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[fp]

Dominion has been growing recently- and with that questions regarding competitive Dominon has started to come forth. Does it exist? How does it work? And so on. Another question is: How does one make it fair and fun?

That is a tricky question. Dominion certainly does have its unfun moments and unfun moments- and many times that are induced by unlucky occurrences: not going first, bad shuffles, or most especially poor openings.

Now we are going to compare the situation to Bridge. In Bridge, there are deals where one pair is clearly favored to gain points on the hand just based upon where the cards lie. In order to mitigate that luck factor, Bridge tournaments typically feature a “Duplicate Bridge” format where the exact same deal is played by a large proportion of pairs. The each pair scores points NOT based upon whether they win or lose on the hand, but how they perform relative to the other pairs.

A similar concept could be implemented with Isotropic (or similar electronic scheme) in Dominion.

Simply put, the idea is simple: Given a large number of players playing the same board, all of the players in first position (or second) will have the exact same shuffles.

The technical details are as follows:
At the start of the game, the game generates 80 (or however many) random permutations of the numbers 1 through 100 for each position (e.g. the first player and the second player) which is kept secret. For the i-th shuffle, the i-th permutation (restricted to the appropriate numbers) is used to determine the order for that shuffle. Where the numbers corresponds to cards in the order in which they were added to the deck.

Example 1:
This scheme guarantees that all of the players playing first have the same opening hands and that the players playing second have the same opening splits.

Example 2:
If the first permutation (restricted to 1 through 12) for the first player is (6,3,9,10,12,1,4,2,7,5,8,11), then the after the first shuffle, the two cards (the 11th and 12th cards) bought before the first shuffle will be placed in the 12th and 5th position. If the player playing first neglects to buy a card during his first two turns, the single card bought will be placed in in the 11th position (as the 12 in the permutation is ignored). The key point here is that in order to promote fair and fun games, ALL of the players playing first for this game will have a “dead” buy.

There are, of course, other finer details to hammer out, but before I present them in a boring detailed manner, I was wondering if this idea interests people at all. Keep in mind that players need not be aware of any of the details.

[ARTjoMS]

Interesting, but unlike in bridge in dominion you can only win or lose (or tie). I suspect that many times (if this gets to a really high levels) it will be like one position player wins in all games (+0;+10;+99), and everyone gets 50% and you don't really learn anything. If it mattered by how much points we win or lose then i think this would raise this game to a whole different competitive level.

This would require huge concentration throughout the whole game in high levels and way more important decisions to make.

[fp]

That is a good point.

One potential solution to that is that players play 3-5 boards (e.g. games) in one round. That way, instead of Win, Lose, and Tie, there is closer to a continuum of outcomes: (for 5 games: 0-5, 1-4, 2-3, 3-2, 4-1, 5-0).

[WanderingWinder]

There are a number of reasons I don't think this would work very well, and the reason it's so different from bridge is that there are unlimited reshuffles of the deck. You can play thousand turn games - there are some possibilities with monument or bishop, possession, and a kc-masq type lock where the locking player is behind. These are inherent problems with dominion actually, but in real life any sane arbiter is going to declare a draw. Or maybe in some of these cases, somebody's actually going to win, but it might take a thousand turns.
Also, I don't really see how this helps actually. Guaranteeing player 1 and player 2 the same draw across all boards is great in terms of fixing the board-to-board luck skill, but what about the inequity between players 1 and 2? You can't really have them play the same game over, because now they KNOW what they're going to draw. So apart from it being a huge practical nightmare, I don't think it has much positive point.
Luck is simply part of the game, and you can't get rid of that - even in the bridge example, there are chances for the game theory to add some randomness. Bluffing is actually pretty big in high-level trick-taking-games, and while I haven't played a lot of bridge, from what I do know, I don't think it should be any different there.

[DG]

I think it's still going to have problems. The card sequence effectively becomes random between players as soon as they use different action cards on turn 3. Consider a mint, market, trading post, wharf, treasury, outpost, tactician, harvest, hunting party, lab, venture, royal seal, ghost ship, rabble, ....

[cherdano]

Player A opens Ambassador/Silver, and player B opens Silver/Ambassador...

