the long end, but I'd have expected the entire leaderboard to consist of slog-provoking attacks.

It is worth noting that the sample size for the individual card data is very low. If you can explain what on earth are Navigator and Venture doing near the extreme ends of the list, then maybe I'll be inclined to take that data a bit more seriously, but otherwise I wouldn't put too much weight on it.
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JW

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Re: Patterns in Game Length
« Reply #3 on: September 04, 2018, 01:01:11 pm »
+2

  • For expensive stuff like Inheritance and King's Court, the acceleration they give would be offset by greater game complexity and people deferring their first Province purchase to afford them. Plus, Colony games will be longer, and King's Court correlates with Colony.

Inheritance and King's Court seem particularly likely to lead to run-away games when one person resigns early.
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samath

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Re: Patterns in Game Length
« Reply #4 on: September 04, 2018, 03:33:33 pm »
+1

I think JW is right about the reason Inheritance and King's Court are short -- they provide the most runaway acceleration leading to quick resigns.

Remember that short games turn-wise are not always short time-wise. Donate games in particular can lead to a TON of thinking at the beginning of the game, particularly because the near elimination of the role of chance gives you more opportunity to think turns ahead like in chess. Conversely, slogs are often pretty fast to play since there isn't a lot to think about on your turn.

I don't think this is nearly all signal-less; Black Market is exactly where I'd expect it to be. But yeah, looking further down the list leads to rarely-bought cards like Navigator and Venture that seem to be mostly the noise of the rest of the kingdoms they happened to be part of.
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Awaclus

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Re: Patterns in Game Length
« Reply #5 on: September 04, 2018, 03:49:17 pm »
+14

I don't think this is nearly all signal-less; Black Market is exactly where I'd expect it to be. But yeah, looking further down the list leads to rarely-bought cards like Navigator and Venture that seem to be mostly the noise of the rest of the kingdoms they happened to be part of.

Well, I agree that I'd expect Black Market to be near the top most time-consuming cards, but we can't just look at the list and conclude that the parts that we already expected to see are signal and the unexpected parts are noise, and then use that as evidence to reaffirm our expectations.
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faust

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Re: Patterns in Game Length
« Reply #6 on: September 04, 2018, 04:17:20 pm »
+1

I don't think this is nearly all signal-less; Black Market is exactly where I'd expect it to be. But yeah, looking further down the list leads to rarely-bought cards like Navigator and Venture that seem to be mostly the noise of the rest of the kingdoms they happened to be part of.

Well, I agree that I'd expect Black Market to be near the top most time-consuming cards, but we can't just look at the list and conclude that the parts that we already expected to see are signal and the unexpected parts are noise, and then use that as evidence to reaffirm our expectations.
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samath

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Re: Patterns in Game Length
« Reply #7 on: September 05, 2018, 12:45:54 am »
+6

I don't think this is nearly all signal-less; Black Market is exactly where I'd expect it to be. But yeah, looking further down the list leads to rarely-bought cards like Navigator and Venture that seem to be mostly the noise of the rest of the kingdoms they happened to be part of.

Well, I agree that I'd expect Black Market to be near the top most time-consuming cards, but we can't just look at the list and conclude that the parts that we already expected to see are signal and the unexpected parts are noise, and then use that as evidence to reaffirm our expectations.

Short: I dug into those Venture games and discovered one reason that Venture does make games longer: it's from Prosperity, so Venture games are more likely to be Colony games! However, that's a fairly small effect, but it did happen to be noticeable in a couple of the games I played.

Long: So let's dig into those games to see if those cards mattered! For instance, let's look at Venture, which I don't expect contributes to the signal. We'll focus on the games with Venture in them that were longer than the median to see if it had an effect.

#17259294 vs Philip (37:09) - a Hamlet-Watchtower engine on a Pooka board that piled Curses, Hamlets, and Farmer's Market's. One Venture gained and subsequently trashed to Salvager.
#17395519 vs Jangus (36:34) - a Herald-Jester-Courtier engine with Forge trashing. One Venture gained by Jangus, I have no idea why.
#15876496 vs f_____t_ (35:43) - the most notable thing about this game is that 5 Ghosts were gained, 2 by me and 3 by f_____t_. No Ventures gained, though, even though they can be trashed to get a Ghost.
#17812665 vs Obi Wan Bonogi (30:29) - a Colony game where Crossroads, Magpie, and Necromancer piled with 2 colonies left. No Ventures gained. Rabble also on the board so unclear if Venture caused it to be a Colony game.
#16172946 vs yudai214 (29:59) - another Colony game (with Venture as the only Prosperity card). One Venture gained by me, no idea why.
#17255797 vs Philip (29:51) - a Page game with Necromancer/Secret Passage for trashing and Dominate to build to. One Venture gained by Philip, no idea why.
#17145573 vs nasmith99 (24:22) - Ambassador war fought closely, Menagerie, Wolf Den, Grand Market. No Ventures gained.

So at most 1 Venture was gained in each of those games. That said, one or two were Colony games because of Venture, which will happen about 10% of the time Venture is on the board. And indeed, Colony games tend to be about 3-4 minutes longer on average:

TypeCountAverage Length
Normal39618:24
Colony3121:51
Shelters4017:28
Colony/Shelters414:36

So my conclusion is that there's a tiny signal just from Venture being in Prosperity, but its position is mostly noise.
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ipofanes

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Re: Patterns in Game Length
« Reply #8 on: September 05, 2018, 04:16:32 am »
+2

... but we can't just look at the list and conclude that the parts that we already expected to see are signal and the unexpected parts are noise, and then use that as evidence to reaffirm our expectations.

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