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Messages - Toskk

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1
Dominion General Discussion / Re: Homage to the Best Card
« on: January 16, 2014, 01:09:10 pm »
Excellent, I believe this thread is back on track.  ;D Also, yes, I did heavily debate using 'fewer' vs. 'less' before ultimately deciding on the more lol-cat-worthy 'less'. ;)

2
Dominion General Discussion / Re: Homage to the Best Card
« on: January 15, 2014, 01:06:25 pm »

3
Game Reports / Re: My Hand Produces Only $2... For 15 Straight Turns
« on: December 04, 2013, 03:47:32 pm »
I wouldn't think any non-Sea-Hag opener here would have been sufficient to compete with a Sea Hag/Lookout opening, but the 5/2 split forcing you to open Sea Hag/Crossroads is a bummer. :( As DG already mentioned, though, I feel like buying power is really what limited you in the early game. i.e. no Silver. Both Sea Hag and Lookout are notorious for drastically limiting your deck's buying power, and imo really require a heavy investment in your deck economy to compensate for. Edit: with the curse-heavy game, and only the slow trashing of Lookout to clear them out, this isn't going to be a good set for an engine, thus the need for a big economy to out-slog the opponent. :P

Definitely some bad luck on the Sea Hag hits, too, though. :P

4
I think a big part of Innovation's lack of 'take-off' online is the game's lack of overall appeal. For example, look at the Board Game Geeks listing for it: it's ranked #158. Dominion, by contrast, is rated #17. Sure, BGG isn't necessarily the same community that would play online Innovation, but imo it's a good rough sampling of the overall gamer community. Dominion is a lot more accessible of a game than Innovation is.. not to mention prettier. In my opinion, Innovation also suffers from a few balancing issues that can really keep casual players from enjoying it, in particular how poor the game is with more than two players, but that's a topic for another thread. ;)

Just as an aside, the game I'd most like to see made isotropic-style (or more preferably made with the option of AI play)? 7 Wonders. It's ranked #15 on BGG, and imo is very solid (and accessible). It replaced Dominion for the most part in my RL gaming group.

5
Simulation / Re: Simulator able to do small number of turns?
« on: October 29, 2013, 04:46:55 pm »
of course, if you're playing IRL you can just have symmetric opening turns...

*hehe* This is very true. ;) A lot of players don't seem to like this option (maybe because it's more of a house 'rule'), though. Not to mention I don't know of any tournament/competition that uses symmetric opening turns. Artificial kingdom selection, though, is often used for competitive play, so having the option to have a card picker automatically check for really lopsided 5/2 vs. 4/3 split openers makes sense to me.. provided I can come up with some method of adequately (and on average) evaluating the relative 'strength' of each 5/2 and 4/3 opener pair available in the Kingdom. :P

6
Simulation / Re: Simulator able to do small number of turns?
« on: October 29, 2013, 04:36:07 pm »
I don't think you're goign to convince anyone that money density after 4 turns  (or any other $ based metric) is the end-all and be-all way to measure the discrepancy you're after, though I might be a bit more sympathetic to it than SCSN.  The effects of trashers, attacks, and gainers are all ignored by that kind of metric (or at you don't see their full benefits), and that means you're missing a lot.  Money is always useful, but it's not always the priority.

That's not to say that as an approximation, the metric you're suggesting isn't worth investigating. If you got it working, you could look at what kinds of boards it rejects, and ask whether it's filtering out the right things.

Hi Flies,

Oh I agree.. overall I was much happier with using the councilroom.com best and worst buys database, and I really wish a new version of it could be built around Goko's logs. :P Even that, though, had definite problems at times, based on the exact Kingdom composition (in particular with combo cards that are bought right after the openers). An effective-treasure-value assessment after 4 turns (or 8, or 10, or any number of turns) seems like a pretty crude method of checking for overly-strong 5/2 or 4/3 openers, but I'm at a loss for coming up with a better one currently. :P Also important is the question of just how 'close' does the 'best' 5/2 vs. 4/3 opening need to be, for players not to feel like the match came down to just opening split luck. For example, if Witch/Chapel (or god forbid something like Mint/Fool's Gold) is available as an opener, what 4/3 opening is 'good enough' to still have a competitive/non-luck-based match? That's somewhat subjective, certainly, and based on the opinions of the players involved.

