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[Jerk of All trades]

1 rule I like from Androminion is that for plat and shelter use you get a 10% chance per card from that expansion (prosperity and DA).  SO if you had all DA cards it'd be a 100% chance for shelters, 50% with 5.  Simple right?

A quick way to do this is to make a deck of 10 cards with all copper plus 1 gold for each prosperity card in the supply. Draw 1 card, if it's the gold, use platinum.  Then do the same thing again with 1 gold per DA card in the supply.  If you pull the Gold, use shelters instead of estates.

After DA came out we played with shelters every game, but then we realized it makes certain cards like Baron, upgrade and remake a LOT weaker.  And it's ok to have useless cards in the supply, but it was lame having a bunch of cards significantly weaker in every game.  Also we could never decide on when to use Platinum. I still love it when my friends buy remake with poorhouse in the game though. (oh God, so many terminal collisions, ahhh!)

[eHalcyon]

This rule isn't from Androminion.  It comes straight out of the official rules.  IRL, you just use the randomizers for the kingdom cards -- no need to make an extra deck out of Coppers and Gold.

[Jerk of All trades]

Ohh good call!  This was just something we thought of last night after pulling baron/remake with our "always use shelters" convention.

[WheresMyElephant]

This rule isn't from Androminion.  It comes straight out of the official rules.  IRL, you just use the randomizers for the kingdom cards -- no need to make an extra deck out of Coppers and Gold.

Incidentally, if you have access to Androminion, you also have access to Dominion Shuffle and various other apps which do all this for you.

[SirPeebles]

Yeah, shuffle the randomizers.  If the top card is from Prosperity, play with Colony.  If the bottom card (or second card, if your prefer) is from Dark Ages, play with Shelters.

[werothegreat]

See, I just ignore those "rules," particularly since they're only in there because a lot of Dominion players need specific guidelines for when to do something (for some reason).  For IRL games, I'll add Platinum/Colony and/or Shelters if I feel they add to the kingdom.

[eHalcyon]

See, I just ignore those "rules," particularly since they're only in there because a lot of Dominion players need specific guidelines for when to do something (for some reason).  For IRL games, I'll add Platinum/Colony and/or Shelters if I feel they add to the kingdom.

But then how do you discover when they add to the kingdom in ways you didn't expect?

[WheresMyElephant]

See, I just ignore those "rules," particularly since they're only in there because a lot of Dominion players need specific guidelines for when to do something (for some reason).  For IRL games, I'll add Platinum/Colony and/or Shelters if I feel they add to the kingdom.

The funny thing is, some of the best Platinum/Colony games are the ones where a Province rush is viable. And you don't get nearly as many of those with high-powered Prosperity cards in play, making Plat and Colony stronger than they need to be.

[Awaclus]

Yeah, shuffle the randomizers.  If the top card is from Prosperity, play with Colony.  If the bottom card (or second card, if your prefer) is from Dark Ages, play with Shelters.

Why shuffle the randomizers twice? If you have used them to randomize the kingdom, they are shuffled already.

[WanderingWinder]

If you want the choices for colony/shelters to actually be independent, you need to do two picks (with replacement)- if you only do one, since no card is from both prosperity and dark ages, you are more likely to get one or the other, but you never get both.

[SirPeebles]

If you want the choices for colony/shelters to actually be independent, you need to do two picks (with replacement)- if you only do one, since no card is from both prosperity and dark ages, you are more likely to get one or the other, but you never get both.

Deciding ahead of time that the top card determines colony/plat and the bottom card determines shelters is sufficient.  Presuming that you want to probability of one of these being present to be equal to the proportion of cards from that expansion.

Edit:  I see what you mean, Awaclus.  You're right. (Except I forget if one determines colony/shelters before or after selecting a bane)

[jonts26]

If you want the choices for colony/shelters to actually be independent, you need to do two picks (with replacement)- if you only do one, since no card is from both prosperity and dark ages, you are more likely to get one or the other, but you never get both.

Deciding ahead of time that the top card determines colony/plat and the bottom card determines shelters is sufficient.  Presuming that you want to probability of one of these being present to be equal to the proportion of cards from that expansion.

Edit:  I see what you mean, Awaclus.  You're right. (Except I forget if one determines colony/shelters before or after selecting a bane)

We've had this discussion elsewhere, but no, it's not the same. Sampling with and without replacement gives different results. You can do the top/bottom method because it's easier and close to right, but the probability will not be in direct proportion.

EDIT: found it http://forum.dominionstrategy.com/index.php?topic=4638.msg104981#msg104981

[heron]

Edit: Nothing to see here except boasting and false confidence...

