Page 1 of 4

Weighted Card Draw

Posted: November 29th, 2025, 5:15 am
by Logitude
I have an idea!

The Idea:

For the card draw house rule, I tried to strike a balance between making the game too predictable and too random. I can see now from the data that the limits I chose are barely below what you get with random draw anyway, so they rarely kick in.

However, there are reasons to not simply lower the limits. One reason is that lower limits can complicate the implementation of Victoria Falls.

I think I have a solution that keeps the current hard limits while balancing out the card draw in a way that strikes a better balance between predictability and randomness.

The idea is to use weighted probabilities. In addition to being limits, the numbers in the table become the weighted probability that a given type of card will be drawn:

Image

The trick is that once a particular type of card has been selected, the number for that type of card gets reduced by one for the weighting of drawing the next card.

This could be implemented in person by writing the types of cards on slips of paper and putting them into a hat. For 4 players, you'd put 7 slips of paper in the hat that say "Building", 3 that say "War", and 5 for each other type of card. Then you split the deck by card type and shuffle each of those decks. When you draw a slip of paper from the hat, draw that type of card. Don't return any slips of paper to the hat until the next round. And even then, count the number of cards that stay on the board of each type, and don't return the slips for those cards. If you ever draw a slip of paper and there are no remaining cards of that type, keep that slip of paper aside and draw again.

In other words, as you draw cards of a certain type, the probability that you draw more of that type goes down, hence the probability that you draw something else goes up.

The Data:

I ran some experiments. I tried random draw (Random), the current card-draw-limit house rule (Limits), and the proposed weighted-probability card draw (Weighted). For each method, and for each player count, I filled the progress board 1000 times as if it were round 1A.

One metric I collected is how often there wasn't every type of card:

weighted_1.png
weighted_1.png (4.51 KiB) Viewed 973 times

and how often there wasn't every type of non-war card:

weighted_2.png
weighted_2.png (4.98 KiB) Viewed 973 times

I think the above shows that the current house rule doesn't have much impact, while showing that the proposal has an impact without being too severe.

Another set of metrics I collected was histograms of how many of a particular type of card made it to the progress board. Here are the distributions for buildings, colonies, and wars, for 4 players:

weighted_3.png
weighted_3.png (6.83 KiB) Viewed 973 times
weighted_4.png
weighted_4.png (6.18 KiB) Viewed 973 times
weighted_5.png
weighted_5.png (6.01 KiB) Viewed 973 times

As one might expect, the distributions are all roughly Gaussian. Again, the random draw and hard limits are not all that different. The one exception being wars because there are a bunch of wars in the deck.

The Analysis:

The weighted card draw appears to generally reduce the standard deviation, which means increased consistency. It does this without needing reduce the hard limit. You can still get 7 buildings, just with much lower probability. It happened 1/1000 in my experiment.

With the weighted card draw, the average number of buildings drawn went down slightly, from ~3.5 to ~2.8, while the number of other non-war cards went up from ~1.4 to ~2.0. Perhaps of interest, 2.0 * 7/5 = 2.8, so the average for buildings is proportional to its limit of 7 and other cards to their limit of 5. Wars have an average of ~1.2, which is 3/5 of 2.0, so same story. Also, wars go back to being Gaussian instead of a somewhat uniform distribution between 1, 2, and 3.

I think the weighted card draw strikes a much better balance between consistency and randomness than the current hard limits. I don't like having lower hard limits, in part because it completely removes the possibility of having more of that type of card. Also, when there are many of each type of card in the deck, the probability of the next card being any given type barely changes, whereas the weighted card draw centers the averages proportional to the initial weights while still allowing for reasonable variance in each category.

The Question:

What should I do?

I like the proposed weighted-probability card-draw method. I also think the current house rule isn't doing much. For these reasons, I think it's best to basically replace the current house rule with the new one.

My current thinking is I have a cut-over where the "Card Draw" house rule starts meaning the weighted probability method instead of the simple hard limits. Any match started before that will continue to use the simple limits. This is necessary because the matches need to play out the same way given the same inputs.

Another option would be to retain the ability to select the current card-draw house rule, either indefinitely or during a phase-out period. I am not in favor of this since the current house rule is close to not having a house rule.

The Request:

Please provide your opinion now. This is your chance to influence the site and potentially your enjoyment of it.

Re: Weighted Card Draw

Posted: November 29th, 2025, 8:03 am
by ga683919
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)

We had a similar house rule as “garentee”. Instead of having a cap limits. Every new draw has a minimum of at least 1 of each card shows up on the board. Then goes to random

I believe the weigh probability should not count the card currently on board(or at least not when age change) it could cause a potential issue of certain cards are not showing up
(Ex: leaving a lot of unwanted blue/ red. Causing new age card less likely to show)

Having a weigh probability selection does seem to run better reducing the extreme. But will the modification selectable ?
( less war / less battle/ less advisor etc)?

Re: Weighted Card Draw

Posted: November 29th, 2025, 11:38 am
by Kayser
I like this as a ”more balanced” approach. It’s better than the first one.
Did you consider doubling the balancing over Eras instead of rounds? It would perhaps retain the variety/volatility and create weird ”fun” situations, but they’d be balanced out the round after, so no more 4-5 rounds without military but still have a fair chance to create occasional rounds without them.