[theory]

One way around it (and which would change Dominion dramatically, probably for the worse) is to let players manually control their shuffles. 

[WanderingWinder]

One way around it (and which would change Dominion dramatically, probably for the worse) is to let players manually control their shuffles. 

That's not even dominion any more, but an entirely different game, where, assuming you can look at how your opponent stacks his deck, the later player you are, the bigger advantage you probably have.

[fp]

There are a number of reasons I don't think this would work very well, and the reason it's so different from bridge is that there are unlimited reshuffles of the deck. You can play thousand turn games - there are some possibilities with monument or bishop, possession, and a kc-masq type lock where the locking player is behind. These are inherent problems with dominion actually, but in real life any sane arbiter is going to declare a draw. Or maybe in some of these cases, somebody's actually going to win, but it might take a thousand turns.

While off-topic: Do you actually have an example where a game, optimally played would take thousands of turns?

Regarding the topic, it would practical, say after the 50th shuffle, to just make the shuffles random. Even though this might not duplicate the matter precisely, since most games do not go beyond 50 shuffles, this would not affect the duplication issue much at all. And if a game truly does take a thousand turns, there would other bigger issues (i.e. physical time) that would be more substantial.

Also, I don't really see how this helps actually. Guaranteeing player 1 and player 2 the same draw across all boards is great in terms of fixing the board-to-board luck skill, but what about the inequity between players 1 and 2? You can't really have them play the same game over, because now they KNOW what they're going to draw. So apart from it being a huge practical nightmare, I don't think it has much positive point.

That is a good question. In order to have an effective ranking, you have to have ways of effectively comparing players to another. The key here, while counterintuitive, is that the games do not rank player A against player B well, but rather help rank all of the player A's against each other (as with all of the player B's).

I think it's still going to have problems. The card sequence effectively becomes random between players as soon as they use different action cards on turn 3. Consider a mint, market, trading post, wharf, treasury, outpost, tactician, harvest, hunting party, lab, venture, royal seal, ghost ship, rabble, ....

Even if this were the case, I do not understand how this is a problem. The most important consequence of having duplicated shuffles is that the first few shuffles are the same. Thereafter, it is not as big of a consequence. What if only the first 3 shuffles were duplicated?

[DG]

Even if this were the case, I do not understand how this is a problem.

The hands can become completely different immediately. There is no point having an ordering if it becomes indistinguishable from random draws after the second shuffle since players have used different action cards. Just shuffle some cards and compare a herbalist/royal seal opening to a courtyard/trading post opening. Then try lighthouse/tactician.

[fp]

Even if this were the case, I do not understand how this is a problem.

The hands can become completely different immediately. There is no point having an ordering if it becomes indistinguishable from random draws after the second shuffle since players have used different action cards. Just shuffle some cards and compare a herbalist/royal seal opening to a courtyard/trading post opening. Then try lighthouse/tactician.

The intention of the duplicateness is that the same choices yield the same results. The fact that different choices yield vastly different scenarios is expected. In any case, I do not see how having a fixed shuffle pattern is any worse than random ones in the rare event players do make vastly different choices. Specifically, while as you point out an ordering would not be relevant if the choices made are vastly different, it is important if the choices are very similar.

[Superdad]

I also think that in a large tournament, having to re-order hundreds of different decks, possibly several times per turn, is a logical nightmare.

Each round would take hours.

[Deadlock39]

I also think that in a large tournament, having to re-order hundreds of different decks, possibly several times per turn, is a logical nightmare.

Each round would take hours.

This would certainly be implemented on isotropic or a similar system, and not done manually.  I am pretty sure the OP indicated this.

To second the comments that fp already made, it does not matter that different openings produce different results.  In this type of system (unless I am missing something) all the match-ups would be playing the same board for a game (or multiple games), and lots of players will be taking the same opening, (and potentially even playing identically for many more turns).  If you have 100 games being played and everyone who gets 5/2 opens Mountebank/Chapel, it isn't a fair comparison between all the players if some of them get Chapel/C/E/E/E and Mountebank/C/C/C/C turns 3 and 4, and some of them have Chapel, Mountebank and their turn 3 and 4 buys all collide on turn 5.  If this particular nightmare scenario was part of the predetermined random sequence for that game, then every single player in that position would experience the same "bad luck", and can still be ranked against each other according to how they handled it.