No, it really is the same.
That is, if by same you mean using top/bottom card is the same/(or not the same) as drawing a random card from the selected randomizers for plat/colony, replacing it, and drawing another random card for shelters.

If you have 4/10 prosperity cards, there is a 4/10 chance that the first card is from prosperity. If you have 3/10 dark age cards there is a 3/10 chance that the last card is from dark ages. This is indisputable.

If by same you were comparing random draw and replace with random draw and don't replace, well, you were right, and I wasted a post explaining something that was obvious.

But I have to talk about math right now, because I just got honorable mention in a math competition and regained my spot as best freshman in my counties math league!

End math spiel/boasting/confusingness

[SirPeebles]

If you want the choices for colony/shelters to actually be independent, you need to do two picks (with replacement)- if you only do one, since no card is from both prosperity and dark ages, you are more likely to get one or the other, but you never get both.

Deciding ahead of time that the top card determines colony/plat and the bottom card determines shelters is sufficient.  Presuming that you want to probability of one of these being present to be equal to the proportion of cards from that expansion.

Edit:  I see what you mean, Awaclus.  You're right. (Except I forget if one determines colony/shelters before or after selecting a bane)

We've had this discussion elsewhere, but no, it's not the same. Sampling with and without replacement gives different results. You can do the top/bottom method because it's easier and close to right, but the probability will not be in direct proportion.

EDIT: found it http://forum.dominionstrategy.com/index.php?topic=4638.msg104981#msg104981

The probability will still be in direct proportion, but the choices will not be independent.  There will be a bias towards having either both or neither, with a decreased chance of having only one.

Edit:  more specifically, there will be a bias if using the top/bottom method.

[pacovf]

If there is one DA card and one prosperity card, the odds of getting both shelters and colonies are:
-1/100 when shuffling a second time;
-1/90 when using the top/bottom technique.

Not really intuitive, but that's how it is.

[heron]

Argh you're right.
So much for my math brilliance 

Edit: For my 4 Prosperity 3 Dark ages example

With top/bottom:
4/10*3/9=2/15 chance of both.
4/10*6/9+3/10*5/9=13/30 chance of 1 but not the other.
13/30 chance of neither.

With draw/replace:
4/10*3/10=3/25 chance of both.
4/10*7/10+3/10*6/10=23/50 chance of one but not the other.
6/10*7/10=21/50 chance of neither.

[rages at self's incompetence]

[cluckyb]

If you want the choices for colony/shelters to actually be independent, you need to do two picks (with replacement)- if you only do one, since no card is from both prosperity and dark ages, you are more likely to get one or the other, but you never get both.

The rulebook for Prosperty says look at the first one, the rulebook for Dark Ages says pick the last one, so they are not supposed to be independent.

Also you're slightly more likely to get both, both also more likely to get neither, if you don't replace the card you selected for Prosperity before selecting the DA card. (If I have nine cards from Propserty and one from Dark Ages and do not replace my selection, then every game with Shelters must also have Platinum and I have 1/10 odds of that event occurring. If I do replace my selection, the odds drop to 9/100)

[WanderingWinder]

If you want the choices for colony/shelters to actually be independent, you need to do two picks (with replacement)- if you only do one, since no card is from both prosperity and dark ages, you are more likely to get one or the other, but you never get both.

The rulebook for Prosperty says look at the first one, the rulebook for Dark Ages says pick the last one, so they are not supposed to be independent.

Also you're slightly more likely to get both, both also more likely to get neither, if you don't replace the card you selected for Prosperity before selecting the DA card. (If I have nine cards from Propserty and one from Dark Ages and do not replace my selection, then every game with Shelters must also have Platinum and I have 1/10 odds of that event occurring. If I do replace my selection, the odds drop to 9/100)

Actually, they both just say to use the proportion of cards from the set to determine - the top and bottom things are only examples. If you follow strictly to the proportion, i.e. if you assume you want the chances for each are exactly the same as the proportion of kingdom cards from the set, then you need to do the replacement thing.
But I don't think there's really a 'supposed to' going on here.

[SirPeebles]

If you want the choices for colony/shelters to actually be independent, you need to do two picks (with replacement)- if you only do one, since no card is from both prosperity and dark ages, you are more likely to get one or the other, but you never get both.

The rulebook for Prosperty says look at the first one, the rulebook for Dark Ages says pick the last one, so they are not supposed to be independent.

