Dominion Strategy Forum

Dominion => Variants and Fan Cards => Topic started by: TerrySpeed on March 24, 2021, 07:58:55 pm

Title: Variants to make the game more fair & less luck dependent?
Post by: TerrySpeed on March 24, 2021, 07:58:55 pm
I like Dominion, but luck plays a considerable role in who wins.

My friends and I came up with the following variants to make the game more fair:

(1) If the game would end with the starting player having had more turns than the last player, the last player gets an extra turn. This ensures everyone plays the exact same number of turns.

(2) Players select their first starting hand from their deck - meaning they can either pick 4/3 coppers or 5/2 coppers, their choice. This limits the impact of drawing 4/3 when the board is very favorable to 5/2 hands, and vise versa.

Both variant are simple to implement, and diminish the impact of non-skill factors (starting player, starting hand) without affecting the strategy of the game.

Are there other variants out there to make the game more fair?
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: mathdude on March 24, 2021, 09:15:25 pm
Admittedly, luck does play a role. It's part of this (and most) games. And you can make whatever changes you want within your games, because that helps you have more fun. But I'll address both of your concerns anyway.

1) The game already has a mechanism for addressing first player advantage... sort of (as long as there are no attacks). In a 2-player game, there are 8 provinces (4/ player). With 3, there are still 4 each. With 4, 5, or 6, there are 3 each.

Let's say there is an ideal way to get provinces fastest. Everyone does it (and they all draw the same cards every turn). Pile runs out and everyone has the same number and it's a tie. But if someone doesn't play ideal (in a 2 or 6 player game or anything in between), and there's a chance someone could get more points. But let's say there still ends up being a tie. If the person who bought the last one had one more turn than the other, the game says that person loses.

Of course, it's still not that simple. There's a 3-pile ending possible. That may be fine/fair with 2 or 5 players. But with 3, that first player has an advantage to get one extra village... or laboratory, smithy, etc. And then attacks change things too... first player has a better chance of drawing their purchased attack first, giving an even bigger advantage. It's not perfect.

So some tournaments I've heard play multiple games between the same 2 players determine a winner of each round (for example, 6 games total with each starting 3 games). They can still go 3-3, but the chances of 4-2 or 3-2 and a tie (or others) definitely help break most ties.

Our own house rule is that whoever wins one game goes last the next... playing multiple games the same day or even if it's a week later. If I win, the player to my left starts the next game. It's okay if one person has a slight advantage because someone else likely will the next game.

You can still continue letting people play after the game ends until everyone had equal turns (likely giving people at least a chance to buy a duchy). It's a house rule, like putting money in the centre for Monopoly and collecting it when you land on Free Parking (that's not actually in the rules!)

2) Much shorter answer here. I believe also in some official tournaments, players have been able to choose their starting copper split. It makes sense since some boards strongly advantage one over the other.

It's even more powerful with some cards... Pooka (with Cursed Gold heirloom) and Fisherman are two I can think of. Imagine drawing 5-then-2 with Fisherman against someone else who draws 2-then-5.

I like the randomness in the starting draw. It adds an additional challenge when starting with a non-ideal opening. Although, now I'm thinking we should probably let my daughter (6 years old and loves playing, competitively too!) the chance to choose her opening to balance it out a bit.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: TerrySpeed on March 24, 2021, 10:14:12 pm
1) The game already has a mechanism for addressing first player advantage... sort of (as long as there are no attacks). In a 2-player game, there are 8 provinces (4/ player). With 3, there are still 4 each. With 4, 5, or 6, there are 3 each.

The mechanism is insufficient. The game often ends up with the first player winning and getting an extra turn, while the second player could have won if only they had had the opportunity to buy a Duchy on their turn.

You can still continue letting people play after the game ends until everyone had equal turns (likely giving people at least a chance to buy a duchy). It's a house rule, like putting money in the centre for Monopoly and collecting it when you land on Free Parking (that's not actually in the rules!)

That Monopoly rule breaks the game, mine makes it less luck dependent.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: pubby on March 24, 2021, 10:21:40 pm
I think the game is less interesting if you can open 5/2 every time. A better implementation is to have the first player shuffle, then have all players match their opening (so if they open 4/3, everyone opens 4/3).
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: TerrySpeed on March 24, 2021, 10:39:02 pm
I think the game is less interesting if you can open 5/2 every time. A better implementation is to have the first player shuffle, then have all players match their opening (so if they open 4/3, everyone opens 4/3).

I think both variants are interesting.

Having the first person shuffle, then have all players match the shuffle, is more interesting when 5/2 (or 4/3) is clearly the superior option.

Letting the player choose either 5/2 or 4/3, is more interesting when both openings are roughly as good.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: mathdude on March 24, 2021, 11:46:59 pm
1) The game already has a mechanism for addressing first player advantage... sort of (as long as there are no attacks). In a 2-player game, there are 8 provinces (4/ player). With 3, there are still 4 each. With 4, 5, or 6, there are 3 each.

The mechanism is insufficient. The game often ends up with the first player winning and getting an extra turn, while the second player could have won if only they had had the opportunity to buy a Duchy on their turn.