[rrenaud]

Imagine there are two strategies that are equally good in the long run, but which change the deck order dramatically.

Maybe silver/smithy vs silver/moneylender is a decent example.  The merits of smithy vs moneylender are unimportant, just assume that the strengths of two openings are about on par, but they follow very different deck paths.

If the estates are in position 9 and 10 and the moneylender/smithy is in position 5, then if you opened smithy, you will draw with your first turn, and then the estates at position 9 and 10 are going to be stuck in the shuffle and only seen once in the first two shuffles, but the moneylender player will see them twice.

It's not that smithy is a better choice in the long run over many cases, but for this particular deck order, it was a much better choice. 

Certainly duplicate dominion buys you something in the case where everyone continues to do the same thing, but once players branch (even if the choices are very close to each in 'overall winning space'), they can be very different for a particular controlled deck order.

[Thisisnotasmile]

In addition to the above, what happens if I open Moneylender/Silver and so does the other guy. Then we both draw Moneylender with 4 coppers turn 3. We both trash a copper and buy a Gold. So far, we're exactly equal, right? Well no, I trashed the copper that was assigned the number "1" during randomisation and the other guy trashed copper "4". We've both done exactly the same thing, yet suddenly our decks will no longer shuffle in the same way.

[Superdad]

I'm not sure if this is what deadlock was trying to say, but pre-determining the cards can actually literally lose someone a game.

For example, lets say we have a chapel/Militia board and the shuffler decides that turn 3 will be: MCCCC and turn 4 will be ChCEEE.

Whoever goes first in that board is basically getting screwed by luck.

Turn 3 player A:
Militia, CCCC, buy gold. Draws ChCEEE

Turn 3 player B:
Miltia, CC, buy a $4. Draws his ChEEE

Turn 4, player A's chapel got messed up by pre-determined militia.
Turn 4 Player B gets a full 3-estate + 1 copper chapeling.

While this will happen with complete randomness, pre-determined randomness leaves a much more bitter taste in the mouth (my opinion).

[Deadlock39]

I guess I wouldn't be bothered at all by pre-determined randomness.  Random is random and sometimes it will screw you.  In a tournament setting, I would feel better about being screwed by randomness if I knew that every other player that was in position 2 got screwed by the Militia too (assuming Player 1 opened with it).  Also, The randomness would the same for each pairing, but not for both players in the same match.   

From your example, everyone in first position that opened Chapel/Militia would get Militia, CCCC, and then ChCEEE, but player 2 wouldn't necessarily end up with Militia, CCCC.  It is true that that opening might (nearly) win the game for player 1 on that board (just like opening 5/2 with Mountebank/Chapel might). The important thing is that every person in first position in the tournament was given that same good luck, and when that set of games is looked at, player 1 will have won a disproportionate number of those matches.  For that particular match, player 2 wins, and player 1 losses can be weighted more heavily than the rest. 

rrenaud's point about openings of equal strength being effected differently does have weight, but I have no idea how big of an effect something like that could have on results.  If the psudo-random set used in one of the matches introduced that type of variance between strategies, it might be more significant than if it only happened in one or two games.  I'm not sure how to judge if it is more fair to affect a large set of players with this, or just a few.  My assumption would be that if an otherwise good player got hit with one of these bad luck situations, it would be easier for them to fall back into their correct place in the standings if a significant number of others were hit with the same problem.

In any format, you would need to play enough games to account for the random variance inherent in the game.  My non-mathematically-backed opinion is that the idea from the OP would help reduce variance across the field.

[rinkworks]

The thing about the pre-determined randomness is, as Deadlock says, that every other tournament player in that position gets screwed in the same way.

The thing we're missing about what makes Duplicate Bridge work is that the object becomes not to win the game but to perform better than every other player in your seat.  It's possible to lose every single rubber in a Duplicate Bridge tournament and yet win the tournament -- because you did better than every other player in your seat at the other tables.  That's how the luck of the draw is eliminated from being a factor.  You can have Jack-high hands all night, but if you can hold your opponents to fewer tricks than the other people in your seat at the other tables can, you're doing really well.

