Weighted Card Draw

[Logitude]

First of all. The stats shows ur limit does already have an impact.
We have player already sense how it makes military dominance nation less winnable ( which is a good thing)

I disagree that the data shows the current limits having much impact. Except for wars, the two left histograms look similar to me, as well as the "Random" and "Limits" columns of the tables, keeping in mind the data has noise.

Here's another histogram showing actual matches that have been played, only counting ones with the current house rule enabled. In those matches, there have been a total of 2924 rounds where the progress board has been filled. In 2448 of those rounds, not a single card was discarded due to the house rule.

discards.png (3.87 KiB) Viewed 709 times

Of the total 636 cards discarded, 252 of them were wars.

[Kayser]

More than one war can still play a very significant role. Firstly, they are different in terms of penalties. Secondly, they take up space, which is actually an element of variability I like. Thirdly, a war left on row 3 appears on row 1 the next round, which can be highly significant.

Specifically, two wars on row 3 at the start of a round guarantees at least one war on row 1 the round after (barring an Alhazen swap-out). I like that kind of situation.

[ga683919]

True, from the prospective of 【does it has effect】, ur data shows little performance that takes effect

However, turning thoes war down already shows it has it effect. it depends on how we want" everything to show" not "avoid too much of somthing"

the weight prob does generate datawise even distribution. but does even draw help the matter we currently discuss with
" winning player winmore"

should we start with the element of what kind of condition this will occur?

"Not showing something" does look like a common cause of player monolopying a certain type of card,
like haveing 【no red】 horde the battle and colony for one player

having at least one of someting likely to show does somehow helps, but also does not prevet from it being block by player

so if we want to play the weight prob, will the distrbution more likely to be "1 of each kind" filling for the future?

ur hat-explation help a bit more understnading, just not sure if stay on board card comes with unwanted outcome again

sometime, is better to have a surge of something in later turn" ususally 2+" is how it can aviod dominaion in 2~3 player game

in 4~5 player game, is more likely of how player plays around, there are enough buying power to utilita most card other than war

[Logitude]

The reasoning behind the house rule as described on BGG is that Nations has a base deck, which has certain ratios of cards. It also has the advanced, expert, and now Dynasties decks. When you combine the decks, even if you keep the ratios the same, it's more likely you'll get clumps of the same type of card. In fact, this is brought up in the rule book, where it states,

"For balanced Progress Card decks, construct the decks for each age by starting with the base cards and then exchange some base cards with advanced and/or expert cards of the same type as the exchanged base card (e.g. replace a base set Advisor with an expert Advisor)."

The house rule is a different way to enforce something similar. The house rule on BGG imposes hard limits on card types. That's largely for simplicity of implementation. I could instead do what the rule book suggests, selecting some number of each type of card ahead of time so that the total of each type matches the base deck. However, that doesn't work for more than 4 players and doesn't take into account Dynasties.

I think the weighted card draw, while trickier to implement in person, is a better solution to the problem of clumping, and is easy to implement in software.

[Logitude]

Certainly any one card can affect the outcome of a match at times. No dispute there.

[ga683919]

The reasoning behind the house rule as described on BGG is that Nations has a base deck, which has certain ratios of cards. It also has the advanced, expert, and now Dynasties decks. When you combine the decks, even if you keep the ratios the same, it's more likely you'll get clumps of the same type of card. In fact, this is brought up in the rule book, where it states,

"For balanced Progress Card decks, construct the decks for each age by starting with the base cards and then exchange some base cards with advanced and/or expert cards of the same type as the exchanged base card (e.g. replace a base set Advisor with an expert Advisor)."

The house rule is a different way to enforce something similar. The house rule on BGG imposes hard limits on card types. That's largely for simplicity of implementation. I could instead do what the rule book suggests, selecting some number of each type of card ahead of time so that the total of each type matches the base deck. However, that doesn't work for more than 4 players and doesn't take into account Dynasties.