Re: Weighted Card Draw

Posted: November 29th, 2025, 1:01 pm
by Logitude
I’m not sure, but maybe it is better to ignore the leftover cards. I would like more people to chime in on that decision.

I don’t plan to make the limits configurable. Any house rule is already a community-fragmenting feature. For better or worse, I think we need to compromise and live with that.

I hadn’t thought about stretching the limits across ages. Now that I have, I don’t think it would be better. It means you would oscillate between more random card draw in the A rounds and having a very good idea of what to expect in the B rounds.

Re: Weighted Card Draw

Posted: November 29th, 2025, 5:06 pm
by Fiyero
What is the most important problem to solve by adjusting the deck weights? Having a clear answer for that will make it easier to decide on the best choice of weights.

I suspect the goal is to avoid a game state where someone has a commanding lead in military or buildings, and then no military or buildings appear for multiple rounds. But in my recollection (~80 games) that has only happened a handful of times. And IMO the games where it does happen are interesting and memorable, even if not as competitive.

Re: Weighted Card Draw

Posted: November 29th, 2025, 5:34 pm
by Mr_Vandal
I suspect the goal is to avoid a game state where someone has a commanding lead in military or buildings, and then no military or buildings appear for multiple rounds. But in my recollection (~80 games) that has only happened a handful of times. And IMO the games where it does happen are interesting and memorable, even if not as competitive.
Exactly this, this is what makes Nations interesting, and very different from Through the Ages. I respect the Card Draw as something more "pure euro" people might want, but I would never play it or take part in a tournament using it.

Re: Weighted Card Draw

Posted: November 29th, 2025, 11:45 pm
by Logitude
For me, I find games less fun when the cards fall in my lap or someone else's. Unless someone manages to defy the odds, I might remember the match more — as being less enjoyable.

I want difficult choices, like, "Is it better to go for a colony, a stability building, a military upgrade, a good advisor, or a good wonder first this round?" If the cards offer a bunch of one thing and one of another, then I buy the one, without the enjoyment of evaluating the possibilities.

At least in asynchronous tournaments with multiple matches per round, the variance gets averaged out some and the more-skilled players end up advancing most of the time. However, I prefer to not have any one match that's just a complete bust for any player.

For me, one of the reasons I prefer Nations over Through the Ages is that Through the Ages has card draw each turn. I dislike one player having access to cards that the previous player didn't. I like being able to read out a round in Nations once the event is revealed. Another is that Through the Ages has a take-that mechanic where you have to decide who to target when you attack, but that's less relevant to this discussion.

For me, I think the large decks create enough card-draw variance to keep things interesting due to the variance within each type of card. My goal is to rein in the variance that leads to heavily favoring one player or creating uninteresting turns.

Re: Weighted Card Draw

Posted: November 30th, 2025, 12:57 am
by SirOwnzalot
So long as any weighted or house card rule implementation is kept an optional choice in setting game parameters... choices are nice :D

However to me the complete randomness/unpredictability of the draw is an essential element that needs to be maintained, as it is a core part of what Nations strategic depth is.

A random draw, along with the mayhem that the events can then add to the mix, ensures noone can perfectly plan an optimal path every game or that certain nations can expect to be continually fed a card type that it needs, by being "guaranteed" at least 1 of a certain card type to each round; preventing what can be very deterministic openings.

This is what is so captivating about nations and that it forces you to adapt on the fly.

This is what creates such memorable game moments and matches.

~

Sometimes you are the bug, sometimes you are Rome :lol:

Re: Weighted Card Draw

Posted: November 30th, 2025, 2:01 am
by ga683919
In a addition, i think both the 【hand limit】 and the new 【weight】 should both exist, is also a better way to test out how the outcome goes while maintaining all the current game ongoing

For now, what i see and play here are mostly 2~3 player game, where the 【denial】and 【serire of no card】show are the most server
2~3 player generally has less buying power to clear the row of card, it naturally makes refresinh card less both in number and chance

which is why i prupose not to count the remaining card on board when doing the weight prob. simplay the distrbution itself

how card 【left on board】 likely effect the next card drawn is also a unfavor preduction , we can predict the card likely or not base on both 【left on board】 and 【purchased】, cause thats the natural effect of a deck, u can count cards.
but lettiing card type left on board only to effect the weight might cause a very out of game situation where u 【control】certain card to show more/less

Both house rule in my take are having the same goal "cutting down the extreme outcome and card hording, having a more competitive and consisntcy

Perhapse should run more tiral or augmant on 2 and 3 player game, that is the event of what u metion more likely to happend

Re: Weighted Card Draw

Posted: November 30th, 2025, 2:20 am
by Fiyero
Logitude wrote: November 29th, 2025, 11:45 pm I want difficult choices, like, "Is it better to go for a colony, a stability building, a military upgrade, a good advisor, or a good wonder first this round?" If the cards offer a bunch of one thing and one of another, then I buy the one, without the enjoyment of evaluating the possibilities.
Gotcha. I also like increasing the decision space on the first action. But I think that can happen when there are 0 or 4 buildings, perhaps even more so than if there are 1-2 buildings.

I wonder if a more explicit cap just for wars would be a simple solution to create better distributions. Since wars are the only card type that can't be bought more than once per round, they can junk up the decision space. Maybe max 2 wars drawn per round or 5 per age.