Arnak Deck Math: Knowing Your Next Hand

Welcome to Level 3. At Level 2 you learned to judge a card by how many times you will use it. Now you can be exact about when you will draw it. Lost Ruins of Arnak has a quirk most deck builders do not: you never reshuffle your whole deck. That makes much of your next hand predictable, and a predictable hand is one you can plan around.

All rules here follow the current English rulebook from Czech Games Edition.

The three layers of your deck

The rules set up your deck in layers:

1. At setup you shuffle your 6 starting cards. That is the only full shuffle of the game.
2. During a round, each item you buy goes face down on the bottom of your deck.
3. At the end of the round, you shuffle your play area and put it under your deck. The rulebook points out that items bought this round now sit above all those shuffled cards.

So when the next round starts, your deck runs, from the top:

• Layer 1: cards you did not draw this round, in their old order.
• Layer 2: items you bought this round, the first one bought on top.
• Layer 3: the freshly shuffled play area.

You draw up to 5 from the top. Layers 1 and 2 are known cards. Only the draws that reach layer 3 are random.

A worked example

Round I. You draw 5 of your 6 starting cards, so one card stays in your deck. Say it is an Exploration. During the round you buy one item and one artifact, and you bring home one Fear card from a guardian.

At the end of the round, your play area holds the 5 cards you drew, the artifact, and the new Fear: 7 cards. Three of them are Fear (your two starting Fear plus the new one). Shuffle them under the item.

Round II, from the top: Exploration, your new item, then the 7 shuffled cards. You draw 5, so you know 2 of them and draw 3 at random from the 7.

• Chance of no Fear in those 3 draws: 4 in 35, about 11%.
• Expected Fear in your hand: 3 times 3 over 7, about 1.3 cards.

Now change one thing. During round I you used an exile effect on a Fear card. The pile is now 6 cards with 2 Fear. The chance of no Fear rises to 20%, and the expected Fear in hand drops to 1.0. One exile, a better hand on average every time those cards come around.

The trap: a second item may wait

Keep following the example. In round II you drew only 3 of the 7 shuffled cards, so 4 stay on top of your deck. Those 4 are layer 1 for round III.

If you buy two items in round II, the first sits fifth from the top. The second sits sixth and will not reach your round III hand. It waits for round IV, unless a draw effect finds it.

The rulebook says an item “usually” shows up next round. This is the “usually.” The bigger your deck, the more undrawn cards sit in layer 1, and the further back a new item lands. Before you buy an item you need soon, count the cards above where it will go.

Odds on the shuffled layer

When your known cards leave room for random draws, this table gives the chance of drawing at least one of the cards you want. It assumes you know how many cards are in the shuffled layer and how many of them you want.

Two lessons stand out:

• One specific card in a shuffled pile is a coin flip or worse. If you need a particular card next round, the reliable way is an item bought while layer 1 is short, not hope.
• Redundancy beats luck. Two cards that make the same resource raise your odds a lot: in a 7-card pile with 3 draws, 43% becomes 71%.

Draw effects and an empty deck

Most draw effects take the top card, which is layer 1, then layer 2. A few cards, such as the Obsidian Earring, draw from the bottom instead. The rulebook’s FAQ adds a useful case: if your deck is empty and you buy an item, that item is now both the top and the bottom of your deck. A draw effect later in the same round puts it straight into your hand.

Saving cards changes the count too. Cards you keep in hand at the end of a round count toward your 5, so each saved card is one fewer draw.

The planning habit

Before you pass, count:

1. Cards left in your deck: these are next round’s first draws.
2. Items bought: they come next, in order.
3. Whatever room is left: that is your random share.

If the role of chance in a game like this interests you, our article on luck and skill in board games explores how good players shrink the luck they face.