I think the weighted card draw, while trickier to implement in person, is a better solution to the problem of clumping, and is easy to implement in software.

me trying to dumbdown the question
So
- A bigger/ thicker deck but only the same space， getting no show + one tyye card flode causeing bad experience
- try to equalise card showing chance and patterm more evenly, less 【extreme】
- 【CAP】way shows little effect making card show balance, so we play with chaosbag methond 【WP】 of drawing and refilling the chance every round

GLipse of idea
- sound soild, giving a higher chance for no show or less show card likely appear regardless of space left


Following Question
1. We do not alther with thier Proportion from the original deck size (increase/decreas the hat slip of something from start?)
2. Does Age matter? (weight changed/ distrubion change)
3. will both Cap and WP can be used together?
4. how does counting what's left on board, withouth couting left on board makes the different in stats?

[Logitude]

Following Question
1. We do not alther with thier Proportion from the original deck size (increase/decreas the hat slip of something from start?)
2. Does Age matter? (weight changed/ distrubion change)
3. will both Cap and WP can be used together?
4. how does counting what's left on board, withouth couting left on board makes the different in stats?

1. I chose the numbers in the current table partly based on the distribution of the deck, and partly based on what cards are more important to see more of, hence a low number for wars for example. I chose numbers that add up to roughly 2.5 times the number of cards available on the progress board each round.

2. There is some variation by age, but not much. Here's a card list, BTW:
https://docs.google.com/spreadsheets/d/ ... =338278585
I have not verified its accuracy.

3. Since the scheme using weighted probability involves decrementing the weight for each type of card when it is drawn, the hard limits are implied by the scheme. Without decrementing, I don't think the weighted probability would have much effect.

4. I don't know, but I think you've convinced me to not count them.

[ga683919]

Following Question
1. We do not alther with thier Proportion from the original deck size (increase/decreas the hat slip of something from start?)
2. Does Age matter? (weight changed/ distrubion change)
3. will both Cap and WP can be used together?
4. how does counting what's left on board, withouth couting left on board makes the different in stats?

1. I chose the numbers in the current table partly based on the distribution of the deck, and partly based on what cards are more important to see more of, hence a low number for wars for example. I chose numbers that add up to roughly 2.5 times the number of cards available on the progress board each round.

2. There is some variation by age, but not much. Here's a card list, BTW:
https://docs.google.com/spreadsheets/d/ ... =338278585
I have not verified its accuracy.

4. I don't know, but I think you've convinced me to not count them.

So
- You do alter the weight (for good and needed card)，so this is adjustable
- the accuracy will matter in following proposal
- i show unwanted concren cross age, so Dont count the remaining card on board , count the remaing card in deck


Idea
1. generate a 【base】/【remaing】 portion of each type progress card base on 【current age】/what age of card u will be giving
2. generate A 【Factor】 base on ur answer 1 ( ex: building 2.5 war 0.5 colony 1 ), comes up with 【WP】
3. distribute the card base on your 【WP】for the this round

- protion of card in a same age is limited, this makes no show in age less likely to happend (a lot of red show up/ less red next round)
- You can count card, so couting or expcting card from the same age is doable( i doubt ppl be that serious), but shouldnt happend or have effect between age
- this should not make victoria fall a problem, since this should use the same way without problem


see how this plays out in stats, or if there is way to test it
sorry im clueless comes to programming

[Logitude]

I don’t completely understand what you’re describing, but I wonder if it works out to be what Kayser proposed, which is to not reset the weights between the A and B rounds of each age.

[ga683919]

I don’t completely understand what you’re describing, but I wonder if it works out to be what Kayser proposed, which is to not reset the weights between the A and B rounds of each age.

Yea, Pretty much the same. just mindful the different deck size of each age

Come to think about it, porb need to check the different of resetting and not resetting the weight

IS the weight a fix number accross all age? or does the weight itslef change everyturn