Anybody knows how chaff scale the bouts?

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Oberlus
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Re: Anybody knows how chaff scale the bouts?

#16 Post by Oberlus » Mon Nov 25, 2019 12:24 pm

Blue team
1 x robo 2xLaser 2xZortrium (2 shots per bout, 5 hits to die)

Red team 1
1 x robo 2L 2Z
0 chaff for mutual annihilation 100% at bout 3. With 1 chaff chances for blue team victory increase but still some possibilities of mutual annihilation.

Red team 2
1 x robo 2L 2Z
11 chaff.

Red team 3
3 x robo 2L 2Z
Blue robo needs to survive 7 bouts (and die on the 8th). Minimum chaff is way more than 2x11. There are too many bouts and randomness is a nightmare. However the right number is around 40 chaff.

Red team 4
4 x robo 2L 2Z
Blue robo needs to survive 10 bouts. Aprox. chaff is 78.

A simple approximation could be
BlueFleet.Chaff = RedFleet.ShotsPerBout*RedFleet.HitsToDie/BlueFleet.ShotsPerBout - BlueFleet.HitsToDie + C
C is to account for the randomness of overkill shots and the chances for the blue robo to get hit sooner than expected.

This gives us
- vs Red team 1: 5 - 5 + C = 0 + C
- vs Red team 2: 20 - 5 + C = 15 + C (here C would be negative)
- vs Red team 3: 45 - 5 + C = 40 + C (C close to 0)
- vs Red team 4: 80 - 5 + C = 75 + C (C possitive)
- vs Red team 5: 125 - 5 + C = 120 + C

Going from N to N+1 red robos means you need (2N+1)*RedShip.ShotsPerBout*RedShip.HitsToDie/BlueFleet.ShotsPerBout.
From 4 to 5 we get 9*2*5/2 = 45 (correct).

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Re: Anybody knows how chaff scale the bouts?

#17 Post by Ophiuchus » Mon Dec 02, 2019 5:50 pm

Thank you for the numbers, and the scaling of the number of ships. I do not understand though how to compare the bouts themselves.

Something like taking Blue Team vs Red Team 2/3 but doubling/tripling the number of bouts and the hits to die?
Any code or patches in anything posted here is released under the CC and GPL licences in use for the FO project.

Furthermore, I propse... we should default to four combat rounds instead of three ...for the good of playerkind.

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Re: Anybody knows how chaff scale the bouts?

#18 Post by Oberlus » Mon Dec 02, 2019 7:21 pm

Ophiuchus wrote:
Mon Dec 02, 2019 5:50 pm
Thank you for the numbers, and the scaling of the number of ships. I do not understand though how to compare the bouts themselves.

Something like taking Blue Team vs Red Team 2/3 but doubling/tripling the number of bouts and the hits to die?
Sorry, I don't understand the example you provide here. Could you elaborate more? I don't understand the sentence :oops:

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Re: Anybody knows how chaff scale the bouts?

#19 Post by Ophiuchus » Mon Dec 02, 2019 8:36 pm

Oberlus wrote:
Mon Dec 02, 2019 7:21 pm
Ophiuchus wrote:
Mon Dec 02, 2019 5:50 pm
Thank you for the numbers, and the scaling of the number of ships. I do not understand though how to compare the bouts themselves.

Something like taking Blue Team vs Red Team 2/3 but doubling/tripling the number of bouts and the hits to die?
Sorry, I don't understand the example you provide here. Could you elaborate more? I don't understand the sentence :oops:
I meant could you please try:

Blue team: 2 shots per bout, 5 hits to die
vs
Red team 2: 11 chaff, 2 shots per bout, Variant A: 10 hits to die (Variant B: 15 hits to die)
And look at double/triple the bout number from the 5-hits-to-die run (Variant Zero with 5 bouts?? so 10 and 15 bouts)


And

Blue team: 2 shots per bout, 5 hits to die
vs
Red team 3: 40 chaff, 2 shots per bout, Variant A: 10 hits to die (Variant B: 15 hits to die)
And look at the state around bouts 14-16 (Variant A) or 21-24 (Variant B)
Any code or patches in anything posted here is released under the CC and GPL licences in use for the FO project.

Furthermore, I propse... we should default to four combat rounds instead of three ...for the good of playerkind.

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Re: Anybody knows how chaff scale the bouts?

#20 Post by Oberlus » Tue Dec 03, 2019 9:25 am

Ophiuchus wrote:
Mon Dec 02, 2019 8:36 pm
Blue team: 2 shots per bout, 5 hits to die
vs
Red team 2: 11 chaff, 2 shots per bout, 10 hits to die
Blue team has nothing to do:
100% red team kills the single blue team ship at bout 3.
The 6 shots from blue team are able to kill at most 6 of the chaff. 0% to kill the red team ship.
Ophiuchus wrote:
Mon Dec 02, 2019 8:36 pm
Blue team: 2 shots per bout, 5 hits to die
vs
Red team 2: 11 chaff, 2 shots per bout, 15 hits to die
Identical results.