I find the vast majority of games I play that whoever buys the last province wins (if the game ends with province pile empty).  But it's not a majority that it's the first player doing it.  Consider the match-style play I discussed earlier.  That was based on ideal/perfect draws of cards, but "on average" it would work similarly in real games.  If 1st player has bought a province, 2nd probably should be doing so as well (and 3rd, if playing, and 4th...)  In a 2-player game, if you both have 3 provinces and the 1st player buys a duchy, they are now 3 points ahead.  You (if 2nd player) don't buy the 7th province, because then if 1st player buys the final province, they win.  You match-play... if they bought a duchy, you buy a duchy even if you have $8, unless you're fairly confident they can't buy that last one (maybe you've played a militia and they are unlikely to get it with 3 cards in hand).

But that's part of what I find as the beauty of the strategy of this game.  Figuring out what to do, and when.  Do you (and if so, when and how many) trash some/most of your initial cards?  Do you go mostly money or more Action cards?  Do you buy Province at your first hand with $8 even if you've only bought 1 gold (or even none yet)?

Most games, I try to track points (at least roughly) in my head as we're going, to see if we're even, or if someone's ahead by "about" 3 or 6 or 9.  That helps influence when I buy what kind of green cards.  Ideally, I try to stay slightly ahead.  But as a minimum, I try to stay close to even (unless someone has clearly started buying greens too early... or if we're going for different strategies, like one for Provinces and the other for Gardens).

Here's a strategy article that's a good read.  This is just one of the many things to consider... that whole idea about buying that 2nd last Province is a part of the game design.
http://wiki.dominionstrategy.com/index.php/Penultimate_Province_Rule
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: Chris is me on March 25, 2021, 12:10:20 am
the best variant to make the game "less luck dependent" is to play multiple games. like hands of poker, it's best not to judge an individual game as an absolute arbiter of skill. variance is fine!
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: LastFootnote on March 25, 2021, 12:12:03 am
Our own house rule is that whoever wins one game goes last the next... playing multiple games the same day or even if it's a week later. If I win, the player to my left starts the next game.

That's actually an official rule in the rulebook.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: LastFootnote on March 25, 2021, 01:04:54 am
"The goal of Dominion is not to have the most points when the game ends, but to end the game when you have the most points." - Tables

The problem with equal turns in Dominion is that the game isn't on a timer (12 turns, or whatever) and players have a massive amount of control over how close the game is to ending. If you institute an equal turns rule, then the last player is often playing a very different game than the others. They can know whether ending the game will cause them to win. The other players have no such certainty. So this rule likely replaces a mild first-player advantage with an often even more significant last player advantage.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: segura on March 25, 2021, 05:55:38 am
Indeed. I'd even argue that in terms of creating player interaction this is the most important element of the game.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: The Alchemist on March 29, 2021, 10:08:20 am
The first rule doesn't work in practice. I and many others have had the exact same idea, but it doesn't work.

What the first rule essentially says is only the 2nd player is allowed to win the game by pileout. Considering around 30% of games are won that way, you've just replaced a 10% first player advantage with near total second player advantage.

As for the second rule, it doesn't work with any of the cards that change your second hand, like noble brigand or cavalry.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: GendoIkari on March 29, 2021, 11:09:58 am
As for the second rule, it doesn't work with any of the cards that change your second hand, like noble brigand or cavalry.

Well you can always implement it as "each player can arrange their starting deck as they want".

I think the real problem with that rule is that there's really nothing special about the arrangement of your starting deck compared to the arrangement of your deck after any shuffle... I think people tend to think of it as different probably because the shuffling happened during the game setup rather than during the game itself. But what order your cards are in when you shuffle for the first time (usually at the end of turn 2) generally matters more than the starting order does in terms of luck. So if you are going to allow players to order their starting deck, why not allow them to order their first shuffle?
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: LastFootnote on March 29, 2021, 11:31:06 am
As for the second rule, it doesn't work with any of the cards that change your second hand, like noble brigand or cavalry.

Well you can always implement it as "each player can arrange their starting deck as they want".

I think the real problem with that rule is that there's really nothing special about the arrangement of your starting deck compared to the arrangement of your deck after any shuffle... I think people tend to think of it as different probably because the shuffling happened during the game setup rather than during the game itself. But what order your cards are in when you shuffle for the first time (usually at the end of turn 2) generally matters more than the starting order does in terms of luck. So if you are going to allow players to order their starting deck, why not allow them to order their first shuffle?

And continuing down that line of thinking, why not allow players to order their deck whenever they "shuffle"?
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: silverspawn on March 29, 2021, 11:59:27 am
You can also play chess instead of dominion. Solves all randomness issues.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: Wizard_Amul on March 29, 2021, 01:02:26 pm
You can also play chess instead of dominion. Solves all randomness issues.

Yeah, if you want to avoid randomness entirely, Dominion isn't a great game.

