So, since this is something I'm working on for a game tonight, let's talk (prolly for the 3rd or 4th time) about designing the underlying math for a game.

The first thing to know when you're designing the math for a game is your desired outcome for that math. Want to know how much a particularly activity should be worth in victory points? Well, how many VPs should a player earn approximately over a game?

If you're looking at me for that info, just make it up. Make some basic assumptions about the gameplay, like "Every player should earn ~100 VPs." and then work backwards from that. So, if the game is 25 turns long and you want scores to average 100, the average VP/turn is 4.

For instance, in Arkham Horror 2e I wanted the average monster to move ~1/3 of the time. So, I divvied the monster pool up into 3 equal piles and had one of the three piles move each turn, more or less. We spiced it up here and there, but that's the basic structure.

How tough should monsters be? Well, how many attacks should it take to defeat the average monster, and how much damage does the average attack do? If you want a monster defeated in 1.5 attacks and attacks do ~2-4 damage, you'll want the monster to have 4-5 wounds.

The breakpoints are actually where some of the more interesting math takes place. Like, let's say that no attack does more than 4 damage. Well, it's now a big deal whether a monster has 4 or 5 wounds. At 4, a 1-shot defeat is possible. At 5, it'll take at least 2 hits.

You can make the players 'feel' the math even if they aren't sitting there calculating everything out if you're good. Like, let's say a hero levels up and can now do 5 damage in a hit? Well, all those monsters with 5 wounds are suddenly significantly weaker for them.

There's a lot of interesting psychological underpinning for game math, too. Even without getting really into game theory, people assess risk in known, predictable ways, and static numbers are psychologically much different than variable numbers.

Any 'sure thing' you include in a game of chance should only be slightly better than a poor random outcome. Humans overestimate a sure thing in excess of its real value. Like, would you rather have $100, or a 75% of $200? The vast majority of folks will say $100, the sure thing.

However, if you look at the 'expected value' of the two options, the first has a value of $100 (100*1), while the second has an expected value of $150 (200*.75). So, particularly in a game where you'd make that choice a lot, you'd average $150 a turn instead of $100 / turn.

Now, that's a bit of an oversimplification to make my point about sure things in games, and you'll want to conceal the raw math in your designs a bit better than that unless you want them 'solved' on the internet in the first week they're out, but you see what I'm saying.

Good math design for a game takes your basic goals and meshes them with an understanding of player psychology to reach the best outcome. Who are you designing it for? What emotional atmosphere do you want to create? Different answers to these questions call for different math.