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Author Topic: Clean Shuffles  (Read 345 times)

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Titandrake

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Clean Shuffles
« on: October 19, 2019, 10:34:06 pm »
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Renaissance introduced 2 cards that are useful in the opening: Lackeys, and Silk Merchant. They both draw 2 cards, while coming with some Villagers.

These are useful opening cards because they heavily increase your odds of a clean shuffle: ending your turn with 0 cards left in your draw deck. Assuming you gain 2 cards on turns 1 + 2, and the other card you gain doesn't draw cards, then you are guaranteed to see all 12 cards in your deck by the end of turn 4 as long as either Lackeys or Silk Merchant is drawn on turns 3 or 4, and the Villagers guarantees you can play the other card you bought if it's terminal.

I mean, you still have the Lackeys or Silk Merchant left over, and the Villagers won't last forever, so you have to be a bit careful, but it's part of what plays into their power level.

You don't have to go all the way to a clean shuffle either. Think of it this way: what sucks the most is when cards you open miss the reshuffle. This happens if they're near the bottom of your deck and you don't draw down far enough. Let's say there's one card you really want to draw before the reshuffle (say a trasher like Steward, or a gainer like Ironworks). Assuming it's terminal, there's a 1/6 chance the card misses the reshuffle (2 out of 12 cards).

Let's say you open Cantrip/Steward. Now, if you draw that cantrip on turn 3 or 4, you draw down 11 cards instead of 10. The math is a bit nontrivial, but it works out to about a 1/11 chance of missing the Steward. breppert has the exact number in their Opening Probabilities article, if you are curious.

Everyone knows that Ironmonger is a great opening card. I mean, this is obvious if you open it a few times and notice that your deck just feels cleaner. But now I'm thinking the reason it's good is because you usually reveal and discard a Copper, and that effectively lets you see all 12 cards unless the Ironmonger is bottom decked.

I don't know if this is something you should be thinking about past the opening, but it's neat.
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pacovf

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Re: Clean Shuffles
« Reply #1 on: October 20, 2019, 03:39:15 am »
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Let's say you open Cantrip/Steward. Now, if you draw that cantrip on turn 3 or 4, you draw down 11 cards instead of 10. The math is a bit nontrivial, but it works out to about a 1/11 chance of missing the Steward. breppert has the exact number in their Opening Probabilities article, if you are curious.

I know it's not really the point of your post, but the probability is exactly 1/11. You can think of it as the cantrip being "free" draw-wise, so your deck effectively only has 11 cards, hence the result. The odds of the cantrip itself missing the second shuffle remain 2/12, however.
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