7
Simulation / Re: Simulator able to do small number of turns?
« on: October 29, 2013, 12:17:48 pm »
Treating card draw as effective treasure amounts is an acceptable approach only when you consider Big Money strategies, that is, when you ignore almost everything Dominion is really about.

An example game where I trash down to only 6 cards after T8, at which point my only buying power comes from a Market and a Count. I proceed to gain a whole bunch of stuff (including Duchies for VP) by developing Fortresses, and the only real "buying power" I eventually amass is but an unfortunate side-effect of playing a Pillage each turn, for Spoils are not much better than Curses in a Double-Tactician engine. If you'd do a buying-power/turn analysis, my strategy would be judged as really awful, yet it worked out pretty good ;)

Another example, here I go for some early buying power because I want the Forge, but then I trash down to only $4 buying power halfway T12, after which I bring it back up to $8. I could actually build it quite a bit further, say, to $16. A "buying power" analysis would conclude that this is better, but it's not: due to the lack of +buy, 16 is as good as 8. Furthermore, such an analysis would also say that a strategy that does not use 2 Forges to trash Fortresses into Provinces but does get to 8 a little faster is better, yet it clearly isn't.

Hi SheCan'tSayNo,

I think I haven't been clear-enough as to the intent of the analysis. I'm not looking to play an entire match using an effective-treasure-value method. I'm interested in developing another method (my previous one used the councilroom.com best and worst buys data) for determining (and minimizing) the potential discrepancy between the 'best' 5/2 opener and the 'best' 4/3 opener on the outcome of a match (i.e. artificial kingdom selection). Basically, a checkbox option for the card picker program (found here, in case you're interested: http://inprogressgaming.com/dominion-card-picker/) that would attempt to compare the best-available 5/2 opening with the best-available 4/3 opening, and throw out the kingdom set if the strength discrepancy (e.g. the likelihood of the 4/3 player to immediately capitulate on seeing their opponent open with the 5/2) was outside of a specific range. As something like the councilroom.com best and worst buys data isn't available anymore, I've been looking for another method of approximating this same kind of data, and I'm currently looking into the possibility of evaluating the starting/early-game deck using effective-treasure-value methods to do this.

Looking at your two example games there, yes, both of them involved 'upgrade'-focused strategies (the first one being a Fortress -> Duchy Develop 3-pile game, and the second being a Fortress -> Province Forge game), which would certainly cause an effective-treasure-value analysis some problems mid-to-late-game.. but if you look at only your opening buys, in both cases you follow the effective-treasure-value method to the letter:

In your first match you open Count/-, with a higher effective-treasure-value (potential) than any other 5/2 opening available (thanks to the +3 coins available on Count). In your second match you open Conspirator/Silver, once again, when taking into consideration the (eventual) opportunity to activate Conspirator's draw ability, the highest effective-treasure-value opener available for a 4/3 opening.

But once again, I'm interested in using this method to evaluate the Kingdom selection, rather than the specific plays. In your first match, Wareagle opened Silver/Silver against your Count/-. I certainly wouldn't say that match came down to luck on the opener.. you played a very different strategy than Wareagle did. So an effective-treasure-value method of kingdom selection would need to not rule that opening strength difference as 'too great'. In your second match, you opened Conspirator/Silver against Masterpiece+1/Silver, both of which come out a bit 'stronger' for effective-treasure-value than something like Rabble/-, and somewhat similar to the value of Cache/-. Neither of you got the 5/2 opening, but again I wouldn't think that an effective-treasure-value comparison of those 5/2 options to the 4/3 options would have suggested that one or the other was out-of-line strong or weak.

8
Simulation / Re: Simulator able to do small number of turns?
« on: October 28, 2013, 11:37:09 pm »
Ultimately, I'm interested in (once again) building a method of determining opener 'strength' into my card picker program, to provide an option for minimizing the impact of the 4/3 vs. 5/2 split on the game 'decisions'. I'm not entirely sure if attacks and heavy trashing can be adequately evaluated in terms of opening strength, however. :P

Early buying power negatively correlates with a strategy's long-term strength when you consider reasonable strategies only (e.g. not things like opening double Curse).

Umm.. can you provide examples of this? Treating card draw as effective treasure amounts, I don't really see how that is possible (barring deck-junking attack strategies). Smithy/Silver, for example, is mathematically superior to Silver/Silver specifically because the effective treasure value of the +3 cards is greater than that of the Silver (for the vast majority of the game).

