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[jeb56]

The last part of the discussion revolves around the interpretation of

... Do not use the same card to choose ...

Some people interpret this as

... Do not use the same card draw to choose ...

These people are content if the second draw happens to be the same card as the first draw.

Others require the second card to be different.

[Watno]

Do not use the same card to choose whether or not to use Shelters as you use to choose whether or not to use Platinum and Colony (from Prosperity)

This is the reason why Option 1/3 is the correct one. Option 2 leaves the possibility of getting the same card twice.
It clearly leads to dependancy.

[ftl]

Huh? IF you're guaranteed NOT to draw the same card twice, that leads to dependency.

You have to leave open the possibility of getting the same card twice if you want the two choices to actually be independent.

[Watno]

What I meant is taht the rules clearly demand to have dependancy

[HiveMindEmulator]

I interpreted the "Do not use the same card..." sentence to be part of the example, not a separate rule. It wouldn't make sense for this to be a rule, since you're not required to use a card at all to make either decision.

[ftl]

Yep. For that matter, I think you're not even required to have the probability of using plat/col or shelters to be equal to the fraction of cards which are from prosperity or DA; everyone sort of assumes it has to be, but the rules just say "based on", there's a lot of ways to pick whether to use p/c or sh "based on" the number of cards from an expansion.

[Watno]

I interpreted the "Do not use the same card..." sentence to be part of the example, not a separate rule. It wouldn't make sense for this to be a rule, since you're not required to use a card at all to make either decision.

To me, this doesn't make sense at all, obviously the last card is different than the first.

The rules leave room for other random approaches, but what they suggest is option 1/3

[HiveMindEmulator]

I interpreted the "Do not use the same card..." sentence to be part of the example, not a separate rule. It wouldn't make sense for this to be a rule, since you're not required to use a card at all to make either decision.

To me, this doesn't make sense at all, obviously the last card is different than the first.

Who says you aren't using the last card to decide if you're using Colony/Platinum? Using the first card was merely a suggestion in a different rulebook.

[Schneau]

Since the main thing you want to avoid is using the same card for Prosperity-deciding and Dark-Ages-deciding, Option 3 seems closer to the intent than Option 2.

No, the thing you want to do is have the chance of using Colonies be proportional to the number of Prosperity supply cards and the chance of using Shelters be proportional to the number of Dark Ages supply cards. Option 2 is correct (and different from Options 1 & 3 which are, as reported, the same)

I trust the user who's name is a math pun.

The last part of the discussion revolves around the interpretation of

... Do not use the same card to choose ...

Some people interpret this as

... Do not use the same card draw to choose ...

These people are content if the second draw happens to be the same card as the first draw.

Others require the second card to be different.

I also think this is wise. I think that the rules could be interpreted in different ways, which are all fine in practice (hey, do what makes you happy, right?).

In my interpretation, both Prosperity and DA rules have the following:

the use of [Plat+Col / Shelters] should be determined randomly, based on the proportion of [Prosperity / Dark Ages] cards in use.

As a math person, this clearly says that if X out of 10 of the kingdom cards are [Prosperity / DA], then there should be a 10X% chance of using [Plat+Col / Shelters]. Option 2 satisfies this, but not options 1 and 3. At the same time, the suggestion of not using the same card to decide Plat+Col and Shelters can be interpreted to contradict this. Here, I agree with the excellent point of jeb56, that it can also be interpreted to mean that you use a different card draw to determine Shelters.

Anyway, as I said, both interpretations lead to fine results, and people should do what seems right to them.

[HiveMindEmulator]

the use of [Plat+Col / Shelters] should be determined randomly, based on the proportion of [Prosperity / Dark Ages] cards in use.

As a math person, this clearly says that if X out of 10 of the kingdom cards are [Prosperity / DA], then there should be a 10X% chance of using [Plat+Col / Shelters]. Option 2 satisfies this, but not options 1 and 3.

How do options 1 and 3 not satisfy this? They assign a X/10 chance to use Plat+Col and Y/10 chance to Shelters for X Prosperity cards and Y DA cards.

[Schneau]

the use of [Plat+Col / Shelters] should be determined randomly, based on the proportion of [Prosperity / Dark Ages] cards in use.

As a math person, this clearly says that if X out of 10 of the kingdom cards are [Prosperity / DA], then there should be a 10X% chance of using [Plat+Col / Shelters]. Option 2 satisfies this, but not options 1 and 3.

How do options 1 and 3 not satisfy this? They assign a X/10 chance to use Plat+Col and Y/10 chance to Shelters for X Prosperity cards and Y DA cards.

Ha, I think you're right! 1 and 3 have different joint probabilities (ex. the chance of using both Plat+Col and Shelters together goes from 25% to 27.8% with 5 DA cards, 5 Prosp cards), but the probability of Shelters stays the same and the probability of Plat+Col stays the same. Interesting!

[Powerman]

All three are functionally the same.  Randomly taking out a card doesn't affect the probability.

[RiemannZetaJones]

the use of [Plat+Col / Shelters] should be determined randomly, based on the proportion of [Prosperity / Dark Ages] cards in use.

As a math person, this clearly says that if X out of 10 of the kingdom cards are [Prosperity / DA], then there should be a 10X% chance of using [Plat+Col / Shelters]. Option 2 satisfies this, but not options 1 and 3.

How do options 1 and 3 not satisfy this? They assign a X/10 chance to use Plat+Col and Y/10 chance to Shelters for X Prosperity cards and Y DA cards.

Ha, I think you're right! 1 and 3 have different joint probabilities (ex. the chance of using both Plat+Col and Shelters together goes from 25% to 27.8% with 5 DA cards, 5 Prosp cards), but the probability of Shelters stays the same and the probability of Plat+Col stays the same. Interesting!

I think all three methods are legal.

I interpret the 'do not use the same card' provision of the Dark Ages rulebook to mean that the same card-draw should not be used. That said, the rules leave something to be desired in this area.

The probabilities of using Shelters and Colonies are mandated, but nothing is directly said about the probability of using both Shelters and Colonies. The only thing that is said about the dependence of the two events is the 'do not use the same card' clause, which doesn't literally apply if we use some other method than card-draw to choose whether to use Shelters or Colonies.

There are two interpretations of this clause. First, the 'do not use the same card draw' prohibition, which says 1. you know what the probabilities of using Colonies and Shelters should be and 2. using Colonies does not prohibit the use of Shelters. Point 2. seems reasonable to me, which is why I interpret the rules as meaning 'do not use the same card draw'.

You could however interpret the rules as saying 1. you know what the probabilities of using Colonies and Shelters should be 2. using Colonies does not prohibit the use of Shelters and 3. these probabilities are not independent. This is what the 'draw a card, then draw a different card' interpretation of the rules amounts to. It doesn't make sense that anyone would specifically prohibit the independence using Probabilities and using Shelters, so I reject this interpretation of the rules.

[RiemannZetaJones]

All three are functionally the same.  Randomly taking out a card doesn't affect the probability.

Consider a kingdom in which there is one Dark Ages card and nine Prosperity. Using method 1 it is not possible to get Shelters without Colonies. Using method 2 it is.