I highly recommend Prismata--only randomness is the unit pool available for purchase (like Dominion's random kingdom). One of the initial design ideas was to make something like a deck-building game where you always have your whole deck in hand--avoids randomness of draws. It doesn't really feel like a card game, but I recommend trying it out. It was called MCDS in development, which stands for Magic, Chess, Dominion, and Starcraft.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: silverspawn on March 29, 2021, 01:51:45 pm
Yeah Prismata is excellent
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: GendoIkari on March 30, 2021, 04:41:59 pm
As for the second rule, it doesn't work with any of the cards that change your second hand, like noble brigand or cavalry.

Well you can always implement it as "each player can arrange their starting deck as they want".

I think the real problem with that rule is that there's really nothing special about the arrangement of your starting deck compared to the arrangement of your deck after any shuffle... I think people tend to think of it as different probably because the shuffling happened during the game setup rather than during the game itself. But what order your cards are in when you shuffle for the first time (usually at the end of turn 2) generally matters more than the starting order does in terms of luck. So if you are going to allow players to order their starting deck, why not allow them to order their first shuffle?

And continuing down that line of thinking, why not allow players to order their deck whenever they "shuffle"?

Well sort of. At a certain point, you can say that you make your own shuffle luck... building a consistent deck that doesn't get screwed by bad shuffle luck is part of the skill. And to an extent, that exists in the first shuffle (don't buy 2 terminal draw cards in your opening), but for the most part you don't have any control over deck consistency yet.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: TerrySpeed on April 01, 2021, 10:27:15 am
The first rule doesn't work in practice. I and many others have had the exact same idea, but it doesn't work.

What the first rule essentially says is only the 2nd player is allowed to win the game by pileout. Considering around 30% of games are won that way, you've just replaced a 10% first player advantage with near total second player advantage.

How is that the case? The first player can still win by pileout, they just no longer get the unfair advantage of an extra turn.

Even if pileouts are specifically a problem, the rule could be amended so the extra turn only applies on province depletion.

I think the real problem with that rule is that there's really nothing special about the arrangement of your starting deck compared to the arrangement of your deck after any shuffle...

The starting hand is special: since no decision was made prior to drawing the initial hand, the randomness can be eliminated without reducing strategy in any way.

And continuing down that line of thinking, why not allow players to order their deck whenever they "shuffle"?

Contrarily to the ordering the starting hand, ordering any subsequent hand impacts the strategy of the game.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: GendoIkari on April 01, 2021, 06:03:27 pm
The first rule doesn't work in practice. I and many others have had the exact same idea, but it doesn't work.

What the first rule essentially says is only the 2nd player is allowed to win the game by pileout. Considering around 30% of games are won that way, you've just replaced a 10% first player advantage with near total second player advantage.

How is that the case? The first player can still win by pileout, they just no longer get the unfair advantage of an extra turn.


If the first player has a way that he can empty 3 piles while also being ahead by a couple of points, then he would no longer be able to win that way, because all the second player has to do is buy a Duchy. In fact, it would be almost always impossible for the first player to ever win a game by only a couple of points; player 1 would have to not only end the game while ahead, but end the game while ahead by a comfortable lead. Meanwhile, second player can continue to do things that involve getting ahead by a single point and ending the game for the win.

Quote
Even if pileouts are specifically a problem, the rule could be amended so the extra turn only applies on province depletion.

The problem would be more common with pileouts simply because it's more common for a very close game to end that way; games that end on Provinces often have at least a 12 point difference in the score. But it's still the same issue with a Province ending... if player 1 buying the last Province would put him ahead by 2 points, then he can't safely do that because he probably won't win. Player 1 can only buy the last Province if it puts him ahead by more points than player 2 can get with the remaining turn.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: LastFootnote on April 03, 2021, 11:23:41 am
The starting hand is special: since no decision was made prior to drawing the initial hand, the randomness can be eliminated without reducing strategy in any way.

Not special! Only special in your mind.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: silverspawn on April 03, 2021, 11:52:46 am
pretty sure 'special' isn't precisely enough defined to determine whether or not it's special.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: LostPhoenix on April 03, 2021, 02:23:33 pm
I think the real problem with that rule is that there's really nothing special about the arrangement of your starting deck compared to the arrangement of your deck after any shuffle...

The starting hand is special: since no decision was made prior to drawing the initial hand, the randomness can be eliminated without reducing strategy in any way.


Contrary to popular belief, reducing randomness does not mean increasing strategy. Part of the strategy of Dominion is responding to the randomness the game gives you.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: LastFootnote on April 04, 2021, 05:52:56 pm
Contrary to popular belief, reducing randomness does not mean increasing strategy. Part of the strategy of Dominion is responding to the randomness the game gives you.

Adding randomness to a game may not "reduce strategy", but it absolutely does reduce the degree to which good strategy leads to victory, and for some people that is unacceptable.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: DunnoItAll on April 05, 2021, 02:07:42 pm
Contrary to popular belief, reducing randomness does not mean increasing strategy. Part of the strategy of Dominion is responding to the randomness the game gives you.

Adding randomness to a game may not "reduce strategy", but it absolutely does reduce the degree to which good strategy leads to victory, and for some people that is unacceptable.

