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[GendoIkari]

I have not thought it through completely, but I think you can guarantee to get your deck down to Chapel-Ironworks-Hamet-Scheme-Bridge in 9 turns when you start Chapel-Scheme, and from there it should take 5 turns for a Highway-Market Square megaturn into 13 Duchy-Dukes, which beats 8 Provinces, or one more for additional 10 Markets if you want to pile out.

Remember that BMU will be buying some Duchies in the meantime though.

3  4  3  6  6  6  4  8  9  8  8  8  0  8  8  8

BMU is busy buying Provinces....

Ah right, it's "best-case" BMU, so no Duchies.

[scott_pilgrim]

I have not thought it through completely, but I think you can guarantee to get your deck down to Chapel-Ironworks-Hamet-Scheme-Bridge in 9 turns when you start Chapel-Scheme, and from there it should take 5 turns for a Highway-Market Square megaturn into 13 Duchy-Dukes, which beats 8 Provinces, or one more for additional 10 Markets if you want to pile out.

Remember that BMU will be buying some Duchies in the meantime though.

3  4  3  6  6  6  4  8  9  8  8  8  0  8  8  8

BMU is busy buying Provinces....

Ah right, it's "best-case" BMU, so no Duchies.

Well, if you're going for a Duke-Duchy strategy, then the best case might not be the one which always hits $8.  The challenge is to find an algorithm that guaranteed beats BMU, which means that it has to beat it in every possible case, not just in some pre-determined "best case".  So the "best case" might vary depending on what strategy it is competing against.

[Davio]

Best case BMU doesn't deal with attacks though.
Adding even a single Militia may severely hamper it.
It will start buying Duchies and slow down to a crawl until (Estates and) Duchies are gone and only then it starts buying some economy again.

[Kirian]

Best case BMU doesn't deal with attacks though.
Adding even a single Militia may severely hamper it.
It will start buying Duchies and slow down to a crawl until (Estates and) Duchies are gone and only then it starts buying some economy again.

It shouldn't; BMU doesn't buy Duchies until at least four Provinces are gone.

[Davio]

Well, eventually it will get to 4 Provinces, but have trouble buying more and it drops down to Duchies and keeps buying them until he has all 8. At that point he will start with his regular Gold and Silver again, but it will take a lot longer to get the game to completion this way.

Enough time, even in best case perhaps, for a VP-token based strategy to overcome it with a worst case scenario.

[Kirian]

Well, eventually it will get to 4 Provinces, but have trouble buying more and it drops down to Duchies and keeps buying them until he has all 8. At that point he will start with his regular Gold and Silver again, but it will take a lot longer to get the game to completion this way.

I think a strategy that hits it with Militia two out of three turns (or more) is going to delay Provinces for a very long while; the BMU bot has to be holding GGSXX or better to grab a Province.  That sort of density will take a long time.  GSSXX just gets it another Gold.

[Davio]

Yes, and we're talking about a simple Militia here.
You could even Minion-attack first, then play Militia and it has to get lucky to have a 4-card hand of GGSX instead of GGSXX.

[Watno]

Yes, and we're talking about a simple Militia here.
You could even Minion-attack first, then play Militia and it has to get lucky to have a 4-card hand of GGSX instead of GGSXX.

But requiring luck is not a problem if you assume perfect luck for the opponent. I think Minion is a terrible card to use, since it will only discard hands full of provinces, estates, and maybe coppers.

[Davio]

Well, if we assume perfect luck, Thief always hits 2 VP cards, so that's out as well.

[Awaclus]

Well, if we assume perfect luck, Thief always hits 2 VP cards, so that's out as well.

Unless you're playing more than one Thief per reshuffle.

[Davio]

Well, if we assume perfect luck, Thief always hits 2 VP cards, so that's out as well.

Unless you're playing more than one Thief per reshuffle.

Still I think you could model it that it's pretty bad even when played multiple times.
Remember, we not only have to account for perfect luck for our opponent, but for the worst possible luck for ourselves. So Throne Rooms never find other action cards and terminals always collide.

[Kirian]

Well, if we assume perfect luck, Thief always hits 2 VP cards, so that's out as well.

Unless you're playing more than one Thief per reshuffle.

Still I think you could model it that it's pretty bad even when played multiple times.
Remember, we not only have to account for perfect luck for our opponent, but for the worst possible luck for ourselves. So Throne Rooms never find other action cards and terminals always collide.