Yes, strategies that involve degrading the value of the opponent's deck may negatively correlate with the deck's (early) buying power.. that's one of the reasons I'm interested in using a simulator for this analysis. For example, as mentioned above, if I compare the buying power of Chapel/Witch vs. Big Money, Chapel/Witch doesn't pull ahead until around turn 8-10.. so I'd need to evaluate the relative value of these two at about the turn 8-10 range in order for this method of analyzing the relative strength of 5/2 vs 4/3 openings to work.

Edit: I take it back slightly.. strategies involving VP chip accumulation, or some mega-turn strategies, can't be evaluated using an effective-buying-power method.

9
Simulation / Re: Simulator able to do small number of turns?
« on: October 28, 2013, 05:34:00 pm »
Money graph isalso in dominiate...

Yeah, I looked at Dominiate.. but I wasn't able to figure out how to get it to output an exact value for the average coin amount available at turn x? i.e. labels for the graphed values. Also, it looks like, for the purposes of evaluating the opening strength of various attacks and heavy trashers, I'd need to evaluate the strength of the deck a whole lot later than turn 4. :P Chapel/Witch, for example, doesn't visibly start stomping BM until around turn 10. :P Hmm..

Edit: I forgot to mention the other item that I wasn't able to figure out a way to do in Dominiate.. simulate a (fixed) 5/2 opening for one player vs. a variable (either 4/3 or 5/2) for the other. e.g. How does a Chapel/Witch opening do against both 4/3 and 5/2 BM openings? :P

10
Simulation / Re: Simulator able to do small number of turns?
« on: October 28, 2013, 04:36:21 pm »
@Sparafucile,

Yeah, that's *probably* enough information right there. What sim is that? :) You can choose turn 4 there specifically, it looks like? :)

@MeanderingMercury,

Yes, I've looked through those opening probabilities quite a lot.. and I can do them by hand, if necessary, but I'd really rather not, if a sim can do them for me. ;)

Ultimately, I'm interested in (once again) building a method of determining opener 'strength' into my card picker program, to provide an option for minimizing the impact of the 4/3 vs. 5/2 split on the game 'decisions'. I'm not entirely sure if attacks and heavy trashing can be adequately evaluated in terms of opening strength, however. :P

11
Simulation / Re: Simulator able to do small number of turns?
« on: October 28, 2013, 02:36:41 pm »
I don't think one of them does this by default, if you are willing to set up dominiate i guess it's about 10 lines of code to et it do what you want.  But it's not that easy to set up without expirience, i don't know your background, i could make a branch that does what you want

Hi DStu,

I'm comfortable-enough with coding that I could *probably* hack my way through the necessary changes, but I haven't looked at Dominiate's coding at all before.. so if it would be quick for you to do, that would be awesome (not to mention probably save me a lot of time fumbling around)! ;) Will it be able to output deck percentage breakdowns, though? Dominiate's output (like other simulators) is focused on win/loss ratios, but I actually want to see the deck buying power (averaged is fine) at the fourth-turn state.

12
Simulation / Simulator able to do small number of turns?
« on: October 28, 2013, 01:46:08 pm »
I was hoping someone may know of an existing simulator that can accomplish this.. but I'm wanting to simulate (only) the first four turns of a game, and then determine the percentage distribution of all possible decks.

For example, going Big Money, after four turns what is the percentage breakdown of four silver buys vs. a gold in there? Repeat for various 4/3 and 5/2 openers. I'm really interested in the buying power of the deck after four turns, if that helps (i.e. how many gold and/or silver does the deck contain).

Is there an existing simulator that can handle something like this? :)

13
Dominion General Discussion / Re: Homage to the Best Card
« on: July 03, 2013, 03:44:35 pm »
Yeah, no trasher needed.  NV-Bridge is self-sufficient.

Yep, give NV/Bridge (only) a try, if you haven't ever before. It really doesn't take anything else, and it's a remarkably quick megaturn deck. Turn 12 all-Province piledrives aren't uncommon with it, and even worst-case it'll still be ready to buy 8 VP cards by turn 15-16.

Edit: it is hard to speed up, as well. With Throne Room I've done a turn 11 piledrive once or twice, but you also have a slightly better chance of slowing the deck down, too (e.g. by playing too many TR + NV's, rather than TR + Bridges). Workshop in the mix can net more total VP, but doesn't actually speed up the megaturn at all.