Depends on sample size. If you are playing a single game, sure. If you are playing a series of games, much, much less so (depending of course, on how much the variance has increased). Some people prefer variance, too, so it isn't just good vs. bad.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: LastFootnote on April 05, 2021, 02:25:45 pm
Contrary to popular belief, reducing randomness does not mean increasing strategy. Part of the strategy of Dominion is responding to the randomness the game gives you.

Adding randomness to a game may not "reduce strategy", but it absolutely does reduce the degree to which good strategy leads to victory, and for some people that is unacceptable.

Depends on sample size. If you are playing a single game, sure. If you are playing a series of games, much, much less so (depending of course, on how much the variance has increased). Some people prefer variance, too, so it isn't just good vs. bad.

Agreed. Personally I'm a fan of the variance.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: silverspawn on April 07, 2021, 01:54:49 pm
It doesn't really depend on the sample size. The variance of the mean outcome depends on the sample size, but the amount by which that variance differs for different games is the same for every sample size. Dominion is always high variance compared to Prismata.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: TerrySpeed on April 07, 2021, 09:47:48 pm
I think the real problem with that rule is that there's really nothing special about the arrangement of your starting deck compared to the arrangement of your deck after any shuffle...

The starting hand is special: since no decision was made prior to drawing the initial hand, the randomness can be eliminated without reducing strategy in any way.


Contrary to popular belief, reducing randomness does not mean increasing strategy. Part of the strategy of Dominion is responding to the randomness the game gives you.

I don't think you understood my point. I'm not saying reducing randomness increases strategy. I'm just saying that randomness that serves no purposes (such as randomness favoring a player before the game even started) should be eliminated.

I mean, if you disagree with me, you might as well play with the following variant: before the start of the game, toss a coin. If it lands head, you start out with 3 free vps.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: LastFootnote on April 08, 2021, 08:40:47 am
The purpose it serves is to encourage divergent strategies. There are posts in the forum where Donald X. explains his reasoning.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: GendoIkari on April 08, 2021, 09:04:36 pm
There is certainly a skill in deciding whether you would prefer 4/3 or 5/2. However, there is also just as much skill in determining what the best choice is given a 4/3 start, when the board favors a 5/2 start. If you have the extra option to simply chose 5/2 instead, then that skill of "how do you best use a 4/3 start" is removed from the game. The variant just replaces one type of skill testing with a different one.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: grep on April 08, 2021, 10:59:54 pm
Komi (https://senseis.xmp.net/?Komi) (compensation for the first move) has been invented hundreds of years ago. As the Dominion games are unique, fixed komi won't be fair, so a "pie slicing" algorithm should be used. After determining the kingdom, player A selects the amount of compensation for first move (in halves of VP, may be negative e.g. if Tax is present). Player B chooses if they want to play first; the second player takes the compensation.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: Awaclus on April 09, 2021, 03:50:52 am
I think the real problem with that rule is that there's really nothing special about the arrangement of your starting deck compared to the arrangement of your deck after any shuffle... I think people tend to think of it as different probably because the shuffling happened during the game setup rather than during the game itself. But what order your cards are in when you shuffle for the first time (usually at the end of turn 2) generally matters more than the starting order does in terms of luck. So if you are going to allow players to order their starting deck, why not allow them to order their first shuffle?

There is something special about the starting deck: it gets shuffled before you can make any decisions in the game. Randomness after decisions affects how you should make decisions and therefore adds a skill component to the game. Randomness before decisions affects how you can make decisions and therefore restricts a skill component in the game.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: emtzalex on April 09, 2021, 12:54:21 pm
I think the real problem with that rule is that there's really nothing special about the arrangement of your starting deck compared to the arrangement of your deck after any shuffle... I think people tend to think of it as different probably because the shuffling happened during the game setup rather than during the game itself. But what order your cards are in when you shuffle for the first time (usually at the end of turn 2) generally matters more than the starting order does in terms of luck. So if you are going to allow players to order their starting deck, why not allow them to order their first shuffle?

There is something special about the starting deck: it gets shuffled before you can make any decisions in the game. Randomness after decisions affects how you should make decisions and therefore adds a skill component to the game. Randomness before decisions affects how you can make decisions and therefore restricts a skill component in the game.

Another thing that is unique about the pre-game shuffle is that, generally speaking, it has a significantly lower set of choices than almost any other shuffle. Barring Heirlooms and Shelters (and a couple of other unique cases, like Nomad Camp), there are only four meaningfully different options for a starting deck: $3/$4, $4/$3, $2/$5, and $5/$2. And in many games there is no meaningful difference between $3/$4 and $4/$3 or between $2/$5 and $5/$2.

