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Author Topic: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps  (Read 2346 times)

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Neirai the Forgiven

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A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« on: November 14, 2018, 10:15:37 am »
0

Clickbait title, putting one of my own cards in it, displays my ego...

Anyhow,

I've been working on a randomizer script for Dominion to support my Antiquities set (which officially launches tomorrow!!)

During this I noticed that I was running into a problem with Colonies + Platinums, and Shelters, which is: if you use the stock rules of Prosperity, the chances of the card ever showing up in the game become smaller and smaller the more sets you're rolling with. This is because the formula for including these cards goes something like (Number of Prosperity cards in your Kingdom / 10).

Back when you only owned Dominion, Intrigue, and Prosperity, well, Prosperity was one third of the set and so the inclusion was rather common. Nowadays, if you're like me and you own all of the sets (save Renaissance, Christmas don't be late) and you've created your own 27-card set, the chances are.... I'm not doing the math but the chances of getting Colonies and Platinums according to the written rules are actually significantly less than that of getting any one card in the set.

So, here's what I did.

1) I created an expanded list of "Prosperity-like" cards, which was a list of all Prosperity cards and all other cards that adhered to what Donald X said was the "themes" of Prosperity. Things like alt Treasures (but only ones that provided ways to get richer -- alt attacks for instance were out), VP tokens, non-attack interactions that were beneficial for all players, and cards that interacted with Treasures in a positive way. I did the same thing with Dark Ages, and with Antiquities.

2) That still wasn't good enough so I'm looking at three random Kingdom cards to determine if they are matches; i.e., if any of the three are "Prosperity-like" cards, then Colony and Platinum are in.

Seems to work quite well! I thought you might like to know the thoughts.
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faust

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #1 on: November 14, 2018, 10:36:28 am »
+2

I feel like this is too intricate, and what cards are "Prosperity-like" gives immediate cause for debate.

I think Colonies should just appear at random across all boards. The easiest way to implement this is to create a Landmark that just says "Setup: Put Colonies and Platina in the supply. This does not count towards the total number of Landmarks/Events/Projects".
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majiponi

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #2 on: November 14, 2018, 10:49:32 am »
+1

Treat Empires as Prosperity.
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Fly-Eagles-Fly

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #3 on: November 14, 2018, 10:52:32 am »
+1

I feel like this is too intricate, and what cards are "Prosperity-like" gives immediate cause for debate.

I think Colonies should just appear at random across all boards. The easiest way to implement this is to create a Landmark that just says "Setup: Put Colonies and Platina in the supply. This does not count towards the total number of Landmarks/Events/Projects".
Instead: Add the Colony pile, the Platinum pile, and another Event, Landmark, or Project to the game.
But yeah, I think just always having a chance of them being available would be good. To be honest, though, I don't have Prosperity so wouldn't actually know.
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ObtusePunubiris

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #4 on: November 14, 2018, 11:40:50 am »
+2

I like this idea, but not as much as I like things to be simple.  When this question came up for my group shortly after Empires was released, we decided to go with the simplest of solutions.  We asked ourselves how often we wanted to see those cards and set a flat percentage chance accordingly.  The number we settled on was 20% for both C/P and Shelters (determined separately, or course) and it's worked out nicely for us.
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Holunder9

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #5 on: November 14, 2018, 02:11:51 pm »
+2

I always do it like this: 1 Prosperity / Dark Ages card - chances for Colony / Shelters are 1/3 (just roll a D6). With 2 cards it is 2/3 and with 3 cards from the respective set Colonies respectively Shelters are definitely in the game.
In my experiences this makes up for playing with a collection that is significantly "diluted" by fan cards
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Neirai the Forgiven

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #6 on: November 14, 2018, 04:04:04 pm »
0

I like this idea, but not as much as I like things to be simple.  When this question came up for my group shortly after Empires was released, we decided to go with the simplest of solutions.  We asked ourselves how often we wanted to see those cards and set a flat percentage chance accordingly.  The number we settled on was 20% for both C/P and Shelters (determined separately, or course) and it's worked out nicely for us.