The object of Duplicate Dominion would similarly change.  The object wouldn't be to win any individual Dominion game but to get the best VP score difference than the other people playing your seat.

I've thought about Duplicate Dominion before too, and while I don't think it can work for reasons others have already stated here, getting screwed by a bad Militia/Chapel draw isn't one of them.  Everybody in your seat who makes those same opening moves would get screwed in the same way, but some will recover from it better than others.

[fp]

I'm not sure if this is what deadlock was trying to say, but pre-determining the cards can actually literally lose someone a game.

For example, lets say we have a chapel/Militia board and the shuffler decides that turn 3 will be: MCCCC and turn 4 will be ChCEEE.

Whoever goes first in that board is basically getting screwed by luck.

Turn 3 player A:
Militia, CCCC, buy gold. Draws ChCEEE

Turn 3 player B:
Miltia, CC, buy a $4. Draws his ChEEE

Turn 4, player A's chapel got messed up by pre-determined militia.
Turn 4 Player B gets a full 3-estate + 1 copper chapeling.

While this will happen with complete randomness, pre-determined randomness leaves a much more bitter taste in the mouth (my opinion).

I think it are misunderstanding the concept here. The first premise is that you would have dozens of games with the exact same board. A particular predetermined shuffle only affects one player in each game and only once each game. However, the predetermined shuffles in the prescribed order are identical across all of the games for each player in the same position

To correct your example:
Suppose the shuffler determines for player A (the player in first position) will be: turn 3 MCCCC and turn 4 ChCEEE.
and for player B: turn 3  MEECC and turn 4 ChCCCE

Then for player C (playing first) and player D playing the same game in the tournament, player C will end up with MCCCC and ChCEEE just like player A in his or her game. And likewise player D will end up with MEECC and turn 4 ChCCCE

In this regard, the results between A and B as well as C and D can be accurately compared.

I should also point out that your example, in fact, as very little to do with prescribed shuffles rather more to do with the natural fact that Militia benefits the player that goes first.

[fp]

The object of Duplicate Dominion would similarly change.  The object wouldn't be to win any individual Dominion game but to get the best VP score difference than the other people playing your seat.

I feel pretty confident that players will despise the use of VPs as a primary tool for tournament scoring.

I think winning and losing needs to remain key.

In any case, is there anything bad about playing 4 or 5 games per round in order gain larger continuum of results?

[fp]

In addition to the above, what happens if I open Moneylender/Silver and so does the other guy. Then we both draw Moneylender with 4 coppers turn 3. We both trash a copper and buy a Gold. So far, we're exactly equal, right? Well no, I trashed the copper that was assigned the number "1" during randomisation and the other guy trashed copper "4". We've both done exactly the same thing, yet suddenly our decks will no longer shuffle in the same way.

Just to clarify again, your shuffles are not the same as your opponent's. Rather, your shuffles are the same as all the other players in other games in the same position. So it is not necessarily the case that "we both draw Moneylender with 4 coppers turn 3."

In any case, you still make an excellent point- that the same cards could be assigned different positions, and which one is trashed would affect the randomness to a large degree. This is something that would have to be taken care of in the details. But it is not far-fetched to say that if a card is trashed, the one with the lowest position is the one that is trashed.

[Deadlock39]

I agree that VP total or differential can't really be used.  It certainly doesn't make sense in the race for the ultimate Goons engine, and it would punish a player for buying that last curse to win the game on piles with only a 1 VP difference.  I think playing sets of games would cover most bases. 

Oh, and the Moneylender, which Copper thing. Isotropic doesn't let you choose which Copper you trash, and unless there is some incredibly bizarre coding going on, Isotropic (or any other computer implementation of Dominion) is always going to trash the same Copper from both identical hands.  This issue would be handled automatically by the nature of how computer programs work.

[ElVampiro]

The object of Duplicate Dominion would similarly change.  The object wouldn't be to win any individual Dominion game but to get the best VP score difference than the other people playing your seat.

