Dominion Strategy Forum
Dominion => Game Reports => Topic started by: shark_bait on March 10, 2014, 01:14:18 pm
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6 Bridge
2 Forager
3 Grand Market
5 Scrying Pool
5 Shanty Town
1 Potion
22 cards in deck
For the math inclined, anyone want to calculate the chance of not drawing through the deck at this state? I mean I guess I had a fair bit of Bridges, Foragers and Shanty Towns, but it still seems highly unlikely. And really you just need a single Scrying Pool in hand that can draw another Scrying Pool before hitting the Potion.
Just frustrated after this game
http://www.gokosalvager.com/static/logprettifier.html?/20140310/log.50ea2963e4b0429cfe091cec.1394471337022.txt
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well, bridge, forager and potion are dead cards, and you're basically guaranteed to draw everything with one scrying pool. Grand market can just be ignored because it will replace itself with another card.
Shanty town makes it a little bit harder, but ignoring it we have
9 dead cards and 5 key cards, 9 dead cards out of 14. in order to not draw your deck, you would have to draw 5 cards without having one of the key cards in it. that's 9/14*8/13*7/12*6/11*5/10 = 6,3%
the 2 mistakes here are a) shanty towns are missing and b) you may not draw everything with one scrying pool because of potion. I'd guess the real chance to be about 9%. So, ~90% chance that you do draw everything
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Shanty Town won't usually help from a draw perspective, so they can't be ignored in computing the odds. For my estimation, I'm just considering the odds of not getting a Scrying Pool in your hand, drawing from 19 cards (the deck minus the cantrip Grand Markets). This is the same as silverspawn's computation, but with 5 added to the numerators and denominators, and gives about 17%. The 5 Shanty Towns are needed for the +actions, but they can be a bit of a liability in drawing your deck.
Given that you DO have a Scrying Pool in your last hand, you get especially screwed by not drawing another SP in your next 5 cards. Your 4 remaining SPs all happen to be beneath the potion - probably somewhere around a 5-10% chance.
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Assuming that you have a scrying pool in hand, what are the chances you don't have a second one in hand or the potion and don't draw another one before hitting a potion? It's essentially
1/5 (chances that you find the potion before one of the four other scrying pools) * 8/13*7/12*6/11*5/10 (chances you don't have another scrying pool or a potion) =
~2%
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Shanty Town won't usually help from a draw perspective, so they can't be ignored in computing the odds. For my estimation, I'm just considering the odds of not getting a Scrying Pool in your hand, drawing from 19 cards (the deck minus the cantrip Grand Markets). This is the same as silverspawn's computation, but with 5 added to the numerators and denominators, and gives about 17%. The 5 Shanty Towns are needed for the +actions, but they can be a bit of a liability in drawing your deck.
Given that you DO have a Scrying Pool in your last hand, you get especially screwed by not drawing another SP in your next 5 cards. Your 4 remaining SPs all happen to be beneath the potion - probably somewhere around a 5-10% chance.
i don't think that's correct. Shanty will only be dead when you have more bridges than shanty towns in your hand, which is unlikely, otherwise you can play everything and then draw. In some cases it'll matter whether you're willing to trash a bridge
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Ignoring everything but Pool and Potion, you have a 20% chance of having only one Pool above the Potion. Since that number doesn't include the cases where your initial hand doesn't find a first pool despite there being two above the potion, the actual chance of not drawing your deck is a bit higher, likely 22% or so. So, you were definitely unlucky, but not as unlucky as having a key opening card land in T5.
For that 20% number, consider that none of the other cards matter in any way.
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Ignoring everything but Pool and Potion, you have a 20% chance of having only one Pool above the Potion. Since that number doesn't include the cases where your initial hand doesn't find a first pool despite there being two above the potion, the actual chance of not drawing your deck is a bit higher, likely 22% or so. So, you were definitely unlucky, but not as unlucky as having a key opening card land in T5.
For that 20% number, consider that none of the other cards matter in any way.
But it does include cases where you have your potion in the starting hand OR draw your second pool off of a GM or shanty town.
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i don't think that's correct. Shanty will only be dead when you have more bridges than shanty towns in your hand, which is unlikely, otherwise you can play everything and then draw. In some cases it'll matter whether you're willing to trash a bridge
That's true (almost, ST is also dead when # bridges in hand = # STs in hand), but my point is you can't count on Shanty Town to draw very often. As long as you have more STs than bridges, you'll be able to draw, but only the last ST played will draw. I don't think it's possible for more than 2 of those 5 STs to draw cards. I suspect you're more likely to only get 1 or 0 of them to give you the +2 cards.
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Ignoring everything but Pool and Potion, you have a 20% chance of having only one Pool above the Potion. Since that number doesn't include the cases where your initial hand doesn't find a first pool despite there being two above the potion, the actual chance of not drawing your deck is a bit higher, likely 22% or so. So, you were definitely unlucky, but not as unlucky as having a key opening card land in T5.
For that 20% number, consider that none of the other cards matter in any way.
But it does include cases where you have your potion in the starting hand OR draw your second pool off of a GM or shanty town.
Edge case'd. Yeah, those probably drop the probability a bit under 20% total.
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Don't forget that you might get to discard Potion when you play Scrying Pool. You can't just ignore other cards, because each non-Potion non-Pool makes it less likely this feature will help.
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I'd say the probability of not drawing your deck is about 1/(10-(how important it is on a scale of 1 to 10)). This is the Murphy approximation.