(TFT) HTH simulation results (intermediate)

["Cris Fuhrman" <fuhrmanator@gmail.com>]

So, I got my prototype simulator working last night for HTH. It's still a
little crude, because HTH rules are complicated and I didn't want to try to
manage every possible thing. For now, it's hacked up a bit, since some
heroes try to engage in HTH and others try to leave it if they can.

When I ran the first few cuts at my code, I realized that a hero who is
persistent at engaging (and re-engaging, if the defender manages to
disengage) in HTH can be annoying. Consider this:

Turn 1: Hero A acts first and engages B in HTH. B drops his weapon and
shield per the HTH engagement rules. During his time to act, B choses to
disengage from HTH. With a lucky role, he succeeds; he stands up and moves
to an adjacent hex. By the way, his shield and weapon are in the other hex
where A is now.

Next turn: Hero A is still prone (as far as I understand the rules). Can A
attempt to re-engage B in HTH? Basic Melee doesn't speak of crawling, so I'm
not sure if A can move onto B again.

On the other hand, sometimes it may be to the defender's advantage,
particularly if his DX is less than the HTH-engager, to just stay in HTH and
try to do the most damage. He has a 1-in-6 chance to disengage. If their DX
is equal, it's 50% chance to disengage. Ultimately, I'd make this option
"always attempt to disengage from HTH" an option in the simulator for a
given hero before setting up the bout.

As for statistical outcomes, we suspected it makes sense for a ST 8 DX 16
dagger-wielder to engage a ST 16 DX 8 plate-wearer. The win outcome for the
dagger-wielder is nearly 50% when HTH is used, whereas it was very low when
traditional fighting occurs (roughly 4%).

When the same dagger-wielder takes on a ST 15 DX 9 plate wearer in HTH, his
chances decrease by around 10%. As the starting opponents' ST decreases, the
odds of the ST 8 HTH attacker winning go down to less than 5% vs.
plate-wearers. The only way the ST 8 guy wins these bouts is by doing
double/triple damage rolls, or if his enemy drops/breaks his weapon.

The most damage a dagger in HTH (1d+2) can do (without double/triple damage
roll) is 8 points (6 + 2), with an average of 5.5. Plate armor stops 5 hits.
This gets me to think that a mathematical/statistical model might be easier
than coding up the simulator in Java :-) The problem is, the model seems to
be a mixture of independent states (a la Markov) and dependent events (since
damage is cumulative). Perhaps it's all independent, and I'm just not seeing
how to model cumulative damage with the probabilities.

Also, a HTH-engager who doesn't attack from behind or from the side will
need to have less armor than his target, since that means his MA will be
higher and thus HTH can possibly take place.

All in all, I'm considering a re-design of the GUI of the simulator, so that
the match-ups, with various HTH options, whether to defend, etc., can be
easily chosen and the output used in Excel or something.

If anyone has ideas, please let me know.
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