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[theory]

This is a difficult problem for me to resolve. 

My knee-jerk instinct is that identical opening splits is a simple and sensible tournament variant of the game, in the same way that most competitive video games have different rulesets for competition (see, e.g., SSBM, Starcraft, TF2, Halo).

On the other hand, players are free to alter the rules if they mutually agree, and the default rules that we impose ought to be the rules of Dominion as written.

My ultimate reasoning was grounded in the fact that this default rule comes into play only when one side insists on it and the other insists on the other.  These situations seem likely only to occur when one side stands to gain some sort of advantage from the variance (e.g., a player is significantly worse), and in such situations I'd hate to be siding with the player seeking an advantage through random luck.  I have no problem with -- and indeed, encourage -- players to decide on their own to abandon identical starts.

But I'd love to keep hearing all your thoughts. 

[guided]

I moderately prefer identical starting hands, but I wouldn't rebel and quit the tournament or anything if we randomized the starting hands.

In any case, tournaments in all kinds of games use variants for one reason or another. I don't find the argument "oh, this isn't Dominion anymore" to be convincing.

[Jorbles]

Regardless of the benefits of identical starting hands vs random starting hands isn't it a little late to bring this up? Some people have already played their matches and been knocked out (and other people will likely play while this is being debated). Changing the rules after it has started seems unkosher regardless of whether it would have changed the outcomes of the games already played. This debate should be for the next tournament, not this one.

[popsofctown]

So if I used the combination calculator right, there are 42/252 different ways to draw a 2/5.  Nearly 3% of the time you play a 2/5 mirror.  Nearly 71% of the time you play a 3/4 mirror.  So the remaining 26% of the time either player A or player B gets a unique 5/2 - 13% apiece.


7 * 13% is rather conveniently 91%, nearly 100.  So in my view, if you want the tournament to measure general Dominion skill in the least variant way possible, you designate that each player plays 5/2 against 3/4 each set (you could just write down the first random set you get, then repeatedly pick it until you get the desired result.  Or, much more easily, just pass 4 turns without buying anything until it starts the way you need it to.)
To compensate for the fact that these games are actually a little less than 1/7 apiece, I'd put them at the end of the set rather than the beginning, so they might not get played.

5/2 vs. 5/2 is just 3%, which doesn't even come close to being an expectation to arise in a seven games set.  So there's no reason to micromanage the mirrors, so long as they're mirrors.

That's my two coppers.

[DStu]

You could say that you recommend identical start hand, but if one player insists on random hand, that's the fallback.
So to say two different defaults...

[popsofctown]

Why would you insist on random hands though? I doubt it'd be because of the spirit of Christmas, it'd be because you want to luck out.


This isn't breaking the spirit of Dominion in half or anything.  Jester is specifically written not to snatch Provinces, for instance.

[toaster]

My ultimate reasoning was grounded in the fact that this default rule comes into play only when one side insists on it and the other insists on the other.  These situations seem likely only to occur when one side stands to gain some sort of advantage from the variance (e.g., a player is significantly worse), and in such situations I'd hate to be siding with the player seeking an advantage through random luck.  I have no problem with -- and indeed, encourage -- players to decide on their own to abandon identical starts.

I think the flaw in our argument is your perception of the reasoning for wanting random hand splits.  I'd prefer and wish to insist on them regardless of my seed in relation to that of my opponent, simply because that's Dominion as written and because I value the extra interest created by the potential for asymmetrical starts.  I also think that when a certain setting is added to the default rules, it adds an endorsement behind that options as the preferred approach.  It seems to me that the default rules should be those of the game as written unless there's a reason that that wouldn't work (as in the case of point counters).

[popsofctown]

Do you dislike my method of preserving the asymmetry, toaster?

[theory]

@Jorbles: You're right that we should have discussed this before, but I screwed up and didn't think about it.  It's a small enough decision that if we end up changing our rule, prior results can still stand under harmless error.

@popsofctown: That's way too complicated to expect 256 people to follow.  It might be theoretically appealing, but there's a cost to rules complexity.

@DStu: This is the same as just imposing random start hands as a default rule.  I'm borrowing the contract law principle of default rule, as a baseline imposed only when two parties fail to agree otherwise.

@toaster: I agree that having the default rule tacitly endorse a variant of the rules is problematic.  On the other hand, is it more or less problematic than the potential for screwing up a match?

[popsofctown]

Both players could agree to simpler rules.

I don't think anyone who understands why Goons can't gain you VP chips off a Possession will have trouble with such a rule.

*shrug*

[toaster]

Well, first of all the combinatorics are a bit off.  The probability of a 5/2 split is 1/6 ((5 choose 2) * 2)/(10 choose 3).  Thus, the probabilities of opening hands are:

double 4/3: 25/36
4/3 and 5/2: 10/36
double 5/2: 1/36

When push comes to shove though, I prefer to let the luck of the draw take its course.  It's a part of the game, and especially in a best of 7 series, it shouldn't affect the outcome of the match unless the players were closely matched in skill to begin with.