I'm responding to pretty much every post, but quoted this one because it makes a lot of sense.

If I wasn't writing a python script to crunch this all, I'd have done precisely this. In retrospect as well, from a programming perspective I could/should have just put in a 33% chance and left it like that.

This does of course bring up debates about what cards are Prosperity-like and which ones are Dark Ages-like (and which ones are Antiquities-like) and I made calls and made a set of lists. The script will be open source and you can change it as you like.

The benefit of how I did it is that when you have Colonies you're also going to see cards that boost economies. With Shelters, you'll see trash for benefits and live-with-junk cards. With Boulder Traps, you get non-thinning trashers and discard for benefit and discard pile manipulation.
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ObtusePunubiris

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #7 on: November 14, 2018, 04:48:45 pm »
+1

I like this idea, but not as much as I like things to be simple.  When this question came up for my group shortly after Empires was released, we decided to go with the simplest of solutions.  We asked ourselves how often we wanted to see those cards and set a flat percentage chance accordingly.  The number we settled on was 20% for both C/P and Shelters (determined separately, or course) and it's worked out nicely for us.
The benefit of how I did it is that when you have Colonies you're also going to see cards that boost economies. With Shelters, you'll see trash for benefits and live-with-junk cards. With Boulder Traps, you get non-thinning trashers and discard for benefit and discard pile manipulation.

That's an important distinction and is one we considered.  In the end we decided there were enough cards that did those things scattered throughout all of the sets that it wouldn't often be an issue for us.  Even when we do roll up a kingdom that, for example, has C/P, but not much economy, we just consider it another facet of that particular game that we have to build our strategies around.  Of course, that's not the experience everyone is looking for, so I certainly understand preferring to link those things the way you have.
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NoMoreFun

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #8 on: November 14, 2018, 05:00:10 pm »
+4

Rebuild should give a 100% chance of being a Shelters game
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ObtusePunubiris

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #9 on: November 14, 2018, 05:41:35 pm »
+1

Rebuild should give a 10 0% chance of being a Shelters game.  FTFY

Truth be told, I will play with Rebuild, but it is the only card I actually don't like and I don't like it quite a bit.
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ConMan

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #10 on: November 14, 2018, 08:03:27 pm »
+1

I thought about some options a while ago. I would like to see more options for having Colonies and Shelters in games, and I kind of like my third option the best - after drawing your kingdom, flip one card from the kingdom and one from the unused randomisers and if either is from Prosperity then you add Colonies; then do the same to check for Shelters.
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Neirai the Forgiven

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #11 on: November 15, 2018, 11:08:14 am »
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I thought about some options a while ago. I would like to see more options for having Colonies and Shelters in games, and I kind of like my third option the best - after drawing your kingdom, flip one card from the kingdom and one from the unused randomisers and if either is from Prosperity then you add Colonies; then do the same to check for Shelters.

TL;DR: Neirai, who admits to not being able to do probability maths, challenges Method 1 on the basis of the number of total possible Kingdom cards, runs the numbers, and finds that he's more or less wrong although he is hoping for a method that gives approximately 2x higher chances of inclusion.

So there's a problem with this method... and I'm going to try to math it out for you.
Disclaimer: Probability math is one of the few maths I can't seem to get my head around. I'm using online calculators to try do the probabilities but while I'm confident enough to say that my errors aren't going to be so huge that you throw out my argument altogether but.. there's going to be some math errors. Probably take everything I say at +or- 10%.