Also you're slightly more likely to get both, both also more likely to get neither, if you don't replace the card you selected for Prosperity before selecting the DA card. (If I have nine cards from Propserty and one from Dark Ages and do not replace my selection, then every game with Shelters must also have Platinum and I have 1/10 odds of that event occurring. If I do replace my selection, the odds drop to 9/100)

Actually, they both just say to use the proportion of cards from the set to determine - the top and bottom things are only examples. If you follow strictly to the proportion, i.e. if you assume you want the chances for each are exactly the same as the proportion of kingdom cards from the set, then you need to do the replacement thing.
But I don't think there's really a 'supposed to' going on here.

No, you don't need replacement for that.  You only need replacement if you want the presence of Shelters and Colonies to be independent of one another.  But not to get the strict proportionality.  In a 2 card kingdom, say Bishop and Fortress, the top/bottom method both give a 50% of both and a 50% of neither.  Overall, you'd have a 50% chance of Colonies and a 50% chance of Shelters; but it wouldn't be possible to have one without the other.  Also, the game would be one of those dreadful Bishop/Fortress games, and really not worth playing out regardless, since you'd just trash all of your starting cards and never buy either Provinces or Colonies.

[theory]

Moved the rest of the topic here: http://forum.dominionstrategy.com/index.php?topic=6405.0

Offtopic discussion is OK but that was so offtopic I think it benefits from its own thread

[serakfalcon]

I usually setup based on randomizers, and I like biasing slightly towards colonies/platinums as well as shelters, so I just shuffle, let a member of the group pick one card (face down), mix the cards up again, and let them pick again, if either card is from Dark Ages or from Prosperity then I add Plat/Colony and shelters appropriately.
It's proportional, so it follows the rules as set in the rulebook, but also it gives a slightly higher chance of playing with those cards, also it avoids arguments like "I thought we'd pick for Prosperity first and then Dark Ages, not the other way around"

[eHalcyon]

I usually setup based on randomizers, and I like biasing slightly towards colonies/platinums as well as shelters, so I just shuffle, let a member of the group pick one card (face down), mix the cards up again, and let them pick again, if either card is from Dark Ages or from Prosperity then I add Plat/Colony and shelters appropriately.
It's proportional, so it follows the rules as set in the rulebook, but also it gives a slightly higher chance of playing with those cards, also it avoids arguments like "I thought we'd pick for Prosperity first and then Dark Ages, not the other way around"

That should double the chance of either one appearing.

[serakfalcon]

That should double the chance of either one appearing.

Sort of. It doesn't dramatically affect the odds of only one appearing, but it dramatically increases the chances of both appearing.
Though it levels out as you increase in numbers, for example, the odds of a 5/5 Prosp/DA are exactly the same either method.

[WanderingWinder]

That should double the chance of either one appearing.

Sort of. It doesn't dramatically affect the odds of only one appearing, but it dramatically increases the chances of both appearing.
Though it levels out as you increase in numbers, for example, the odds of a 5/5 Prosp/DA are exactly the same either method.

Naw, it dramatically increases the chance of either one. I had this problem last night, actually, thinking people were suggesting to do it this way, rather than specifying with your two draws 'this one is for col/plat' and 'this one is for shelters' before doing the draw.

In your 5/5 example, if you do it your way, well I can't tell if you're replacing the first card or not. If you are, then there's a 75% chance you get either one - overall there's a 25% chance for just shelters, 25% for just col/plat, and 50% for both. If you do it without replacement, then there's a 5/9 chance of getting both, 2/9 of getting just the one, and 2/9 getting the other.

[cluckyb]

If you want the choices for colony/shelters to actually be independent, you need to do two picks (with replacement)- if you only do one, since no card is from both prosperity and dark ages, you are more likely to get one or the other, but you never get both.

The rulebook for Prosperty says look at the first one, the rulebook for Dark Ages says pick the last one, so they are not supposed to be independent.

Also you're slightly more likely to get both, both also more likely to get neither, if you don't replace the card you selected for Prosperity before selecting the DA card. (If I have nine cards from Propserty and one from Dark Ages and do not replace my selection, then every game with Shelters must also have Platinum and I have 1/10 odds of that event occurring. If I do replace my selection, the odds drop to 9/100)

Actually, they both just say to use the proportion of cards from the set to determine - the top and bottom things are only examples. If you follow strictly to the proportion, i.e. if you assume you want the chances for each are exactly the same as the proportion of kingdom cards from the set, then you need to do the replacement thing.
But I don't think there's really a 'supposed to' going on here.

If you have P prosperity cards and D dark ages cards, both ways will let you play with Platinum P*10% of the time and shelters D*10% of the dime and so are "proportional".  They don't say if the events should be independent or not, but given the example implies non-independent events that's what I'd figure the 'proper' way of doing this is.