Are you sure this is what you wanted to test? Those are not near any annihilation scenario.

Ophiuchus wrote:
Mon Dec 02, 2019 8:36 pm
And look at double/triple the bout number from the 5-hits-to-die run (Variant Zero with 5 bouts?? so 10 and 15 bouts)
The bouts I'm calculating are the bouts you need to reach annihilation of one (or both) teams.
What do you mean by "look at double the bout number"? By adding chaff or more armed ships to the blue team? Otherwise there's no way blue team can survive bout 3.
Also, "variant zero with 5 bouts?"? What 5 bouts? I don't understand, sorry.
Ophiuchus wrote:
Mon Dec 02, 2019 8:36 pm
Blue team: 2 shots per bout, 5 hits to die
vs
Red team 3: 40 chaff, 2 shots per bout, 10 hits to die
Identical results, red team kills blue ship at bout 3.
Same for variant B with red ship with 15 hits to die.
Ophiuchus wrote:
Mon Dec 02, 2019 8:36 pm
And look at the state around bouts 14-16 (Variant A) or 21-24 (Variant B)
Well, the state at bout 3 was blue team is obliterated, so the same happens at any following bout, red stays dead and there is no battle.
So I'm sure I haven't understood your question.

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Re: Anybody knows how chaff scale the bouts?

#21 Post by Ophiuchus » Tue Dec 03, 2019 11:40 am

Oberlus wrote:
Tue Dec 03, 2019 9:25 am
Are you sure this is what you wanted to test? Those are not near any annihilation scenario.
Jeez I must have been very tired. The scenarios do not make any sense the way i wrote them. Chaff should be on the blue side and also hits-to-die needs to be scaled on the blue side. Red team should have multiple ships. I wanted to take known annihilation scenarios and compare what changes if we scale the number of bouts and structure in unison.

So going back to annihilation game for a moment:

Blue team: 2 shots per bout, Variant A: 10 hits to die (Variant B: 15 hits to die)
vs
Red team 2: 2 ships with each 2 shots per bout, and each Variant A: 10 hits to die (Variant B: 15 hits to die)


And


Blue team: 2 shots per bout, Variant A: 10 hits to die (Variant B: 15 hits to die)
vs
Red team 3: 3 ships with each 2 shots per bout, and each Variant A: 10 hits to die (Variant B: 15 hits to die)



If chaff scales completely linear (which it probably won't), the amount of chaff the blue teams need should also double (and also the necessary number of bouts). So against red team 2 we would expect about 22 chaff (Variant B: 33) and against red team 3 about 80 (Variant B: 120) chaff

edit1:
with your suggested formula (BlueFleet.Chaff = RedFleet.ShotsPerBout*RedFleet.HitsToDie/BlueFleet.ShotsPerBout - BlueFleet.HitsToDie + C) we would expect:

Variant A Red Team 2: 30 = 40 - 10 + C
Variant A Red Team 3: 80 = 90 - 10 + C

Variant B Red Team 2: 45 = 60 - 15 + C
Variant B Red Team 3: 120 = 135 - 15 + C
Any code or patches in anything posted here is released under the CC and GPL licences in use for the FO project.

Furthermore, I propse... we should default to four combat rounds instead of three ...for the good of playerkind.

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Re: Anybody knows how chaff scale the bouts?

#22 Post by Oberlus » Tue Dec 03, 2019 12:49 pm

Ophiuchus wrote:
Tue Dec 03, 2019 11:40 am
If chaff scales completely linear (which it probably won't)
It doesn't.
Oberlus wrote:
Mon Nov 25, 2019 12:24 pm
A simple approximation could be
BlueFleet.Chaff = RedFleet.ShotsPerBout*RedFleet.HitsToDie/BlueFleet.ShotsPerBout - BlueFleet.HitsToDie + C
C is to account for the randomness of overkill shots and the chances for the blue robo to get hit sooner than expected.

[...]

Going from N to N+1 red robos means blue (chaff) team needs (2N+1)*RedShip.ShotsPerBout*RedShip.HitsToDie/BlueFleet.ShotsPerBout.
Assuming RedShip.ShotsPerBout*RedShip.HitsToDie/BlueFleet.ShotsPerBout is constant, for each extra red ship blue team will need 2N+1 extra chaff.
Changes in the HitsToDie or in the ShotsPerBout of the red ships do play an important role, as well as blue ship's ShotsPerBout.
On the other hand, HitsToDie of the blue ship isn't relevant except versus fighting only 1 or 2 red ships. If red ships have greater numbers, HitsToDie of the blue ship are irrelevant and blue team is way better focusing on getting more ShotsPerBout.