Starting with the first shuffle of the game, things quickly get much more complicated. Even if you opened Silver Silver (and even barring any 2nd shuffle purchases that would be gained onto the deck or immediately played or would otherwise draw/discard/affect the order of your deck, so that the order of the first two purchases don't matter), possible hands include (the third item is just the first two cards of the 3rd hand, which will include cards from the 3rd shuffle):

$7/$4/$0+
$7/$3/$1+
$7/$2/$2+
$7/$1/$3+
$7/$0/$4+
$6/$5/$0+
$6/$4/$1+
$6/$3/$2+
$6/$2/$3+
$6/$1/$4+
$5/$5/$1+
$5/$4/$2+
$5/$3/$3+
$5/$2/$4+
$4/$4/$3+
$4/$3/$4+

That's already eight times the number of choices you had in the initial shuffle, under the simplest of circumstances. I would expect (although I haven't done the math) that possibilities grow exponentially from there. Having to wait while another player decided this order would substantially slow down the game in a way that would be extremely unpleasant.

By contrast, even with Shelters or Heirlooms, the choices for the pre-game shuffle stay relatively simple. For most of the Heirlooms--Magic Lamp, Haunted Mirror, Pasture, and [usually] Lucky Coin--it doesn't matter which first shuffle hand they end up it. Pouch will sometime matter, but generally only if you are looking to buy $2/$2/$3. Where Goat and Cursed Gold land is more substantive, and does increase the number of options quite a bit. Similarly, which Estate is replaced by which Shelter usually will not matter, unless (1) there is a Way that makes Necropolis useful, or (2) you're going to open by buying a Victory card (a fairly unusual play, although conceivable with Tunnel or maybe Mill), and want Hovel in that hand.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: GendoIkari on April 09, 2021, 04:54:41 pm
Restricting choices you can make doesn't restrict skill; in fact the opposite. The fact that you can't just choose to open 5/2 adds the skill of choosing what to do with your 4/3 opening. The fact that you can't just buy a Province if you only have (http://wiki.dominionstrategy.com/images/thumb/2/2a/Coin4.png/16px-Coin4.png) to spend on a turn adds the skill of choosing of how to spend that (http://wiki.dominionstrategy.com/images/thumb/2/2a/Coin4.png/16px-Coin4.png). Restrictions on what you are allowed to do doesn't just take away a skill; it replaces it with a different skill.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: Awaclus on April 09, 2021, 05:07:24 pm
Restricting choices you can make doesn't restrict skill; in fact the opposite. The fact that you can't just choose to open 5/2 adds the skill of choosing what to do with your 4/3 opening. The fact that you can't just buy a Province if you only have (http://wiki.dominionstrategy.com/images/thumb/2/2a/Coin4.png/16px-Coin4.png) to spend on a turn adds the skill of choosing of how to spend that (http://wiki.dominionstrategy.com/images/thumb/2/2a/Coin4.png/16px-Coin4.png). Restrictions on what you are allowed to do doesn't just take away a skill; it replaces it with a different skill.

If you can choose between 5/2 and 4/3, you need to choose what to do with your 4/3 opening and what to do with your 5/2 opening, and then decide which one of them is better. It sounds like you're taking it for a granted that the 5/2 is always better so you don't even need to consider the 4/3, but that's not even close to being true.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: mxdata on April 09, 2021, 05:14:22 pm
Komi (https://senseis.xmp.net/?Komi) (compensation for the first move) has been invented hundreds of years ago. As the Dominion games are unique, fixed komi won't be fair, so a "pie slicing" algorithm should be used. After determining the kingdom, player A selects the amount of compensation for first move (in halves of VP, may be negative e.g. if Tax is present). Player B chooses if they want to play first; the second player takes the compensation.

A Komi-like system could be very easily implemented with VP tokens.  No real need for half-VP, just agree that the second player wins in the event of a tie (and "negative" komi could be implemented by giving player 1 VP tokens)
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: GendoIkari on April 09, 2021, 05:18:45 pm
Restricting choices you can make doesn't restrict skill; in fact the opposite. The fact that you can't just choose to open 5/2 adds the skill of choosing what to do with your 4/3 opening. The fact that you can't just buy a Province if you only have (http://wiki.dominionstrategy.com/images/thumb/2/2a/Coin4.png/16px-Coin4.png) to spend on a turn adds the skill of choosing of how to spend that (http://wiki.dominionstrategy.com/images/thumb/2/2a/Coin4.png/16px-Coin4.png). Restrictions on what you are allowed to do doesn't just take away a skill; it replaces it with a different skill.

If you can choose between 5/2 and 4/3, you need to choose what to do with your 4/3 opening and what to do with your 5/2 opening, and then decide which one of them is better. It sounds like you're taking it for a granted that the 5/2 is always better so you don't even need to consider the 4/3, but that's not even close to being true.

No, I intended everything I said to be including a vice-versa for when 4/3 is better and you draw 5/2. I just wasn't clear on that point. Yes, there are also boards where which one is correct isn't a clear choice, but there are plenty of others where it is. And any time one option is obviously better than the other; you remove one element of skill if you allow freely choosing between them.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: Awaclus on April 09, 2021, 06:00:35 pm
Restricting choices you can make doesn't restrict skill; in fact the opposite. The fact that you can't just choose to open 5/2 adds the skill of choosing what to do with your 4/3 opening. The fact that you can't just buy a Province if you only have (http://wiki.dominionstrategy.com/images/thumb/2/2a/Coin4.png/16px-Coin4.png) to spend on a turn adds the skill of choosing of how to spend that (http://wiki.dominionstrategy.com/images/thumb/2/2a/Coin4.png/16px-Coin4.png). Restrictions on what you are allowed to do doesn't just take away a skill; it replaces it with a different skill.

