Weighted Card Draw

[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.

OK back to question than

- is The weight remain the same throght all trun and age if u reset it?
- Will the number of card left from each age change the weight if u reset it?

[Logitude]

- is The weight remain the same throght all trun and age if u reset it?

I think the answer is yes.

- Will the number of card left from each age change the weight if u reset it?

No. The numbers in the table need to be low whole numbers to have much effect. I don't think there's much variation between ages to account for. If one type of card was drawn more during an A round, I think it's fine to reset its weight during the B round unless it runs out, in which case I make that weight zero.

[chrisstoni]

I didnt read the exact analysis on this, but in my 6 games it became apparent, that the current card draw option only has a very minor effect.

That regularly leads to rounds in which 1 player can do close to nothing. Several of my 6 games (all 2p) i was lacking 1 resource and just nothing came up for 4-6 rounds. Be it Gold, Stone, Food, Stability. That was very annoying and something which i very rarely experienced with the "real" semi-official card draw rule from the BGG forums.

So i suggest to use their numbers, which is for 2p max 5 blue+red and max 2 every other color. This would vastly decrease the luck/randomness and therefore increase the game by a lot.

I like that you brought up this thread. Also, great implementation of Nations in general!

[Logitude]

Overview:

The suggestion in the rule book is to use weights equal to the base cards, which has 8 buildings and 4 of everything else per age.

The semi-official variant is to use card limits. I think limiting the cards is a much easier way to refill the progress board in person. In the online implementation, that doesn't need to be a consideration. Also, there is not a single set of limits. For instance, there's this simpler one and this more precise one.

Two problems with the suggestion in the rule book though are that the base set doesn't have natural wonders and that it doesn't scale with the number of players. I've taken a stab at using weights, like in the rule book, and scaling with natural wonders included:

Details:

CardWeights.png (25 KiB) Viewed 605 times

"Deck" shows the number of cards in each age deck with all of the cards included. (The Age 1 deck has one fewer golden ages (8), and the Age 4 deck has one fewer natural wonders (4).) "Base" is just the base cards per age (no advanced, expert, or Dynasties cards). "Total" is the sum of the weights across all card types. "Board" is the number of progress cards on the board at the beginning of each round. "Ratio" is Total/Board.

You can see that the base set has 8 buildings per age and 4 of everything else. In other words, buildings are about 2x the other types of cards. For different player counts, I have scaled the weights with similar ratios to each other and to the number of cards on the board. I bumped up the priority of militaries since that can be a sore spot.

Analysis:

Here is the effect on 2-player for buildings. This time, the middle is using the simple card limits linked above, not what's implemented on the site now.

weighted_6.png (6.52 KiB) Viewed 605 times

You can see that for both the hard limit and the weighted probability, the chance of getting 0 or 1 building went down. You're most likely to get 2 or 3. With weighted, you have some chance to get 6 or 7, but with very small probability. The result is that limits and weighted are similar for 2-player.

The story is slightly different for 4-player:

weighted_7.png (6.84 KiB) Viewed 605 times

You can see above that the hard limit cuts off the Gaussian distribution at the limit and adds the probabilities of 7+ to the probabilities of 5 and 6. The weighted card draw allows the distribution to continue beyond 6 while tightening the standard deviation, making it less likely you get 1 or 2 buildings.

Conclusion:

Overall, I like this approach. It uses the rule book's suggestion, and I think it results in desirable distributions.

I am undecided on whether to reset the weights between the A and B rounds of each age. The potential downside is that it makes the B rounds too predictable, but since the ratios are about 2.75, not 2.0, you won't be able to predict the exact distribution.

I think, as I said before, that I won't include the leftover cards in the counts. So the question is whether to reset between every round or not.

Thoughts?

[Kayser]

Weighted sounds nice, and I would be OK with either reset option (every Age or every Round).

[ga683919]

Hi carefully read through the post here are some more question and predciton

- Does your Analysis base on【every card is removed from a round】than【refill】?, u might want to run with number that only over half of the card is replace( row3 >row1) and check if the number is still effective

- in reality, 2~3 player likely have only slightly over 2/3 card refille, 3~6 player likely to have most of the space refill, different buying power

- If the core issue is one player remaining【domination of certain type of card】
Reset between A/B round will likely still result of not getting desire card( like only one red for 2 turn) since the ratio is the same, as you said not resetting makes prediction , but is already doable if u have a list of remaining cards, and the predction is not exact.

- vote for not reset betweem A/B, this setting will very likely to fix the problem of one player dominate a certain card , in normal conditon, after a burst of one color, it should be normal for other card to show more as well. and liklyhood of less card in A show more in B, is a good sign

[Logitude]

The only difference not counting the remaining cards would make is reducing the "Board" number. It would slightly shift the distributions to the left.

OK, one vote for not resetting the weights for B rounds.

[Logitude]

I checked, and the change with drawing 2 fewer cards is barely noticeable in the histogram, even for 2 players.

[ga683919]

so far only i have a dirct vote of reset weight every ageXD

does that mean we can give it a shot now?

i seem to understand why u do not want to implaint too many experiment. u have to keep all setting avaiavle for previous or on going game

[markop4]

Personaly I think that game should stay as it is. Life is not always fair. Sometimes you do everything right, but result is bad. It is un-predictable. So it is the game of nations. Normaly I play with my friend and we are making quite a ritual when drawing the cards and throwing a cube who will start the game, when first set of cards is already displayed. Only thing regulated could be (by my opinion) that order for drawing cards and order who begins the play is distrubuted amoung players fairly..