#### Math? In MY Level Design?

That's right! In the intro post, I mentioned wanted 8-10 minutes of gameplay. It's not much, but even this little can be tricky to reach if the levels aren't planned out with those figures in mind. (Unless the player is forced to grind, of course. Let's not do that!) The last time I tried making a similarly small game, I actually ended up short on content. This time, I thought it might be worth trying a more careful, numbers-based approach to avoid this problem.The time that a player spends on this game can be summarized like so:

Time (total) = Time (walking) + Time (fighting)

-or-

Ttotal = Tmove + Tfight

We can break this equation down further. Movement time can be summarized as the distance traveled divided by the speed. Since this game has tile-based movement, we can get an estimated movement time like so:

Ttotal = (Tiles / Speed) + Tfight

Both of these variables can be controlled, one through settings and the other through level design. We can do the same for combat:

Ttotal = (Distance / Speed) + (Encounters * Turns * 2)

We can go further, and break down the encounter count too:

Ttotal = (Distance / Speed) + ((Distance * Encounter Chance) * Turns * 2)

We can go further, and break down the encounter count too:

Ttotal = (Distance / Speed) + ((Distance * Encounter Chance) * Turns * 2)

In case you're wondering, your average turn lasts about 2 seconds. If we multiply the average number of turns by the average number of encounters, we can use that value to figure out roughly how much time will be spent in combat.

Bear in mind that these calculations won't be 100% accurate. They ignore a ton of variables, such as the player's level, how often they 'cut corners' by moving diagonally, how long they stop to think about things, and so on. Even so, I think it's a good method for guessing about how much the game needs.

#### Applying the Equation

Let's try solving the equation now. We want the game to last between 8-10 minutes, which we can replace with 540 seconds (9 minutes):

540 = (D / S) + ((D * C) * 2T)

This gives us a few variables that we can play with:

- Distance
- Movement Speed
- Encounter Chance
- Encounter Turn Count

Speed is the easiest value to test, so let's start there. In Halberd, speed is currently measured in pixels per second. I've already picked a tile resolution of 24x24, so I've set up some tests using multiples of that.

3 tiles per second seems like a pretty good pace. 2 could also work, but I'm a bit worried that without a 'run' option it might feel just slightly

1 tile/s |

2 tiles/s |

3 tiles/s |

4 tiles/s |

*too slow.*
540 = D / 3 + (D * C * 2T)

1620 = D + (D * C * 2T * 3)

(1620 / D) - 1 = C * 2T * 3

1620 = D + (D * C * 2T * 3)

(1620 / D) - 1 = C * 2T * 3

With this addition, the easiest next step is to figure out how long the player should spend fighting. Given how simple fights are, I'd feel a little uncomfortable making them last more than 4-5 turns. So, I'm going to aim for around 4:

(1620 / D) - 1 = C * 8 * 3

(1620 / D) - 1 = C * 24

( (1620 / D) - 1) / 24 = C

(1620 / D) - 1 = C * 24

( (1620 / D) - 1) / 24 = C

Now, this only leaves the encounter chance and distance. Honestly, I'm not sure what I want to do for these two. However, we

Looking at these numbers, the distances in the 200-300 range look most appealing to me. For now, I'm going to start with an average of about 250 tiles of movement per area and a 2.5% encounter rate. For reference, 250 tiles is about 10 640-wide "screens" in size. It's on the bigger end, but considering the target time I'm going for it should fit rather well.

My next step would be building a test environment to try out these numbers for real, but my mouse is pretty much out of commission so that'll have to wait. I have a replacement coming in a few days, so I'll probably spend the downtime working on Halberd's code instead.

*have*simplified the equation enough to some real number-crunching. So, let's examine some possibilities with a spreadsheet:My next step would be building a test environment to try out these numbers for real, but my mouse is pretty much out of commission so that'll have to wait. I have a replacement coming in a few days, so I'll probably spend the downtime working on Halberd's code instead.

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