14
Now, where am I going with this? Well, two places. First, this is evidence to me that Goko's rating system sucks.

Yes, Goko's rating system is abysmal when it comes to accuracy. Players are already in general placing low value on the 'meaningfulness' of the ratings by how they round.. i.e. you described the player as rated ~5300, or in short the numbers after the hundreds column don't mean anything. The reality is Goko's implementation is whole lot less accurate than that. I'd estimate the system as adequately 'meaningful' at the level of ~ +/- 1000 or so. So a rating of 5300 could be a player of 4300, or a player of 6300. i.e. it's probably safe to assume that a player of rating 5300 is a statistically-significant-amount better than a player of rating 4300, but that's about as much as can be determined from the ratings. Personally, I'd reduce the Goko rating system to a 100 point scale, for starters. :P

15
Well, it's been a long while since I posted, but I did want to mention that I did just update the Dominion Card Picker program to include Guilds. Image hosting is of course not available yet, but the mouseover tooltips for Guilds cards displays the text of each card. Also included, by request, is the option to deal out up to 16 Kingdom cards (for those who use non-blind veto methods). As always, the card picker program can be found here:

http://inprogressgaming.com/dominion-card-picker/

A more in-depth description of the changes in v1.1.7 can be found here, too:

http://inprogressgaming.com/dominion-card-picker-v1-1-7/

16
Dominion General Discussion / Re: Provincial: Cool looking Dominion AI
« on: February 23, 2013, 10:49:46 pm »
Although a few of the AIs advantages are a bit brutal (wishing well, for example, it can just pick the most likely card left in its deck, which it can always know precisely).

Even brutal would be better than Goko's current AI implementation of Wishing Well, though.. I've watched that AI play Scout.. followed by Wishing Well.. and fail to pick the card on top. :P

17
Quote
Here's a very basic formula I asked the engineer who programed the stats:

rating = μ - (2 * σ)
Where μ is the mean of your estimated skill level and σ is one standard deviation from that mean.

Dominion's initial values for μ and σ are:
μ = 5500
σ = 2250

Quote
That does not mean TrueSkill. I mean, without any method of how you come up with those things, it could be basically anything. Actually 'Elo-like' is more information than this, and more or less satisfying - I wouldn't expect them to give us the exact algorithm, though of course it would be nice.

I agree, knowing they're using an Elo derivative is helpful, although there's still a fair amount of incomplete information even then (for example what method they used to modify Elo for multi-player matches). The item I'm especially interested in, however, is how they dealt with the problem of luck in Dominion matches. For example, the Chess Elo system is partly based around the statistical observation that "White has a 100% expected score with a 390-point (or more) rating advantage, and a 0% expected score with a 460-point (or more) rating disadvantage."

http://www.chessbase.com/newsdetail.asp?newsid=562

i.e. at a 390-point rating advantage, the player will have an effective 100% win rate.. something that is absolutely untrue in Dominion, even with a 10,000-point rating advantage. I really hope their engineer has run a heck of a lot of statistics on matches, to determine a more accurate win/loss ratio-per-rating-point-difference.

18
Dominion General Discussion / Re: Homage to the Best Card
« on: January 23, 2013, 02:02:05 pm »
When I was younger I wanted to be an actor. Then I realized Patrick Stewart had basically already made all future acting irrelevant.

So.. Patrick Stewart's acting is like the Borg? Resistance is futile?

19
Dominion General Discussion / Re: Announcing Dominion Set Generator
« on: January 12, 2013, 12:22:32 am »
Goko definitely implemented something.. although I would agree with a few others here that the algorithm is significantly over-prioritizing certain cards. Using only Base, Intrigue, half of Seaside, and Governor, I got 6 games in a row today with Governor, Laboratory, Throne Room, Mine, Workshop, and Duke. They all had either Village or Fishing Village, as well. :(

20
Dominion General Discussion / Re: Announcing Dominion Set Generator
« on: January 08, 2013, 04:00:09 pm »
Using the uh "fun set of 10" generator with default settings seems like fair game for rating. Engines will be more common I guess? But like, let's say Joe uses the generator because he wants engines that he's good at, and Sam says all-Prosperity for me (in this new world of that not forcing Colony), and Fred says who cares, shut up and deal. I don't feel like now the pro board is a joke (unless the rating system sucks as some people think, but that's a separate issue). You have to be pretty good to crush people consistently in whichever of these formats.

