Re: Core hits and striking the colours (LONG!)

Tom B wrote:
>
>Item III:
>
>What sort of points adjustment is sensible for ships using Strike The
>Colours? I like this from a perspective of 'mission motivation' (and
>probably high or low motivation might affect this).
>
>Item IV:
>
>What sort of points adjustment is sensible for ships using Core
Systems? It
>seems to me this question is especially relevant if two fleets have
>differing hull row counts since the likelihood of getting cored out of
the
>game in a 5-hull-row ship is pretty high and likely far earlier.

TL;DR version: the chance of a ship being destroyed by a core
hit on the 2nd threshold is 22% for escorts, 15% for cruisers,
and 10% for capitals. Striking the Colours is much nastier.

I've done some number crunching to try and get an idea of what
kind of difference striking the colours and/or core systems make
to the game. Maybe it will be useful in deciding points
adjustments.

These are notepad calculations, not from a massively detailed
computer model. All percentages have been rounded off to the
nearest whole integer. For Full Thrust I believe this is still
accurate, because all threshold checks get made only 3 times per
ship per game at most. If FT were like, say, ACTA where a
"critical hit" can occur with every shot, this would be
misleading because even small fractions add up over tens or
hundreds of rolls.

As the basis for calculations I've used Fleet Book 1. Unless you
design your ships on radically different principles (10% hulls?)
the results aren't going to vary significantly.

Both core system hits and striking the colours can cause Bad
Things to happen on threshold checks. First step, what can
happen normally?

I've defined the worst thing that can happen on a threshold as
being fight disabled, unable to shoot at other ships, for at
least one turn. Sure, in some circumstances it might be
disastrous to lose your screens, or drive; but remember the aim
here is to get an approximation and being unable to shoot is
almost guaranteed to be a Bad Thing. It's very nearly a core
bridge hit.

Without core systems this can happen in two ways: either you
lose all your FireCons on the threshold and can't repair any, or
you lose all your weapons and can't repair any.

On the first threshold, chance of losing a single FC or weapon
is 1/6, or 17%. The chance of losing two is 1/6 x 1/6, or 3%.
Chance of losing three is under 1% and therefore ignored.

Chance to repair any one system is 1, 2, or 3 / 6 depending on
how many damage control parties the ship has left.

(Repeating, I am not saying that you can't lose 3 FireCons or 3
weapons on a threshold check, just that the chance of doing so
is sufficiently low that it's an act of $DEITY for any game
without dozens of ships per side.)

The very small escorts in FB1, mass 14 or less, can have a 28%
chance of being disabled. For escorts up to mass 20 it's around
16% to 13%. This seems high, but these are ships that can be
annihilated by a single torpedo. Being hit by anything can be
catastrophic.

Heavy frigates and destroyers mostly have 2 or more weapons so
are primarily at risk of losing their one and only FireCon.
Percentages are 11% or 8% for these bigger escorts, except for
an NSL missile destroyer which only has 2 weapons and thus goes
up to 16%.

Cruisers, and a couple of small battlecruisers with only 2
FireCons, have a 1% chance of being disabled, as they all have
lots of weapons and also more DCPs. The only exception is an NSL
escort cruiser with a single FC which has an 8% chance.

Capital ships (ignoring carriers) don't get disabled on the
first threshold.

On to the second threshold. Here it gets a bit more complicated,
because some systems might have been lost on the 1st and not yet
repaired.

For simplicity, I've assumed best case for FireCons, that any
lost on the first have been repaired; and worst case for
weapons, none repaired. So FireCons have a 2/6 = 33% chance of
being lost after this second threshold and weapons have a 3/6 =
50% chance. There's now a 1% chance or better of losing 4
FireCons or 6 weapons.

As before, there's a 1, 2, or 3 in 6 chance of being able to
repair at least one FC or weapon, ignoring multiple attempts
which are possible with bigger ships.

The really tiny escorts are dead at this point. Corvettes and
light frigates have a 48% to 33% chance of being disabled.
Heavier frigates and destroyers have a 38% to 31% chance, most
often 33%.

Cruisers and 2 FireCon battlecruisers have a 11% to 6% chance of
being disabled, except for the previously mentioned NSL escort
cruiser on 24%. Most are 9% or 6%.

Capitals (again, other than carriers) are no longer immune.
There's a 2% chance for the smaller ones under 180 mass, and 1%
for the superdreadnoughts. (And this is overstating, because
these ships can make multiple repair attempts even after losing
two hull rows.)

To sum up, unless I've made some serious mistakes in my math
(please tell me) the chance of being disabled for at least one
turn without Core Systems or Striking the Colours is:

Frigate or smaller: 28% to 13% on 1st, 48% to 33% on 2nd.
Large escort: 11% to 8% on 1st, 38% to 31% on 2nd.
Cruiser: 1% on 1st, 11% to 6% on 2nd.
Capital: none on 1st, 2% or 1% on 2nd.

OK, now let's add Core Systems. On the second threshold there's
now a 30% chance of 1 core hit, 3% chance of 2, and once again
all 3 is an act of $DEITY which I'll ignore. (Plus, if you've
got both life support and power core hits, bridge problems don't
seem so bad.)