Okay, so right now in the game there's 25 Prosperity Kingdom cards and 314 Kingdom card options (including Prosperity and Renaissance and just in case I'm confusing, this does not include any fan cards at all)
This gives a chance of drawing a single Prosperity randomizer from a stack of all of them of 7.92%
The chances of getting at least 1 Prosperity card in a 10-card Kingdom is slightly less than 37.7%. I say slightly less because you're actually lowering the chance of a subsequent card by 0.03% every time you add a Prosperity card to the Kingdom (removing it from the pool) and increasing it by approximately the same amount because you're also now dealing with a pool that's one card smaller, and you increase it by about 0.03% whenever you put a non-Prosperity card into the pool because those randomizers are gone and this is why this makes my head hurt.

If you use the standard Dominion rule for colonies, you have basically a 10% chance per Prosperity card, so lets say that the chance of doing it with the base set is 3.77% -- 10% of the slightly incorrect number that I said was the chances of getting a set with at least one Prosperity card in it. Which is disgustingly small btw.

Using your method 1, if I'm understanding it correctly, you would be adding an additional step of looking at one of the remaining 304 kingdoms to check if it was a Prosperity card. If you find one, you have a 100% chance of adding Colonies. Let's say for the sake of argument that there's 1 Prosperity card in our kingdom, and 24 left in the randomizers. This gives us an 7.89% chance of getting another Prosperity card. Mashing the two events together in an online calculator, I get... 11.4% chance of either happening.

Now, actually, I started this by saying there's a problem with this. There isn't really: It gives you an 11.4% chance of either happening in the scenario laid out before. If you had 2 Kingdom cards from Prosperity you get a 14.4% chance. If you pulled 0 Kingdom cards you get and 8.22% chance of getting Colonies anyhow.

I tend to write as I think, and not go back, so I said "there's a problem" but there really isn't. If I implement this, I might do a second pull from both pools to inflate the numbers (you get a 15.2% with 0 kingdoms, etc, I'll have to try it out (running out of time aaaaaaaaa)).

It's definitely a nicer method if you're using physical cards, though.
« Last Edit: November 15, 2018, 11:10:07 am by Neirai the Forgiven »
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faust

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #12 on: November 15, 2018, 11:15:35 am »
+2

he benefit of how I did it is that when you have Colonies you're also going to see cards that boost economies.
It debatable whether Prosperity cards are even better than average for economy boost. A lot of cards in there don't work with a Colony deck, particularly most kingdom treasures.
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ConMan

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #13 on: November 15, 2018, 05:25:16 pm »
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I thought about some options a while ago. I would like to see more options for having Colonies and Shelters in games, and I kind of like my third option the best - after drawing your kingdom, flip one card from the kingdom and one from the unused randomisers and if either is from Prosperity then you add Colonies; then do the same to check for Shelters.

TL;DR: Neirai, who admits to not being able to do probability maths, challenges Method 1 on the basis of the number of total possible Kingdom cards, runs the numbers, and finds that he's more or less wrong although he is hoping for a method that gives approximately 2x higher chances of inclusion.
Yeah, all of my calculations are conditional on "If you have already drawn 10 Kingdom cards and N of them are from Prosperity. Also they were done just after (or possibly just before?) Empires came out, so the ones that involve flipping a card from outside the kingdom will be incorrect now. There are plenty of alternatives, too, depending on the actual result you want (I wanted to introduce some small probability that kingdoms could have Colonies and Shelters regardless of their composition, and also make sure that Colony games don't become too rare as the number of expansions increases - my methods don't necessarily manage both, but they do go some way towards them).
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faust

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Re: A new algorithm for Colonies+Platinum, Shelters, Boulder Traps
« Reply #14 on: November 16, 2018, 02:06:06 am »
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I feel like this is too intricate, and what cards are "Prosperity-like" gives immediate cause for debate.

I think Colonies should just appear at random across all boards. The easiest way to implement this is to create a Landmark that just says "Setup: Put Colonies and Platina in the supply. This does not count towards the total number of Landmarks/Events/Projects".
Instead: Add the Colony pile, the Platinum pile, and another Event, Landmark, or Project to the game.
Well that way you'd never play Colony games without sideways cards.
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