Yes, essentially all of the artificial selection methods I've seen/used tend to at the very least slightly prioritize 'engine' games, or at least the presence of a +2 action card in the set (even if there isn't any great use for it with the specific other cards). Many of them also tend to prioritize a +buy or gain x card. I agree that these two options alone aren't likely to give any specific player much of an artificial advantage.. certainly less than being able to select specific expansions would, anyway.

If Onigame is correct, and Goko is going to implement artificial selection options, I'd strongly recommend that they allow them for all rated game types, along with combining all matches generated in this manner into a single rating system (i.e. combine 'pro' games with 'casual' games when their kingdom selection method is the same as that used for 'pro' games).

As for the Pro board.. currently it is indeed a 'joke', simply due to the ability of players to disconnect instead of being counted as a loss. With that fixed (and of course all ratings reset), the second piece comes down to just how meaningful the rating system itself is.. which I've been arguing is a problem for quite some time now. The problem, as I keep trying to explain, is the range/accuracy measurement that accompanies the actual rating number. In short, as total number of matches increases, the overall range/accuracy of player ratings is not decreasing adequately, at least not enough to mask the fact that some percentage of games are going to come down to luck rather than skill (i.e. the win/loss had no meaning, regardless of player rating). For example, my current rating is approximately 7200 on Goko, with roughly 900 matches played, all against bots using true-random kingdom selection. A win vs. a bot will give me anywhere from 7-20 points, and a loss will cost me 195-210 points. This means that over the span of 30 matches, my rating could be ~6500 or it could be ~7500. ~95% of the time it'll stay within a range of 6800-7400. So a 600-point rating interval could well have no meaning whatsoever when it comes to determining win/loss probability vs other players, yet the number of points awarded/lost for each player will vary a considerable amount based on that 600-point swing, when it should vary essentially none (once a sufficient number of matches have been played).

21
Dominion General Discussion / Re: Announcing Dominion Set Generator
« on: January 07, 2013, 04:14:43 pm »
The Goko card picker, as is, will throw up Monument super often, almost always has about three Attacks in it, and almost never has Pirate Ship.

Why would the Goko kingdom picker bias anything? It's specifically billed as 'true random' kingdom selection, so it would have to be a failure of their random number generator, if there's any kind of bias there. I'm a firm believer in artificial kingdom selection (thus all of the artificial selection options in my card picker program on inprogressgaming.com), but in my opinion it is critical that *all* players understand (and agree on) the selection criteria that will be used for any (rated) match. Goko should/would need to be very open about how they are selecting kingdoms *if* they were to be intentionally using anything other than true random.

22
Goko Dominion Online / Re: Match Making
« on: December 28, 2012, 03:07:03 pm »
the 0-10000 point rating scale is too large (no other game or sport uses a rating system of anything remotely like that interval).

OK, so I agree with your other points, but what does the scale matter? I mean, would it be a better rating system if it only displayed the first three digits of that number making it a "0-100" rating scale instead? I bet internally it's always a floating-point number anyway, it's not like isotropic is storing them as integers!

For the scale itself, that is partly related to the (apparently) very large K-factor Goko is using.. For example, I am currently rated at roughly 6700, playing exclusively true-random matches against bots. I have a ~87% win rate against bots, with nearly 900 matches played, and typically gain 25-35 points on a win, and lose 195-210 points on a loss. This means that, depending on the results of the most-recent 20-30 matches I play, my 'current' rating could be anywhere from ~6100 to ~7200.. i.e. a very small difference in win/loss percentage overall has to make a big difference in overall rating average because of the 0-10000 point scale. I suspect the developers chose this scale because they wanted players to always gain some points with any win (they had problems with the coding of this in the past).. again belying the issue that the developers appear to want a progression system rather than a rating system, the result being that they (instead) created a highly-inaccurate rating system.

With an observed range of 6100-7200, yes, I'd definitely advocate for compressing the ratings into smaller groupings. i.e. if the difference between a 6100 rating and a 7200 rating is not meaningful, why not call that 6-7 instead (reduce ratings by 1000x)? The potential problem there, of course, is that players would often see no rating change at all with wins and/or losses.. which is the ideal of a rating system (with enough matches played, eventually a players' rating *should* stabilize). Some players don't like this, however (they want a progression system rather than a rating system).