If you can choose between 5/2 and 4/3, you need to choose what to do with your 4/3 opening and what to do with your 5/2 opening, and then decide which one of them is better. It sounds like you're taking it for a granted that the 5/2 is always better so you don't even need to consider the 4/3, but that's not even close to being true.

No, I intended everything I said to be including a vice-versa for when 4/3 is better and you draw 5/2. I just wasn't clear on that point. Yes, there are also boards where which one is correct isn't a clear choice, but there are plenty of others where it is. And any time one option is obviously better than the other; you remove one element of skill if you allow freely choosing between them.

Considering that there are all of these possibilities:


It's pretty weird for you to focus exclusively on this one case:


To save space, I only included the cases from the 4/3 perspective.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: silverspawn on April 09, 2021, 06:39:16 pm
If you make the set of options smaller, obviously finding the optimum becomes easier.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: GendoIkari on April 09, 2021, 06:58:33 pm
If you make the set of options smaller, obviously finding the optimum becomes easier.

That is definitely not true, and easy to prove that it's not. Take a variant of Dominion where all the rules are exactly the same, except you have 1 additional option: Instead of taking your turn like normal, you can choose to gain all Provinces from the Province pile.

Regular Dominion has a smaller set of options than this variant would, yet it's cleary harder to find the optimum strategy.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: silverspawn on April 09, 2021, 07:16:52 pm
Um. Yes. I'm stupid.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: emtzalex on April 09, 2021, 08:28:15 pm
If you make the set of options smaller, obviously finding the optimum becomes easier.

That is definitely not true, and easy to prove that it's not. Take a variant of Dominion where all the rules are exactly the same, except you have 1 additional option: Instead of taking your turn like normal, you can choose to gain all Provinces from the Province pile.

Regular Dominion has a smaller set of options than this variant would, yet it's cleary harder to find the optimum strategy.

Okay, but that only proves that silverspawn might have been more precise in his language. I would still posit that if you make the set of meaningful options smaller, finding the optimum strategy tends to become easier. Your example is evidence of that. While you technically increased the number of options, you actually decreased the number of meaningful options to one. This made finding the optimum strategy extremely easy.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: GendoIkari on April 10, 2021, 02:52:18 am
If you make the set of options smaller, obviously finding the optimum becomes easier.

That is definitely not true, and easy to prove that it's not. Take a variant of Dominion where all the rules are exactly the same, except you have 1 additional option: Instead of taking your turn like normal, you can choose to gain all Provinces from the Province pile.

Regular Dominion has a smaller set of options than this variant would, yet it's cleary harder to find the optimum strategy.

Okay, but that only proves that silverspawn might have been more precise in his language. I would still posit that if you make the set of meaningful options smaller, finding the optimum strategy tends to become easier. Your example is evidence of that. While you technically increased the number of options, you actually decreased the number of meaningful options to one. This made finding the optimum strategy extremely easy.

And I think that on some boards; allowing you to choose you opening hand would reduce the number of meaningful options. Maybe a lot of boards; I honestly don’t know. Like if Chapel and Mountebank are on the board; or Chapel with a lot of things. Or Cultist or Witch with a lot of things; especially with a good $2. Being forced to randomly start 3/4 forces you to make a tough strategic choice; while being allowed to choose 5/2 would reduce your meaningful choices to one.

And again I’m only listing strong 5/2 boards as examples; partially because 3/4 is a more likely opening hand and partially because $5 cards are a lot stronger on average. And because there are on average fewer choices to make with 5/2 (because you can’t choose silver, and you can’t choose 3/3, etc). But the same thing would apply in the other direction.

I mean, just look at the recent thread about ways to guarantee that you can buy a $5 by your 4th turn. The current rule spawned an entire long discussion about all sorts of combos and cards out there that you can use to accomplish that goal. The variant rule would have completely removed that entire discussion; there wouldn’t be any strategy involved in figuring out how to make sure you get a $5 by your 4th turn. 
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: Awaclus on April 10, 2021, 04:45:49 am
That is definitely not true, and easy to prove that it's not. Take a variant of Dominion where all the rules are exactly the same, except you have 1 additional option: Instead of taking your turn like normal, you can choose to gain all Provinces from the Province pile.

Regular Dominion has a smaller set of options than this variant would, yet it's cleary harder to find the optimum strategy.

This is not representative of the typical case where you're adding more options, because you're adding one option which is disproportionately powerful. By allowing players to order the starting deck, you're adding more options that are roughly as powerful as the existing options (you're only adding options that do in fact already exist in the game that are just randomly made unavailable to some players).

And I think that on some boards; allowing you to choose you opening hand would reduce the number of meaningful options. Maybe a lot of boards; I honestly don’t know. Like if Chapel and Mountebank are on the board; or Chapel with a lot of things. Or Cultist or Witch with a lot of things; especially with a good $2. Being forced to randomly start 3/4 forces you to make a tough strategic choice; while being allowed to choose 5/2 would reduce your meaningful choices to one.

