RANGEBLENDS · THE BALANCE BENCH
That question normally costs you three evenings of play and an argument. Here it costs a millisecond, because the game is a law rather than a feeling. Change the price of an upgrade below and watch the answer move.
Everything on this page is computed in your browser, now, by the same twin that the Python is checked against. Nothing here is a screenshot of a number I once saw.
A tower in this model does not stand at a point on a map. It covers a stretch of the path —
[a, b] in metres along the route the enemies walk. That is the same move the square-shell addressing
makes for terrain: it turns a two-dimensional problem into a line. Everything useful follows from it. The simulation
becomes exact rather than sampled, it is deterministic, and a whole five-wave game runs in a few milliseconds — so
a few hundred games is a pause you barely notice, and a balance question becomes arithmetic instead of taste. The
sweep below reports its own timing on your machine rather than mine, once it has run.
Three upgrades to a tower, each priced as a multiple of what the tower cost to build. The last step is meant to be dear: it is the thing you buy when you have run out of good ground, not a routine purchase. The first two are meant to be real choices.
sweeping…
The sweep is a lot of games at once, which hides what a game feels like. This is a single one: the same three towers, played right through, with what each wave stopped, what got past, and what was in the purse at the end of it.
Priced at 0.8 and 1.3, upgrading a tower loses to simply building another one, and loses badly — the first two steps cost more than the damage they buy. Repricing them to 0.5 and 0.8 makes upgrading a genuine option again, and leaves the build-another win rate exactly where it was, which is how you know the change did only what it was meant to.
That is the whole argument for doing balance this way. The fault was not subtle and it was not a matter of opinion, but it would have survived a dozen evenings of play, because losing slightly more often with one spending habit than another is not something a person can feel. A few hundred games in a millisecond can.
Play Silo Line, which uses this ladder ↗ How a law makes a place ↗