More and more, I'm suspecting that the rating values are not internally floating-point numbers.. or that the actual player rating even *is* some internal-only value, like it is in TrueSkill. From what little we've heard, there is some kind of hidden 'accuracy' value for each player, based on the number of matches played, but the rating value itself may be the only other stored value. By comparison, TrueSkill uses two internal values (for rating and accuracy) and one external value (level), allowing it to fairly effectively blend a rating system with a progression system. As level is a function of rating - some amount of the 'accuracy' value, a players' level can continue to increase (up to the point of maximal 'accuracy') as their number of matches played increases, even if their rating does not.

23
Goko Dominion Online / Re: Match Making
« on: December 27, 2012, 11:22:38 pm »
I've been complaining about the ratings aspect of a match-making feature for some time now, however sadly without much in the way of a response. :P We know that an auto-match feature is in the works (hopefully at least reasonably similar to the one used on Isotropic), however hand in hand with an auto-match feature to pair players with 'similar' ratings up is ensuring that said 'similar' ratings actually mean something.. something which I have been concerned about for some time. Basically, the rating system Goko implemented is very bad. First, it does not appear to increase in accuracy of ratings (in any reasonable fashion) as number of matches increases (if anything, the system gets less and less accurate as number of matches increases). Second, the K-factor (or whatever mechanism they use to calculate points won/lost) they chose is *much* too high.. ratings fluctuate wildly (part of the inaccuracy of #1), which may be partly related to; third, the 0-10000 point rating scale is too large (no other game or sport uses a rating system of anything remotely like that interval). Fourth, the developers seem to be treating the rating system like a point accumulation system rather than a rating system. As an example, when the rating system recently broke (it temporarily reverted players to zero rating after any match), the developers awarded all affected players a 'free' 300-rating-point bonus, over-inflating ratings and adding more total points into the overall point 'pool', further decreasing the accuracy of the system.

I've previously suggested that the developers look more carefully at rating systems like TrueSkill and Elo (particularly how Elo was applied to games of combined luck and skill like Backgammon), or if their intention is to have their rating system be a progression-like point accumulation system (i.e. a system of levels, where players always feel like they can make upward progress) that they should do that instead, but so far we haven't heard any response other than 'auto-matching will fix our rating system problems'.

As a note, in case anyone is going to suggest Goko just use TrueSkill, it may be relevant to note that TrueSkill is not free for commercial developers (it is a proprietary system owned by Microsoft), which is probably the reason they didn't use it. :P

24
Dominion General Discussion / Re: House rule for reducing luck factors?
« on: November 26, 2012, 07:13:40 pm »
The kind of 'luck' Garfield is talking about isn't really what people here are talking about, though. I think a better continuum line would be 'control'.. i.e. how much control does the player have over the outcome of game events by the 'decisions' they make? You have everything from activities with zero control (e.g. Chutes and Ladders), to activities with complete control (e.g. Chess). Basically, what's the correlation factor between making the 'correct' decisions throughout the game and winning the game. In chutes and ladders, players make zero decisions. In Chess, making the 'correct' decisions is 100% correlated with winning the game.

25
Dominion General Discussion / Re: House rule for reducing luck factors?
« on: November 26, 2012, 06:21:22 pm »
Personally, I try to split the luck-based factors into 'kingdom selection factors' and then 'game design factors'. Ultimately, Dominion has a fair amount of luck/randomness to it, and addressing all of those factors would totally remake the game (it wouldn't be Dominion anymore, and it wouldn't be a deck-building game with discrete hands, either). That aside, I feel like there are a few definite ways to minimize the effect of luck/randomness on how the game plays out by artificially selecting kingdoms. The first and biggest one, in my opinion, is the 5/2 vs 4/3 split opening strength difference in some kingdoms. For example a Witch/Chapel opening vs. a Silver/Chapel opening.. that's very likely going to go to the player opening 5/2, *especially* if they're in first seat anyway. I've tried a variety of methods for minimizing this with kingdom selection, but the one I ultimately implemented was to grab the councilroom.com best-and-worst opening buys database (while it was available), and to use it to determine the relative strength of each possible opening. The system implemented in my card picker program takes that data and will reject any kingdom where the strength difference between the best 5/2 opening and the best 4/3 opening is outside of 1.5 levels. Yes, it does rely on a whole lot of averages (i.e. councilroom.com data), and doesn't work at all for Dark Ages (no data). But it seemed to work reasonably well for rejecting the really really broken kingdom sets out there where the 5/2 opening absolutely dominates the game.

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