This, I think, is why so many people struggle with Liberty. If you aren't very attentive about micromanaging your tiles, then you're basically crippling yourself by playing without the Tradition opener.
Tradition gives -25% to an
exponent of the plot culture cost. That exponent is by default 1.1. So, you know, the culture cost grows not only as a multiplier of a pretty substantial constant, but there's an exponent in there, so it grows in difficulty in proportion to how difficult it was for the last single tile.
Even a tiny exponent like 1.1 is no joke. 250 raised to that power is 434. You can't understand this without reference to scale, because it works on the level of scale.
This exponent applies to each term in what becomes an arithmetic series of sums, of plot expand costs. Exponentiation is not linear, so you can't pull it out of the summation, but these numbers do grow. The first plot culture cost is what, 12? The exponent makes that 15. Actual thresholds of, say, 40, 75, maybe 90, those become 57, 115, 141.
75% of 1.1 is 0.825 . This is less than 1, so this exponent shrinks its argument. And it's an exponent, so it's no joke. Here's what convinces me that the tradition opener is like hacking the developers, and taking advantage of how far they goofed the math on this (mind, this is a design problem - a programmer told to write this is just gonna write this; it's a dev/design job to tell this is wrong) . The appropriate comparison to understanding how much of a bonus that 0.825 gives you is to look at its actual difference from 1.0, not its ratio from 1, the actual 1.0 - 0.825 = 0.175 . It's almost twice as effective at reducing the nominal cost of plot accrual as the default value is at hindering it.
Exponentially speaking.
Suppose it costs 50 culture to expand at base. Do you know what the 0.825th power of that number is?
Are you sharp enough to actually know what quantity equals the one just described, maybe actually calculating fractional exponents in your head, maybe a memorized table you're aware of? Either one pretty badass?
The expression 50^0.825, which is 50^(1.1 - 25%*1.1) , comes to 25.214. 25. It comes down to half the cost, and gets
rounded down.
The larger the number is, the more of an impact this exponent has.
What if it cost 500 culture to grab a plot? That actually figures like this: 168.52 .
You pay a
third of what you're supposed to.
That's what Tradition opener does and it's the only thing that operates on this. Religious Settlements Pantheon modifies the culture cost - it just takes off 15% after the fact of all of this.
Here's another way to be sure someone didn't understand numbers on this. They capped the modifiers for culture cost at -85%. But that's just modifiers - like the one mentioned. There is no cap on culture exponent modifiers.
If those modifiers had said -90%, the exponent would be 0.11. If they had been -100%, every plot would cost 1 culture to grab. Try not to complain to much about paying at least 15% of virtually nothing.
If they had ever been positive, the exponent would go up as portions of 1.1 , some arbitrary constant. If anyone ever alters the constant 1.1, it's only at the arbitrary value of 1.33 that Tradition's exponent modifier keeps things in the realm of a penalty.
-----
Pick tradition because tiles are good. You need them to get stuff.
