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Author Topic: Math/probability for silver/potion opening - getting Familiar/Alchemist turn 3/4  (Read 3983 times)

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Reyk

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I think it's not hard to calculate - but I'm bad at these things. Recently I started Silver/Potion on a face2face board with Alchemist/Golem as the only Alchemy cards. There were not many strong alternatives in the 3-/4 range (only remodel seemed to be an alternative) and no 2 cost cards at all. I drew potion/copper/copper/estate/estate at turn 3 and at turn 5 and lost badly.

It has been already discussed that starting potion with Golem as cheapest Alchmey card is bad.
Was it too risky to open potion/silver in this case? Is it less critical to get Alchemist at turn 3 than Familiar (may of course depend on the trashing options).
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DG

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I find it is problem in a kingdom that you typically have to buy the potion and risk the draw for the familiar. You don't want to see your opponents buying familiars and putting curses into your deck, which then create new chances of bad draws.
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Reyk

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I find it is problem in a kingdom that you typically have to buy the potion and risk the draw for the familiar. You don't want to see your opponents buying familiars and putting curses into your deck, which then create new chances of bad draws.

I think that too. But what about Alchemist?
Can anybody post the exact numbers (percentage of the risk to draw potion and 2 money in turn 3/4)?
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WanderingWinder

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Just did this real quick in my head, so don't sue me if it's wrong, but it should be 21/88 that you get this exact draw on turn 3 exactly, plus 7/792 than you get exactly Potion-Copper-Estate-Estate-Estate on turn 3 exactly, for a total of 196/792 or 49/198 to get either of these on turn 3, and then doubling that because you could get it on turn 3 OR turn 4, you get 49/99, which as you can see is JUST under 50%. Then you have to add in the chance that the potion is in one of the last two slots that aren't drawn, which is 1/66, and the chance that you don't get a familiar in turn 3 or 4 is 101/198, or just over 50%.
Somehow that seems a bit too high, and I'm thinking I might have computed something wrong. Anyone care to check me?

theory

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Based on http://dominionstrategy.com/2011/03/09/basic-opening-probabilities/, if you substitute Potion for Chapel, the odds should be about 1.8+0.3+15.9+16.6 = 34.6% that you don't draw $3P on Turn 3 or Turn 4 if you opened Potion/Silver.
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DStu

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Based on http://dominionstrategy.com/2011/03/09/basic-opening-probabilities/, if you substitute Potion for Chapel, the odds should be about 1.8+0.3+15.9+16.6 = 34.6% that you don't draw $3P on Turn 3 or Turn 4 if you opened Potion/Silver.

That sounds quite high, but I think you should substract the 16.6% where the Potion is in turn 5. While this is certainly as bad for you as any other reason why you can't buy the Familiar, when comparing with different openings you should consider that every card you buy instead of the Potion also will be in turn 5, so another opening does not help you in this 16.6%. So we have 18% where the Potion is really wasted in the sense that an other card for $4 would be more helpful.

PS: Is it just me or does anyone else has problems with the editor in this forum? I don't have any linebreaks at the right margin of the editing field, so the line continues to the right where I can't see what I write
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theory

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It occasionally has problems for me too, but if I refresh the page (after copying my post, of course) it goes away.
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DG

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Quote
PS: Is it just me or does anyone else has problems with the editor in this forum? I don't have any linebreaks at the right margin of the editing field, so the line continues to the right where I can't see what I write

I had this problem too. I think I've fixed it by ticking "Show WYSIWYG editor on post page by default." in the profile, look and layout, settings. I'm not sure why this isn't a default.
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Death to Sea Hags

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Based on http://dominionstrategy.com/2011/03/09/basic-opening-probabilities/, if you substitute Potion for Chapel, the odds should be about 1.8+0.3+15.9+16.6 = 34.6% that you don't draw $3P on Turn 3 or Turn 4 if you opened Potion/Silver.

That sounds quite high, but I think you should substract the 16.6% where the Potion is in turn 5. While this is certainly as bad for you as any other reason why you can't buy the Familiar, when comparing with different openings you should consider that every card you buy instead of the Potion also will be in turn 5, so another opening does not help you in this 16.6%. So we have 18% where the Potion is really wasted in the sense that an other card for $4 would be more helpful.

