How many resource cards a deck needs to never miss a turn
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| Games with no missed turn, in per cent | — |
| Games that miss at least one, in per cent | — |
| Which is one game in | — |
There is something worth knowing about that first figure, and it saved this page from claiming the opposite. Missing a turn does not compound across the turns the way risk usually does: needing so many resources by a given turn already implies having had enough on every turn before it, because removing one card from the count removes at most one resource. The chance of never missing through a turn is therefore exactly the chance of being fine on that turn alone, and there is nothing extra hiding in the sequence.
What another two copies buy you
| Resource cards | Games with no missed turn, in per cent | Gained over the row above, in points |
|---|
This is a genuine case of diminishing returns, unlike some that get called that. Each pair of copies buys about half of what the pair below it bought, so the same two cards are worth several points near the bottom of the table and a fraction of one near the top. Somewhere in the middle they stop paying for the slot they take.
Where that point sits is not something arithmetic can settle, because the cost of a resource card is that it is not a threat. The page can tell you exactly what the next two copies are worth and cannot tell you what you are giving up for them, which is why the answer to how many to run has always been an argument rather than a calculation.
The model assumes you put one down whenever you can and never want to hold one back, and it counts a card as available the moment it is drawn. Anything that lets you dig, shuffle away or replace what you have drawn sits outside it, so treat the figure as the deck's own shape rather than as the whole game.
Does the risk of missing add up across the turns?
No, and that is the surprise. Needing a certain number of resources by a given turn already implies having had enough on every turn before it, because taking one card off the count removes at most one resource.
So the chance of never missing through a turn is exactly the chance of being fine on that turn alone. There is nothing extra hiding in the sequence, which is unusual: almost everywhere else, checking many turns is worse than checking the last one.
What do two more copies buy?
About half of what the two below them bought, all the way up. With sixty cards, a hand of seven and one draw a turn, going from thirty four to thirty six is worth over six points and going from forty four to forty six is worth two thirds of one.
The halving is the whole shape of the decision. Somewhere in the middle the two cards stop paying for the slot they occupy, and the table shows where that is for your own numbers.
| Resource cards | No missed turn, in per cent | Gained, in points |
|---|---|---|
| 34 | 80,1739 | — |
| 36 | 86,8179 | 6,6440 |
| 38 | 91,8616 | 5,0437 |
| 40 | 95,4028 | 3,5412 |
| 42 | 97,6727 | 2,2700 |
| 44 | 98,9759 | 1,3032 |
| 46 | 99,6265 | 0,6506 |
So how many should I run?
That is not a question arithmetic can close, and the page does not pretend to. The cost of a resource card is that it is not a threat, and nothing here knows what your threats are worth.
What it can do is price the next two copies exactly, so the argument happens over something measured instead of over a habit.
What does the model assume?
That you put one down whenever you can, that you never want to hold one back, and that a card counts the moment it is drawn.
Anything that digs, shuffles or replaces what you have drawn sits outside it. Treat the figure as the shape of the deck itself rather than as the whole game.
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