Resistance to core hits is number of DCP, or mass. Because FT
has "super" destroyers with mass over 40 and "super" cruisers
with mass over 80, the biggest escorts are as good as cruisers
and the biggest cruisers as battlecruisers. Escorts <= 40 mass
have 1 DCP on the 2nd threshold, super destroyers and most
cruisers <= 80 2 DCP, super cruisers and capitals <= 100 3 DCP,
capitals <= 180 4 or 5 DCP, and the superdreadnoughts all have
at least 6 DCP.

Escorts, cruisers, and small capitals don't have enough DCP to
repair both a core hit and other systems, so the chance of being
disabled by FC/weapon loss goes up. I'm not going to include
these calcs because core system failures are much more
dangerous: if the power core blows up, it doesn't really matter
how many FireCons you have.

A bridge hit can mission kill the ship on a 6. This is the only
FT "critical" that the defending player doesn't have a chance to
negate.

When doing calculations for core systems, I often use an F for
failure term. If the chance of repairing a system is N/6 where N
is 1, 2, or 3 DCPs, the chance of failing is F/6 where F = 6 -
N.

For bridge hits the chance of being disabled on the next turn is
5/6 x F/6. (Any bridge roll other than 6.) I won't go into the
chances of being disabled for 2, 3, ... because the previous
calculations have only looked one turn ahead.

So ships are killed 3% of the time (6 then 6). The chance of
being disabled for 1 or more turns is: escorts with 1 DCP 12%,
cruisers with 2 DCP 9%, super cruisers and up with 3+ DCP 7%.

If you don't try to repair straight away, say because your ship
only has 2 DCP left and you got the 3% chance of a double core
system, it's 14% chanced of being disabled next turn. This only
happens to escorts and cruisers, including super and battle
cruisers, but battleships and up are pretty safe.

Aside from the 3% chance of a mission kill, bridge hits are less
dangerous to escorts and cruisers than the existing odds of
losing all your weapons or FC. For capitals, the chance of being
disabled is higher, but still less than 10%.

A life support hit will kill the ship if it isn't repaired. The
number of repair attempts you get is equal to the number rolled
on the die, and one success is enough. So in T turns the ship is
killed only if every attempt fails, which is (F/6) ^ T (raised
to power T). T is from 1 to 6, each value of T has a probability
1/6, and there's a 1/6 probability of a life support hit to
begin with. Final result is

	 (F/6)^1 + (F/6)^2 + ... (F/6)^6
	 -------   -------	 -------
	    36	      36	    36

As a sanity check, if you make no attempt to repair then F = 6,
the result is 1/36 + 1/36 ... + 1/36 = 6/36, or 1/6 chance.

Final probability of a kill from life support is: escort 9%,
cruiser 5%, super cruiser and up 3%.

Lastly, power core (or "reactor") hits are the trickiest to
calculate. On the first turn, there is a DCP/6 chance of
successful repair. If that fails, there's a 2/6 chance of
explosion. The tricky part is the second and subsequent turns:
the chance of having to roll again is equal to the chance of
neither exploding nor repairing until then.

Explosion = F/6 x 1/3 = F/18
Repair = DCP/6 = (3 x DCP)/18
Chance of neither = 1 - (F + 3 x DCP) / 18
Since F = 6 - DCP,
Chance of neither = 1 - (F + 18 - 3F) / 18,
= (18 - F - 18 + 3F) / 18
= 2F/18 = F/9

So the probability of exploding on any turn T is F/6 x 1/3 x
((F/9) ^ (T-1)) Again, plugging in F = 6 for no repair attempts
gives a 1/3 chance of exploding at T = 1, 2/9 for T = 2, which
looks right to me.

Since there's no duration, it is possible but very, very,
unlikely that this can go for many turns. The actual chance of
exploding falls below 1% quite rapidly, in just 4 turns if
you've got 3 DCP on the job, so the probability (not certainty)
of being destroyed converges on a limit.

Final probability of a kill from power core is only a little bit
worse than life support: escort 10%, cruiser 7%, super cruiser
and up 4%.

Adding bridge rolls of 6, life support, and power core all
together, the probability of being destroyed on the first
threshold is:

Escort: 22%
Cruiser: 15%
Super cruiser and up: 10%

My head hurts, so I'm not going to repeat this for the 3rd
row threshold checks.

What does all this mean? Well, it sucks to be an escort and
bigger is better, but we already knew that.

The odds of a "critical" destroying the ship are reasonably
low in Full Thrust (compared to, say, ACTA B5) and only after
the ship has already taken 50% damage. Me, I wouldn't remove
them. Sometimes a shell hits the magazine, the circuit breakers
pop in the brand new battleship, a fighter crashes into the
bridge of the super star destroyer.

On the other hand, I can see the merits for some kind of crew
quality factor. I suggest rather than taking out core hits
altogether, give better quality crews a "+1" on their damage
control effectiveness. That is, 1 DCP counts as 2, 2 as 3, and 3
as 4. Also replace the Bridge hit 6 result as "6 turns disabled"
rather than permanently out of action. This would make a big
difference to escorts, both on regular thresholds and core
systems, and push the chance of bigger ships being destroyed on
the first threshold down under 5%.

Striking the Colours, though, is really nasty. There's now a 17%
chance of being destroyed on the first threshold, and 33% chance
on the second, far worse than before. So without giving an exact
figure, I suggest that the points reduction for such ships needs
to be a double digit percentage.

If anyone is still awake and wishes to criticize or comment,
please do!

	cheers,
	Hugh Fisher