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Author Topic: Variants to make the game more fair & less luck dependent?  (Read 834 times)

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silverspawn

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Re: Variants to make the game more fair & less luck dependent?
« Reply #25 on: April 07, 2021, 01:54:49 pm »
0

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.
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TerrySpeed

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Re: Variants to make the game more fair & less luck dependent?
« Reply #26 on: April 07, 2021, 09:47:48 pm »
0

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.
« Last Edit: April 07, 2021, 09:59:28 pm by TerrySpeed »
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Re: Variants to make the game more fair & less luck dependent?
« Reply #27 on: April 08, 2021, 08:40:47 am »
+4

The purpose it serves is to encourage divergent strategies. There are posts in the forum where Donald X. explains his reasoning.
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GendoIkari

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Re: Variants to make the game more fair & less luck dependent?
« Reply #28 on: April 08, 2021, 09:04:36 pm »
0

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.
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Re: Variants to make the game more fair & less luck dependent?
« Reply #29 on: April 08, 2021, 10:59:54 pm »
+2

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.
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Re: Variants to make the game more fair & less luck dependent?
« Reply #30 on: April 09, 2021, 03:50:52 am »
+1

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.
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emtzalex

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Re: Variants to make the game more fair & less luck dependent?
« Reply #31 on: April 09, 2021, 12:54:21 pm »
0

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.
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Re: Variants to make the game more fair & less luck dependent?
« Reply #32 on: April 09, 2021, 04:54:41 pm »
+1

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 to spend on a turn adds the skill of choosing of how to spend that . Restrictions on what you are allowed to do doesn't just take away a skill; it replaces it with a different skill.
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Re: Variants to make the game more fair & less luck dependent?
« Reply #33 on: April 09, 2021, 05:07:24 pm »
+2

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 to spend on a turn adds the skill of choosing of how to spend that . 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.
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Re: Variants to make the game more fair & less luck dependent?
« Reply #34 on: April 09, 2021, 05:14:22 pm »
0

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)
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GendoIkari

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Re: Variants to make the game more fair & less luck dependent?
« Reply #35 on: April 09, 2021, 05:18:45 pm »
0

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 to spend on a turn adds the skill of choosing of how to spend that . 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.
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Re: Variants to make the game more fair & less luck dependent?
« Reply #36 on: April 09, 2021, 06:00:35 pm »
+1

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 to spend on a turn adds the skill of choosing of how to spend that . 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 is not obvious what the best 4/3 is, it is not obvious what the best 5/2 is, and it is not obvious if any of the 5/2s are better (choosing is more strategic than shuffling)
  • It is not obvious what the best 4/3 is, it is obvious what the best 5/2 is, and it is not obvious if the best 5/2 is better (choosing is more strategic than shuffling)
  • It is not obvious what the best 4/3 is, it is not obvious what the best 5/2 is, and it is obvious that 4/3 is better than 5/2 (choosing is exactly as strategic as shuffling)
  • It is not obvious what the best 4/3 is, it is obvious what the best 5/2 is, and it is obvious that 4/3 is better than 5/2 (choosing is at least as strategic as shuffling)
  • It is obvious what the best 4/3 is, it is not obvious what the best 5/2 is, and it is not obvious if any of the 5/2s are better (choosing is more strategic than shuffling)
  • It is obvious what the best 4/3 is, it is obvious what the best 5/2 is, and it is not obvious if the 5/2 is better (choosing is more strategic than shuffling)
  • It is obvious what the best 4/3 is, it is obvious what the best 5/2 is, and it is obvious the 4/3 is better (choosing is exactly as strategic as shuffling)

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

  • It is obvious what the best 4/3 is, it is obvious that it's better than any of the 5/2s, and it is not obvious which 5/2 is the best 5/2 (shuffling is at least as strategic as choosing)

To save space, I only included the cases from the 4/3 perspective.
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silverspawn

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Re: Variants to make the game more fair & less luck dependent?
« Reply #37 on: April 09, 2021, 06:39:16 pm »
+1

If you make the set of options smaller, obviously finding the optimum becomes easier.
« Last Edit: April 09, 2021, 07:17:30 pm by silverspawn »
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Re: Variants to make the game more fair & less luck dependent?
« Reply #38 on: April 09, 2021, 06:58:33 pm »
+3

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.
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Re: Variants to make the game more fair & less luck dependent?
« Reply #39 on: April 09, 2021, 07:16:52 pm »
0

Um. Yes. I'm stupid.
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emtzalex

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Re: Variants to make the game more fair & less luck dependent?
« Reply #40 on: April 09, 2021, 08:28:15 pm »
0

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.
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Re: Variants to make the game more fair & less luck dependent?
« Reply #41 on: April 10, 2021, 02:52:18 am »
+2

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. 
« Last Edit: April 10, 2021, 02:53:59 am by GendoIkari »
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Re: Variants to make the game more fair & less luck dependent?
« Reply #42 on: April 10, 2021, 04:45:49 am »
+1

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.
« Last Edit: April 10, 2021, 04:46:50 am by Awaclus »
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Re: Variants to make the game more fair & less luck dependent?
« Reply #43 on: April 10, 2021, 05:18:48 am »
0

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%.

 
« Last Edit: April 10, 2021, 05:24:58 am by Holger »
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Re: Variants to make the game more fair & less luck dependent?
« Reply #44 on: April 10, 2021, 05:32:52 am »
0

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?
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Re: Variants to make the game more fair & less luck dependent?
« Reply #45 on: April 10, 2021, 06:06:31 am »
0

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?
« Last Edit: April 10, 2021, 06:11:42 am by Holger »
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Re: Variants to make the game more fair & less luck dependent?
« Reply #46 on: April 10, 2021, 06:10:54 am »
+1

There's no reason that ANY of these three probabilities should be 50%.

What should they be?
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Re: Variants to make the game more fair & less luck dependent?
« Reply #47 on: April 10, 2021, 06:49:27 am »
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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.
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Re: Variants to make the game more fair & less luck dependent?
« Reply #48 on: April 10, 2021, 04:11:54 pm »
+1

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.
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Re: Variants to make the game more fair & less luck dependent?
« Reply #49 on: April 11, 2021, 10:51:07 am »
0

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).
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