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Author Topic: Can you win this turn 4 (Alchemy)  (Read 1527 times)

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Snyables

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Can you win this turn 4 (Alchemy)
« on: June 15, 2020, 09:12:34 am »
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You have been playing an IRL game of Alchemy with your friend. You have not been paying close enough attention to the cards they have bought. You do remember that you bought a Vineyard last turn and placed all of your Alchemists on top of your deck. You think you can probably end the game this turn, but can you win? Are you guaranteed to do so, or does it depend on the luck of the draw?



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2.71828.....

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Re: Can you win this turn 4 (Alchemy)
« Reply #1 on: June 15, 2020, 09:35:41 am »
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Given only one potion was bought, you are the only one who could have vineyards or any potion cost card.

So you have....
4 familiar + 10 alchemist + 2 golem + 9 transmute + 1 apo + 1 scrying pool + 2 uni = 29 actions
4 vineyards = 4*9= 36vp

Let's assume...opponent has 7 provinces + 9 curses = 33vp

So...basically a guaranteed win unless your 10 alchemists on top of the deck end up drawing 9 transmutes + uni.

So there is some level of shuffle luck,but you can easily trash potion for the last transmute + buy curse, or play 3 gold's for a province (you have 3 gold's from the 3 trashed estates).
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Awaclus

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Re: Can you win this turn 4 (Alchemy)
« Reply #2 on: June 15, 2020, 09:49:30 am »
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It depends on the contents of decks. The worst case scenario is that your opponent has 45 points from 7 Provinces and 3 Estates while you have 27 points from 4 Vineyards and 9 Curses, I don't know why you would have bought those Curses since we know your opponent doesn't have any of the kingdom cards because you have the only Potion, but I guess everything is possible if you haven't been paying attention. You can get 4 points from buying the last Transmute and effectively 1 point from giving the opponent the last remaining Curse, which is not enough.

If it's your opponent that has the Curses, or you have at least two Provinces, you win as long as you can draw into at least one of the following:

A Familiar and a Potion
enough Golds/Silvers to buy the last remaining Province
A Transmute and any Treasure


Your Alchemists only guarantee a handsize of 15 and you definitely have at least 4 Vineyards, 9 Transmutes, 2 Universities and 3 Golds for stop cards. This means that it is possible to draw 4 Vineyards, 9 Transmutes and 2 Universities, which meets none of those conditions. Exactly how likely it is to fail to meet all three conditions depends on the contents of your deck, but it is unlikely regardless.
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Snyables

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Re: Can you win this turn 4 (Alchemy)
« Reply #3 on: June 18, 2020, 03:17:31 pm »
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e, two things:
 
1. The opponent would not be able to have 33 VPs by having 7 provinces and 9 curses.
2. The 10 Alchemists will draw you more than 10 cards in total.


Awaclus:

I don't know why the player would have bought 9 curses themselves either, but I do suppose with the way I worded the puzzle, it would be a possibility. I hadn't intended for that to be an option (I suppose you could have bought all 9 curses and intentionally not played any Familiars you had drawn in previous turns...), so good catch! If you assume the opponent has the 9 curses and all Provinces, as far as I can tell, the one and only one hand you could draw that would not let you win the game is what you said, 4 Vineyards, 9 Transmutes, and 2 Universities. Using the mathematical equation for combinations, we can find the maximum likelihood of that scenario as one over the total combinations of 15 card hands out of a deck of 26 (the minimum number of cards you could have in the puzzle, if you bought anything extra (like extra golds), the odds are even less likely). The total number of combinations are = 26!/(15!11!) = 7,726,160. So, one out of every 7.7 billion times you are placed in this situation, you will be unable to win. 
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Re: Can you win this turn 4 (Alchemy)
« Reply #4 on: June 18, 2020, 04:06:20 pm »
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e, two things:


1. The opponent would not be able to have 33 VPs by having 7 provinces and 9 curses.

Clarification: If it were just the Provinces and Curses, that would work out, but the opponent still has all their Estates because they never bought a Transmute.
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dpm

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Re: Can you win this turn 4 (Alchemy)
« Reply #5 on: June 19, 2020, 10:52:51 am »
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I don't know why the player would have bought 9 curses themselves either, but I do suppose with the way I worded the puzzle, it would be a possibility. I hadn't intended for that to be an option (I suppose you could have bought all 9 curses and intentionally not played any Familiars you had drawn in previous turns...), so good catch! If you assume the opponent has the 9 curses and all Provinces, as far as I can tell, the one and only one hand you could draw that would not let you win the game is what you said, 4 Vineyards, 9 Transmutes, and 2 Universities. Using the mathematical equation for combinations, we can find the maximum likelihood of that scenario as one over the total combinations of 15 card hands out of a deck of 26 (the minimum number of cards you could have in the puzzle, if you bought anything extra (like extra golds), the odds are even less likely). The total number of combinations are = 26!/(15!11!) = 7,726,160. So, one out of every 7.7 billion times you are placed in this situation, you will be unable to win. 

Not quite, you could also draw 14 of those 15 cards, plus Apothecary, and then play Apothecary and draw only the 15th stop card.  Or it could be Familiar instead, though that at least would give out the last curse.  Or maybe some combination of Apos and Familiars...
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Snyables

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Re: Can you win this turn 4 (Alchemy)
« Reply #6 on: June 27, 2020, 11:53:01 am »
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dpm:

Good notice! Yes, you are correct that there are actually several ways to end up with a dead hand. I don't feel like doing the precise math on it, but lets guess that it takes the chances of getting a non-win hand up from 1 in 8 billion to somewhere in the 1 in several hundred millions.


Thanks for playing and thanks for the feedback. New puzzle, Prosperity, will be up momentarily!

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