Yes, that is the one case out of the 8 possible cases I listed. Why is that one case more important than the other 7?

I mean, just look at the recent thread about ways to guarantee that you can buy a $5 by your 4th turn. The current rule spawned an entire long discussion about all sorts of combos and cards out there that you can use to accomplish that goal. The variant rule would have completely removed that entire discussion; there wouldn’t be any strategy involved in figuring out how to make sure you get a $5 by your 4th turn. 

Sure, but that is more of a puzzle than a strategy discussion. As far as your strategy is concerned, the difference between being guaranteed to hit $5 and being very likely to hit $5 doesn't matter very much, and the difference between being unable to hit $5 and having better options than hitting $5 doesn't matter very much either.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: Holger on April 10, 2021, 05:18:48 am
That is definitely not true, and easy to prove that it's not. Take a variant of Dominion where all the rules are exactly the same, except you have 1 additional option: Instead of taking your turn like normal, you can choose to gain all Provinces from the Province pile.

Regular Dominion has a smaller set of options than this variant would, yet it's cleary harder to find the optimum strategy.

This is not representative of the typical case where you're adding more options, because you're adding one option which is disproportionately powerful. By allowing players to order the starting deck, you're adding more options that are roughly as powerful as the existing options (you're only adding options that do in fact already exist in the game that are just randomly made unavailable to some players).

And I think that on some boards; allowing you to choose you opening hand would reduce the number of meaningful options. Maybe a lot of boards; I honestly don’t know. Like if Chapel and Mountebank are on the board; or Chapel with a lot of things. Or Cultist or Witch with a lot of things; especially with a good $2. Being forced to randomly start 3/4 forces you to make a tough strategic choice; while being allowed to choose 5/2 would reduce your meaningful choices to one.

Yes, that is the one case out of the 8 possible cases I listed. Why is that one case more important than the other 7?
Maybe because it happens more often than the other 7 cases? You haven't provided any rationale for why they should all have the same probability. Besides, in the third case in your list,
choosing is also less strategic than shuffling when considering several games: Shuffling forces you to make different choices in different games, choosing splits always gives you the same choice (namely for the better opening split).

I think the 8th case of your list in which shuffling improves strategy is fairly common, certainly more than 1/8=12.5%.

 
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: Awaclus on April 10, 2021, 05:32:52 am
That is definitely not true, and easy to prove that it's not. Take a variant of Dominion where all the rules are exactly the same, except you have 1 additional option: Instead of taking your turn like normal, you can choose to gain all Provinces from the Province pile.

Regular Dominion has a smaller set of options than this variant would, yet it's cleary harder to find the optimum strategy.

This is not representative of the typical case where you're adding more options, because you're adding one option which is disproportionately powerful. By allowing players to order the starting deck, you're adding more options that are roughly as powerful as the existing options (you're only adding options that do in fact already exist in the game that are just randomly made unavailable to some players).

And I think that on some boards; allowing you to choose you opening hand would reduce the number of meaningful options. Maybe a lot of boards; I honestly don’t know. Like if Chapel and Mountebank are on the board; or Chapel with a lot of things. Or Cultist or Witch with a lot of things; especially with a good $2. Being forced to randomly start 3/4 forces you to make a tough strategic choice; while being allowed to choose 5/2 would reduce your meaningful choices to one.

Yes, that is the one case out of the 8 possible cases I listed. Why is that one case more important than the other 7?
Maybe because it happens more often than the other 7 cases? You haven't provided any rationale for why they should all have the same probability. Besides, in the third case in your list,
choosing is also less strategic than shuffling when considering several games: Shuffling forces you to make different choices in different games, choosing splits always gives you the same choice (namely for the better opening split).

I think the 8th case of your list in which shuffling improves strategy is fairly common, certainly more than 1/8=12.5%.

If the best 4/3 is obvious 50% of the time, it's obviously better than any 5/2 50% of the time, and the best 5/2 is not obvious 50% of the time, you get 12.5%. Which of those 50%s you disagree with?
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: Holger on April 10, 2021, 06:06:31 am
That is definitely not true, and easy to prove that it's not. Take a variant of Dominion where all the rules are exactly the same, except you have 1 additional option: Instead of taking your turn like normal, you can choose to gain all Provinces from the Province pile.

Regular Dominion has a smaller set of options than this variant would, yet it's cleary harder to find the optimum strategy.

This is not representative of the typical case where you're adding more options, because you're adding one option which is disproportionately powerful. By allowing players to order the starting deck, you're adding more options that are roughly as powerful as the existing options (you're only adding options that do in fact already exist in the game that are just randomly made unavailable to some players).

And I think that on some boards; allowing you to choose you opening hand would reduce the number of meaningful options. Maybe a lot of boards; I honestly don’t know. Like if Chapel and Mountebank are on the board; or Chapel with a lot of things. Or Cultist or Witch with a lot of things; especially with a good $2. Being forced to randomly start 3/4 forces you to make a tough strategic choice; while being allowed to choose 5/2 would reduce your meaningful choices to one.

