The fundamental problem with caps on model displacement (outside freely reforming units like light troops and skirmishers): It makes it impossible for anyone to know what a legal move is ahead of time.

Here's the problem:

I've convinced myself I (at least used to) know all the math to do this problem. I've done enough to know what a solution probably looks like. It involves calculus (99% sure, to find the maximum) and possibly linear algebra. I'm also pretty sure d is non-zero for some base sizes and rank/file combinations, including some non-trivial cases (I think d should be unconstrained for single rank units). But even though I've convinced myself about a

Anyway, this is not something anyone is calculating on the fly. It's not something anyone knows off the top of their head. The end position here is indeterminable for 99.9% of the players during a game, even knowing the starting position, before actually making the move and checking the model displacements (something which is not trivial to do properly). And yet, knowing how much ground a unit could cover and still wheel some is something everyone playing the game should be able to know.

The fundamental problem, of course, is that the rear outside model's displacement is

If anyone cares to take a whack at finding a general solution and posting their work, I'd love to see it. But it's kind of ridiculous that determining valid end states in a game without repeatedly moving and double checking displacement requires

Here's the problem:

**A unit wants to march mostly straight forward and then finish with a wheel. It wants to use all its march distance. (So D, the forward distance, and d, the wheel distance, sum to March). It also wants to maximize the wheel distance, d. The outside rear model also cannot displace, center to center (R), farther than it's march rate. How far can it wheel while satisfying these conditions? Find a general answer for any number of ranks, files, and any base size. (That is, the function takes # ranks, # files, and base size as input in some fashion).**I've convinced myself I (at least used to) know all the math to do this problem. I've done enough to know what a solution probably looks like. It involves calculus (99% sure, to find the maximum) and possibly linear algebra. I'm also pretty sure d is non-zero for some base sizes and rank/file combinations, including some non-trivial cases (I think d should be unconstrained for single rank units). But even though I've convinced myself about a

*method*to solve the problem, I haven't actually done the work to find the solution. (In part because its hard, and in part because half of the math involved is half remembered at this point - it's been awhile).Anyway, this is not something anyone is calculating on the fly. It's not something anyone knows off the top of their head. The end position here is indeterminable for 99.9% of the players during a game, even knowing the starting position, before actually making the move and checking the model displacements (something which is not trivial to do properly). And yet, knowing how much ground a unit could cover and still wheel some is something everyone playing the game should be able to know.

The fundamental problem, of course, is that the rear outside model's displacement is

*non-trivial to calculate*based on the movement of the front model. (Even ignoring the calculus part, just calculating the rear model's displacement based on the measured movement requires multiple sin and cos functions to calculate the movement that occurs during rotation about the fixed wheel point).If anyone cares to take a whack at finding a general solution and posting their work, I'd love to see it. But it's kind of ridiculous that determining valid end states in a game without repeatedly moving and double checking displacement requires

*calculus*. Especially a game played by pushing physical objects around on a table, where measurements are going to be imprecise. (The end result of which is that many moves people make in actual games, even with top players and ETC quality judges watching, are likely not strictly speaking legal).Just because I'm on the Legal Team doesn't mean I know anything about rules or background in development, and if/when I do, I won't be posting about it. All opinions and speculation are my own - treat them as such.

Legal

Playtester

Chariot Command HQ

The post was edited 2 times, last by Squirrelloid ().