I think the 35% fail rate for t3/4 (before s2) is the more important number.  I you don't buy your familiar until t5, it'll sit out shuffle 2, and won't come back until s3, typically t7 or later.  That's a BIG set-back.

FYI, that's bigger than the odds of two terminal actions colliding in t3/4.  If you don't feel comfortable opening with two terminals, then you should only open Potion-Silver if there's some good consolation buys for your $2+P.
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HiveMindEmulator

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I think the 35% fail rate for t3/4 (before s2) is the more important number.  I you don't buy your familiar until t5, it'll sit out shuffle 2, and won't come back until s3, typically t7 or later.  That's a BIG set-back.

FYI, that's bigger than the odds of two terminal actions colliding in t3/4.  If you don't feel comfortable opening with two terminals, then you should only open Potion-Silver if there's some good consolation buys for your $2+P.

The logic here is not quite complete. The *amount* you benefit/are hurt by getting the right draw matters. Sometimes you open with 2 terminals if they are good enough (particularly when one of them is chapel), because there is a major benefit if you do happen to draw them separately, and drawing some terminal with the chapel is no worse than drawing silver with chapel. But you would probably not want to open something like moneylender/swindler, since the benefit of getting to play both does not outweigh the damage resulting from drawing them together (compared to moneylender/silver for example).

Similarly, when familiar is the only curse-giver on the table, you probably have to take the risk of getting the potion right away, because doing something else is just as likely to lead to a loss as buying potion and missing. Existence of $2+P is little consolation, as if you get a familiar and I get a scrying pool, I lose anyway.
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rogerclee

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You are 5/6 to hit your potion on turns 3 or 4. Assume you hit your potion (5/6).

On the hand where you hit your potion...

if you draw silver (4/11), then you need SPEEE to not hit it, which is 1-1/Binomial(10,3) = 119/120
if you don't draw silver (7/11), then you need either CCCE or CCCC to hit it, which is (Binomial(7,3) * Binomial(3,1) + Binomial(7,4)) / Binomial(10,4) = 2/3

So your chance of hitting 3P on either turns 3 or 4 is

5/6 * (4/11 * 119/120 + 7/11 * 2/3) = 259/396 = .654

or you could just ignore this and read theory's post above.
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DG

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Existence of $2+P is little consolation, as if you get a familiar and I get a scrying pool, I lose anyway.

I've played games where the person who got the 2+potion found out later in the game that buying the university, transmute, or apothecary first was actually the stroke of luck that won the game.
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DStu

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I think the 35% fail rate for t3/4 (before s2) is the more important number.  I you don't buy your familiar until t5, it'll sit out shuffle 2, and won't come back until s3, typically t7 or later.  That's a BIG set-back.

The thing is that in the 16.6% where the Potion misses the shuffle, every other card you bought instead also would miss the shuffle. So it basically does not help to not buy the Potion in this cases (except for the cases that in turn 5 you don't get $3P which nobody has calculated yet). So of course you it's bad for you that this happens, but another decision in turn 1/2 will not improve this. In the other 18%, another decision will help. How much, of course depends on your choices for $4.
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Death to Sea Hags

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I think the 35% fail rate for t3/4 (before s2) is the more important number.  I you don't buy your familiar until t5, it'll sit out shuffle 2, and won't come back until s3, typically t7 or later.  That's a BIG set-back.

The thing is that in the 16.6% where the Potion misses the shuffle, every other card you bought instead also would miss the shuffle. So it basically does not help to not buy the Potion in this cases (except for the cases that in turn 5 you don't get $3P which nobody has calculated yet). So of course you it's bad for you that this happens, but another decision in turn 1/2 will not improve this. In the other 18%, another decision will help. How much, of course depends on your choices for $4.

Not necessarily.  While your $4 card will come t5, your $3 card will have come earlier - so instead of silver, maybe you should have bought something that draws cards, or something that trashes.
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