See, and the problem with this sort of exercise is that the non-BMU player's luck and the BMU bot's luck are entangled.  Rearranging the bot's deck to account for the player's deck changes what is the "worst" for the player's deck, forcing that to be rearranged, which means the bot's deck has to be rearranged, and so on.

[Watno]

The best strategy might involve using Bureaucrat or Cutpurse to see the opponent's hand, so you see wetehr he has a hand you want to discard with Minion. This is kinda twisting my mind.

[DStu]

I have not thought it through completely, but I think you can guarantee to get your deck down to Chapel-Ironworks-Hamet-Scheme-Bridge in 9 turns when you start Chapel-Scheme, and from there it should take 5 turns for a Highway-Market Square megaturn into 13 Duchy-Dukes, which beats 8 Provinces, or one more for additional 10 Markets if you want to pile out.

Remember that BMU will be buying some Duchies in the meantime though.

3  4  3  6  6  6  4  8  9  8  8  8  0  8  8  8

BMU is busy buying Provinces....

Ah right, it's "best-case" BMU, so no Duchies.

Well, if you're going for a Duke-Duchy strategy, then the best case might not be the one which always hits $8.  The challenge is to find an algorithm that guaranteed beats BMU, which means that it has to beat it in every possible case, not just in some pre-determined "best case".  So the "best case" might vary depending on what strategy it is competing against.

I need one more turn to pile Provinces, so I doubt that taking Duchy>Provinces will help BMU much. We could also take Fairgrounds in the Kingdom, which will be easily worth 6VP when I have 13buys.

[Awaclus]

The best strategy might involve using Bureaucrat or Cutpurse to see the opponent's hand, so you see wetehr he has a hand you want to discard with Minion. This is kinda twisting my mind.

Is the best hand against Cutpurse + Minion a hand with a Copper plus enough money to buy whatever he wants, or a hand without copper?

[florrat]

For everyone who thinks there is a problem with this challenge, because "worst possible luck" is ill-defined, there's no problem with that, mathematically speaking. The challenge is "just" to give an strategy for every possible way you and your opponent can shuffle. Many cases will be easy (if you are "lucky"), and there will be some cases which are hard (if you have "bad luck"). There won't be one unique way both players can shuffle which can be called the "most difficult case", so the term "worst possible luck" is indeed not well-defined. There will be different ways to which the players can shuffle, which each bring their own set of complications.

Unfortunately, handling every possible case is quite hard. Giving a separate strategy for every different case is unfeasible. You can group similar shuffles together and give a strategy which works for all of these shuffles. Usually you will lose some efficiency with this, but this might work.

By the way, I'm convinced that you can win 100% of the times against any big money strategy, if the board is strong enough. It should be possible to guarantee to build up a masquerade pin by turn 15 (and it's impossible for big money to get to 8 provinces earlier). If that's not possible, then it should be possible a few turns later, but attacking the big money player enough that he can't get to 8 provinces before that time. It will be very annoying to show that such a strategy will always work, though.

[WanderingWinder]

http://forum.dominionstrategy.com/index.php?topic=462.msg7678#msg7678

[Kirian]

http://forum.dominionstrategy.com/index.php?topic=462.msg7678#msg7678

Well then.  Next question!

[blueblimp]

I thought the point of this thread was to consider strategies that existing simulators can play. (To be fair, in principle you can tweak a Dominiate AI to do anything.)

[Kirian]

I thought the point of this thread was to consider strategies that existing simulators can play. (To be fair, in principle you can tweak a Dominiate AI to do anything.)

It's the "never wins a single game" that forces us into non-bot territory, as people have already demonstrated effective 100% win rates.  However, I'm sure the anti-Lucky Chancellor not is readily programmable.  Since it's a guaranteed win against LC, which will always be faster than BMU, it's a guaranteed 100% win vs BMU too.

[SirPeebles]

I thought the point of this thread was to consider strategies that existing simulators can play. (To be fair, in principle you can tweak a Dominiate AI to do anything.)

It's the "never wins a single game" that forces us into non-bot territory, as people have already demonstrated effective 100% win rates.  However, I'm sure the anti-Lucky Chancellor not is readily programmable.  Since it's a guaranteed win against LC, which will always be faster than BMU, it's a guaranteed 100% win vs BMU too.

Well, one assumption made was that 3 piling was not a worry because the LC bought almost nothing but Provinces.  With a less lucky Chancellor, it at least needs to be addressed that Duchies and Estates may be purchased sooner.  I doubt that will matter much though.