Yes, that is the one case out of the 8 possible cases I listed. Why is that one case more important than the other 7?
Maybe because it happens more often than the other 7 cases? You haven't provided any rationale for why they should all have the same probability. Besides, in the third case in your list,
choosing is also less strategic than shuffling when considering several games: Shuffling forces you to make different choices in different games, choosing splits always gives you the same choice (namely for the better opening split).

I think the 8th case of your list in which shuffling improves strategy is fairly common, certainly more than 1/8=12.5%.

If the best 4/3 is obvious 50% of the time, it's obviously better than any 5/2 50% of the time, and the best 5/2 is not obvious 50% of the time, you get 12.5%. Which of those 50%s you disagree with?

There's no reason that ANY of these three probabilities should be exactly 50%. Why should they?
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: Awaclus on April 10, 2021, 06:10:54 am
There's no reason that ANY of these three probabilities should be 50%.

What should they be?
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: segura on April 10, 2021, 06:49:27 am
Of course it is trivially true that generally more options imply more choices. It is also true that adding a powerful option makes the decision easier. If you can checkmate, there is no need the consider the other 29 possible moves.
But on average the first point matters more as those powerful, trivial decisions are rare.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: scolapasta on April 10, 2021, 04:11:54 pm
Reading through this gave me a thought:

I generally agree that I'd rather randomize my starting hand, but it does sometimes feel unfair when the first player gets the better option of 5/2 or 4/3 (when it's obvious which of those is better), and the 2nd player does not.

One thing we did try was that the 2nd player gets the same hands as the 1st player, but now I have a new idea: what of the 2nd player got the choice? they could choose the same hand OR they could choose to shuffle. That could give them a slight advantage and possible balance the already existing first player advantage (though in many games, it may not make any difference if they shuffle and get the same thing anyway).

In practice, I may never actually do it, but in theory it's interesting to at least consider.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: spineflu on April 11, 2021, 10:51:07 am
Reading through this gave me a thought:

I generally agree that I'd rather randomize my starting hand, but it does sometimes feel unfair when the first player gets the better option of 5/2 or 4/3 (when it's obvious which of those is better), and the 2nd player does not.

One thing we did try was that the 2nd player gets the same hands as the 1st player, but now I have a new idea: what of the 2nd player got the choice? they could choose the same hand OR they could choose to shuffle. That could give them a slight advantage and possible balance the already existing first player advantage (though in many games, it may not make any difference if they shuffle and get the same thing anyway).

In practice, I may never actually do it, but in theory it's interesting to at least consider.

when i was first taught to play back in... 2010? the person teaching me had a house rule that you started with your whole deck in hand and did your first two turns as one (with two buys).
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: GendoIkari on April 11, 2021, 11:04:32 am
Reading through this gave me a thought:

I generally agree that I'd rather randomize my starting hand, but it does sometimes feel unfair when the first player gets the better option of 5/2 or 4/3 (when it's obvious which of those is better), and the 2nd player does not.

One thing we did try was that the 2nd player gets the same hands as the 1st player, but now I have a new idea: what of the 2nd player got the choice? they could choose the same hand OR they could choose to shuffle. That could give them a slight advantage and possible balance the already existing first player advantage (though in many games, it may not make any difference if they shuffle and get the same thing anyway).

In practice, I may never actually do it, but in theory it's interesting to at least consider.

when i was first taught to play back in... 2010? the person teaching me had a house rule that you started with your whole deck in hand and did your first two turns as one (with two buys).

We used to play that way as well. We wouldn’t even take turns; everyone would just grab 2 cards adding up to cost 7 or less and shuffle them into their starting deck. Of course this was before Nomad Camp.
Title: Re: Variants to make the game more fair & less luck dependent?
Post by: emtzalex on April 11, 2021, 05:53:07 pm
Another thing I would point out is that luck dependence and strategy aren't entirely separate aspects of the game. At times, the decision of whether or not (or to what extent) to make your success dependent on luck is itself a strategic question. A very clear example of this is laid out in the strategy article for Treasure Map (https://dominionstrategy.com/2012/02/03/seaside-treasure-map/):

Quote from: theory
Because you can’t open with a pair of Treasure Maps, at a minimum, it will take at least three turns to get 2 Maps, another 2 to hit a reshuffle, and at that point you have to rely on luck . . . Your odds of hitting before the third reshuffle without help are a mere 29 percent . . . Now, 29% is pretty bad in a 2-player game.  But Treasure Map is one of those cards that subtly gets better with more players: you don’t want to be winning just 29% in a two-player game, but 29% looks pretty darn good when you’re sitting in fourth position in a 4-player game against three people who are all better than you.

Now, Treasure Map is the most blatant example where a player has a choice whether or not to make luck a bigger element of the game, but there are other, subtler ways it can happen. On the first discard with Storeroom (assuming you are playing it terminally), the question of whether or not to discard Silvers depends in part on the probability that they will be replaced by a Gold/Platinum (i.e. how good of a bet it is), but also on all of the surrounding circumstances: Will hitting $8 mean you win the game? Will failing to hit it mean you lose?