Keyforge: what being stolen from each turn costs you
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Completing happens at the start of a turn, as soon as you are holding enough, and what you collect arrives afterwards. Nothing here is tied to one game: any race towards a fixed price, against someone reducing what you take in, works out the same way.
Results
| Turn your last goal completes | — |
| Turn it would complete with nothing taken | — |
| Turns lost to what is taken | — |
| What one more point taken would cost | — |
| How much more you would have to be holding to save a turn | — |
What each point taken from you costs
| Taken each turn | Turn you finish | Turns lost in total | What that point alone cost |
|---|
That last column is the whole page. The first point taken from you is cheap and the last one is ruinous, because what is being attacked is not your pile but your rate, and the finish line sits at the price divided by that rate. Halve the rate and you double the wait, which is why the difference between being robbed a little and being robbed a lot is not a matter of degree.
It also explains why stopping the last point of it is worth so much more effort than stopping the first, and why a player who is only slightly behind on that rate is in far less trouble than they look, while one who is badly behind is in far more.
The last row is the other half, and it is the one that costs people games. What you are holding only helps when it crosses a whole turn of collecting: below that it changes nothing at all, so being a couple of points ahead is often worth exactly zero. Look at what it would take to actually save a turn before deciding that a small lead means anything.
Why is being robbed twice as much far worse than twice as bad?
Because what is under attack is your rate, not your pile. The finish line sits at the price divided by what you take in each turn, so halving the rate doubles the wait rather than adding a fixed delay.
With three goals costing six each and four collected a turn, losing one point a turn costs one turn, losing two costs four, and losing three costs thirteen.
| Taken each turn | Turn you finish | Turns lost | What that point alone cost |
|---|---|---|---|
| 0 | 5 | 0 | 0 |
| 1 | 6 | 1 | 1 |
| 2 | 9 | 4 | 3 |
| 3 | 18 | 13 | 9 |
So which point of it should I spend effort stopping?
The last one, by a wide margin. Stopping the point that takes you from three down to two is worth nine turns in the table above; stopping the one that takes you from one to zero is worth one.
The same reading works in reverse for attacking: taking a first point off someone comfortable is nearly free for them, and it only becomes devastating once their rate is already low.
I am a couple of points ahead. Is that worth anything?
Usually nothing at all. What you are holding only helps once it crosses a whole turn of collecting, because a turn is the unit in which the finish moves.
Collecting three a turn against goals costing six, holding nothing, one or two all finish on the same turn. Only at three does the finish move, and it moves by exactly one turn.
What does the page assume?
That you complete a goal at the start of a turn as soon as you are holding enough, that what you collect arrives afterwards, and that both the collecting and the taking are steady.
A swing that happens once, rather than every turn, is a different question: put it in as a change to what you are holding instead of as a rate.
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