[toaster]

@toaster: I agree that having the default rule tacitly endorse a variant of the rules is problematic.  On the other hand, is it more or less problematic than the potential for screwing up a match?

I think the term "screwing up a match" reflects a very strong bias about what the rules of Dominion should be.

[toaster]

This discussion does raise an interesting question: what is the win rate in 4/3 vs 5/2 games in general?

[popsofctown]

I was 1-2% off from rounding errors, and iirc I rounded against my own argument to be fair.

[Kirian]

I value the extra interest created by the potential for asymmetrical starts.

Can you please explain to me how, in a competitive setting, making the outcome of a random subset of games predetermined (to about 90% confidence) makes the game more interesting?

Might as well have both players roll d16 seven times, and if one player rolls a 6 when the other doesn't, give them a 1-0 lead to start.  Some matches will even start 3-1 with only three games needed to determine a winner!

That's not interesting, that's the very definition of dull.  If I wanted to participate in a RPS tournament, I'd go do that.

[Kirian]

It's a part of the game, and especially in a best of 7 series, it shouldn't affect the outcome of the match unless the players were closely matched in skill to begin with.

Please read my post on page 1 for even more combinatorics that show you're wrong.

[popsofctown]

2/5's win 90% of the time?  Where are you getting that figure?

[toaster]

I saw your math...however, for the most important figure (the extent to which an uneven split favors one side or another), you seem to have pulled numbers out of thin air.

[Fabian]

Kirian, I appreciate your side of the argument, but if you're seriously trying to pass off that 90% number (which has now morphed into an automatic 1-0 lead) as real, no one is going to take you seriously.

[Kirian]

2/5's win 90% of the time?  Where are you getting that figure?

No... someone in an unequal split (it could be the 4/3 player with Ambassador or Sea Hag on the table, for instance) has approximately a 90% advantage something like half the time.  I'll admit 90% is an approximation and dependent on the cards on the board--I'd guess Witch/Chapel vs. Silver/Chapel is closer to 95%, but obviously some unequal splits are going to be more in the 70% range... and some will be in the no-advantage range.

I'm also using "advantage" more statistically, which I guess does muddy some things. It is not "win rate."  Maybe two-sigma would be better?  A 75% win rate is way away from the mean.

In my opinion, even a 75% win-rate (both players going BM-Witch, best I could simulate while trying to post in a rapid thread) is devastating to a game.  It's disruptive to the tournament and, most importantly against toaster's argument, dull.

[theory]

To try to keep this civil, someone's done some number crunching on this already.  This is with Isotropic data about a year ago, so before a lot of the newer cards.

It's not an absolute advantage, but it's substantial.  Moreover, the inequality is greater than the win rate difference; 5/2 is a substantial disadvantage with certain cards (Ambassador, Masquerade), and a substantial advantage with others (Mountebank, Chapel).  The fact that these tend to even out doesn't change the fact that the opening split significantly influenced the outcome of the game.

So in other words, it does promote varying strategies, but those varying strategies almost always end up tilting the game to one side rather than just lead to diverging play.

I'm not suggesting that this is enough justification for playing a Dominion tournament variant.  But I'm pretty convinced that allowing random opening splits has an overall negative impact on a competitive tournament.  The question is whether this negative impact outweighs the fact that we're asking people to play with rules that are not officially in the rulebook.

[popsofctown]

If that's what you've simplified the question to, it's pretty slam dunk, people aren't that uncomfortable playing mirrors only.

[Kirian]

Thanks for finding that, theory.  I think there was an even better one at some point on the BGGDL board, but I can't find it.

I'll admit to what seems to be exaggerating but was not intended as such... but the point remains that there will be an average of 2.15 unequal splits in a best-of-seven series.  An average of 4 out of 128 matches will have 5 or more unequal splits. (These can't be exaggerated, only miscalculated; happy to have someone recalculate to check.)  Even if the advantage is only 60% on average, I think that's significant enough to be disruptive.

I'll try to back off a bit, but I'll maintain this lessens, not increases, the interest of the game in a competitive setting.  It is the singular fundamental flaw of Dominion.

[theory]

Well, there are intangible considerations.

Maybe someone ragequits our tournament because he had to open Ambassador/nothing against Tournament/Ambassador.

Maybe someone decides not to play our tournament because he has a distaste for tournaments that make up their own rules reflecting the organizer's bias rather than the official rulebook.

To play devil's advocate, where does it end?  Ignoring practical difficulties, ought a Dominion tournament regulate the turn 3-5 reshuffle as well?

[toaster]

Or, for that matter, the game end rules.  We know that the existing rules have a persistent pro-first player bias...and though it's a smaller magnitude, unlike the split it's an effect that's guaranteed to benefit one player over another in every single match.