I feel pretty confident that players will despise the use of VPs as a primary tool for tournament scoring.

I think winning and losing needs to remain key.

In any case, is there anything bad about playing 4 or 5 games per round in order gain larger continuum of results?

I disagree ---  I think that this HAS to be way to play duplicate dominion.     If you compare it directly to duplicate bridge, your side may have 0 face cards, however if you keep your opponents from making one less trick than everyone else (thus giving you a -420 instead of a -450) you have the top board!   

I think duplicate dominion would have to be kept as simple as possible:

• On each 'board' everyone plays the exact same set of Kingdom cards
• After everyone has played a board your VP score difference is compared to everyone elses   (positive or negative)
• You are assigned a number of 'Match Points' equal to your relative ranking against everybody else who played that same board.
• Your score for the tournament is the sum of your Match Points, winners are ranked by this total
• Everyone plays everyone else in the tournament so you have a full matrix of results to compare against

IMHO, the whole idea of trying to keep the shuffles randomized in the same order has to be completely thrown out.   The only thing you can keep constant between two sets of people playing Dominion are the set of Kingdom cards in play.

-ElVampiro

[guided]

I'm going to go out on a limb and say there is no way whatsoever to make comparison of VP differentials fair. Not even by forcing the same shuffle order for every shuffle. rrenaud hit the nail on the head: different strategies (even if equally strong) will be affected differently by the shuffle order. There is also the issue that VP differential rewards suboptimal play that goes for big VP differentials (increasing the incentive to build a Goons engine, for example) while punishing optimal play for victory-even-by-the-thinnest-margin.

For a sufficiently large, electronic tournament there might be some marginal fairness gain by implementing some light duplicate principles:

1. All tables play the same board for each game.
2. The initial deck order is randomized for each seat, but duplicated per-seat between tables.
3. Players are awarded points based on placement in each game, based on the placing record for that seat and that board across all tables.
4. (possibly helpful?) The shuffle order immediately after the opening (and only this one shuffle) for each seat is duplicated between tables.

The point system could be as simple as this for a 2p tournament: If your seat won X% of the time on that board, you get (100-X) points for winning and 0 for losing. A multiplayer tournament would probably need a more sophisticated system based on placement.

#4 suffers from the aforementioned problem rrenaud pointed out, but I'm of a mind that it probably increases fairness by some better-than-negligible amount. The first shuffle after the opening is (in my estimation) much more important than the opening shuffle in introducing variance, and the biggest reason to lose a game because of this shuffle is that a key card got buried at the 11th or 12th position of the deck. That is to say, it's going to be relatively rare that rrenaud's problem is a major factor if only that one shuffle is duplicated.

With less logistical cost, you could implement everything except #4 in a practical, face-to-face tournament. I think that would be a pretty good format, given enough tables.


This is not remotely as fair as duplicate bridge, but I think it's much more fair than any Dominion tournament system that uses VP differentials, and it's probably more fair (at a significant logistical cost) than a basic tournament that only uses duplicate Kingdoms without duplicating anything else nor awarding points relative to the performance of other players in the same seat at other tables.

[Axe Knight]

For a sufficiently large, electronic tournament there might be some marginal fairness gain by implementing some light duplicate principles:

1. All tables play the same board for each game.
2. The initial deck order is randomized for each seat, but duplicated per-seat between tables.
3. Players are awarded points based on placement in each game, based on the placing record for that seat and that board across all tables.
4. (possibly helpful?) The shuffle order immediately after the opening (and only this one shuffle) for each seat is duplicated between tables.

It's not quite as scientific as your solution, or nearly as complicated as some mentioned here but in the informal tournament I'm currently organizing, I have two rounds.  The first round everyone is divided into groups, with each group having the same $2/$3/$4 card in the supply each round.  In addition, several games are played 1 on 1 within the group to attempt to weed out instances of randomness and bad draws.  The best players are likely to win out in the end given a sample of several games.  Since the order is not completely random, it also compares strategy based around (potentially) the same opening.  It is only after this that they would make a "cut" to round two, with only one or two people in each group winning.