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[GendoIkari]

thank god I used a real language

Prolog?

Scheme.

[popsofctown]

Sounds like stef is getting more $ because the "try to draw a copper instead of an estate" logic?

It seems like discarding the estate is really bad if you're gonna reshuffle later that turn though.

My brain

[werothegreat]

By real language he means Dutch; it makes all of Dominion obvious.

All Dominion instructions should be in Lojban

[Titandrake]

I have always followed strategy 1, because if there's 2 dead cards then actions I'll feel super bad. However, based on this thread I'm starting to believe the other way is better.

Not in the mood to analyze it super rigorously, but let's ignore everything except the first 2 cards. It's given the first card is not an action.

If not action, then not action: then strategy 1 is better. In both scenarios you draw these 2 cards, but strategy 1 gives you a chance to hit an action chain.
If not action, then action: then strategy 2 is better. The only difference between the two is that the Peddler in hand turns into the non-action card that was on top.

Overall, by the point you're considering these decisions, you'll probably have enough actions that you should be guessing towards the latter option. You will have 1 more non-action in your deck if you reshuffle, but you also have 1 more Peddler, so you'll draw 1 more non-action and it comes out to a wash.

[GendoIkari]

Ignoring reshuffles, Estates vs Coppers, Estates in discard vs Estates in hand, multiple Peddlers or multiple Scrying Pools, etc.... I think that while the expected draw might be the same either way, there's a big risk vs reward issue at stake.

Pretend you have 99 actions and only 2 Estates in your deck, with one Estate on top. So the other Estate has a 1 in 100 chance of being in each spot of your deck. 3 possible situations:

1) If the Estate is the very bottom card, then it makes no difference at all what order you play them in; you draw your whole deck. (1% chance)

2) If the Estate is the second from the top, then playing your Scrying Pool first means you draw nothing. Playing your Peddler first means you draw your deck. (1% chance)

3) If the Estate is in any other position at all (X from the top), then playing your Peddler first means drawing X cards, and playing your Scrying Pool first means drawing X+1 cards. (98% chance)

As you can see, 98% of the time it is better to play your Scrying Pool first. However, it is only better by 1 card. The 1% of the time where playing your Peddler first is better, it is 100 times better.

This same basic logic/math should work even when you add other dead cards into the deck.

[JW]

Pretend you have 99 actions and only 2 Estates in your deck, with one Estate on top. So the other Estate has a 1 in 100 chance of being in each spot of your deck. 3 possible situations:

1) If the Estate is the very bottom card, then it makes no difference at all what order you play them in; you draw your whole deck. (1% chance)

2) If the Estate is the second from the top, then playing your Scrying Pool first means you draw nothing. Playing your Peddler first means you draw your deck. (1% chance)

3) If the Estate is in any other position at all (X from the top), then playing your Peddler first means drawing X cards, and playing your Scrying Pool first means drawing X+1 cards. (98% chance)

As you can see, 98% of the time it is better to play your Scrying Pool first. However, it is only better by 1 card. The 1% of the time where playing your Peddler first is better, it is 100 times better.

What you want to know is the distribution of the number of (useful) cards that you will draw is, depending on whether you play Scrying Pool first. It doesn't matter how much your choice to play Scrying Pool first "hurts you" in any one possible arrangement of cards in the deck. In the situation you presented, it seems like the distribution of the number of action cards that you draw will be the same whether you play Pool first or not.

Change it to 1 Estate on top plus 2 coppers in your deck and you'll have more coins for the turn, in the sense of First Order stochastic dominance, by playing Pool first. Stef's simulation above presumably shows the same result (first order stochastic dominance in the number of coins generated by playing Scrying Pool first).

Despite all of these reasons to play Pool first, you may regret it more if you play Pool first and the second Estate is the very next card. 

[popsofctown]

This brand new Dominion: Alchemy expansion seems to presenting new challenges that we haven't encountered or discussed before.