The idea would be: if I use chaff, the armed ships only need to have some more HitsToDie than the chaff itself. 3 HitsToDie is a sensible number, 4 to be sure.
the amount of chaff the blue teams need should also double (and also the necessary number of bouts)
Yes, the number of bouts doubles, the number of chaff grows faster than linear, but not too faster.
Ophiuchus wrote:
Tue Dec 03, 2019 11:40 am
Blue team: 2 shots per bout, Variant A: 10 hits to die (Variant B: 15 hits to die)
vs
Red team 2: 2 ships with each 2 shots per bout, and each Variant A: 10 hits to die (Variant B: 15 hits to die)
For annihilation of red fleet, blue always needs to survive RedFleet.Ships*RedShip.HitsToDie/BlueFleet.ShotsPerBout bouts.

Blue(A or B) vs red-A, blue needs 10-11 bouts.
Blue(A or B) vs red-B, blue needs 15-16 bouts.
Let's call those BoutsToKillRedFleet.

For blue to get alive to bout number BoutsToKillRed, being blue relatively lucky, blue needs Chaff = BoutsToKillRedFleet*RedFleet.ShotsPerBout - Blue.HitsToDie/2
That "/2" is a gross aproximation, but irrelevant once RedFleet.ArmedShips is > 2*BlueFleet.ArmedShips.

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Re: Anybody knows how chaff scale the bouts?

#23 Post by Ophiuchus » Tue Dec 03, 2019 1:45 pm

Hm that reads like you come from theoretical viewpoint. Overkill is hard to reason about. Did you try in the your simulator?
Oberlus wrote:
Tue Dec 03, 2019 12:49 pm
Ophiuchus wrote:
Tue Dec 03, 2019 11:40 am
the amount of chaff the blue teams need should also double (and also the necessary number of bouts)
Yes, the number of bouts doubles, the number of chaff grows faster than linear, but not too faster.
So would you subscribe to the following - If you double the number of combat bouts while doubling the ship structure keeps the balance between "real" ships mostly (e.g. ignoring fighters and stealth) while you need to pay (more than) double the PP to buy chaff to get the same effect .
Any code or patches in anything posted here is released under the CC and GPL licences in use for the FO project.

Furthermore, I propse... we should default to four combat rounds instead of three ...for the good of playerkind.

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Re: Anybody knows how chaff scale the bouts?

#24 Post by Oberlus » Tue Dec 03, 2019 4:25 pm

Ophiuchus wrote:
Tue Dec 03, 2019 1:45 pm
Hm that reads like you come from theoretical viewpoint. Overkill is hard to reason about. Did you try in the your simulator?
It's half theoretical.
I had no time to clear my mind and finish the simulator (otherwise you'd already have the code for your personal use), I can only simulate single bouts. I get a hierarchy of single-bout simulations, with results accurate up to third bout, but then the number of calculations is too big and I begin to ignore the less common cases and focus on the most probable (2 or 3 possibilities after after each bout, so around 15 cases at bout 3). However, since there is only one kind of ship apart from the chaff, the calculations should be rather close to reality even for tens of bouts.

Ophiuchus wrote:
Tue Dec 03, 2019 1:45 pm
So would you subscribe to the following - If you double the number of combat bouts while doubling the ship structure keeps the balance between "real" ships mostly (e.g. ignoring fighters and stealth) while you need to pay (more than) double the PP to buy chaff to get the same effect .
If you mean to get the same results after double of bouts...

Blue team 1 ship x (3 shots, 4 hits) + 4 chaff.
vs
Red team 2 ships x (3 shots, 4 hits)

Bout 1: most probable result (~40%) is 3 chaff down and 1 hit on blue ship.
Bout 2: ~99% blue is dead (if some chaff gets shots more than twice, 0.08% chance, in this and previous bout, way less than 0.08%, blue could survive to a third bout); red have a thin chance to lose 1 ship but probably both ships are alive.

Now, doubling the HitsToDie of all armed ships and doubling (plus some extra) the chaff we should get to 4 bouts, let's see:

Blue team 1 ship x (3 shots, 8 hits) + 10 chaff.
vs
Red team 2 ships x (3 shots, 8 hits)

Bout 1: probable result is 4-5 chaff down and 0-1 hits on blue ship (0-1 overkill shots).
Bout 2: probable result is another 4 chaff down and 1 hit on blue ship (1 overkill shot)
Bout 3: all chaff dead and blue ships has 4 hits to die (1-2 overkill shots).
Bout 4: 100% blue is dead; red has got 12 shots, again a thin chance for one red ship down, but most probably all alive.

So yes, looks like that assumption holds, at least with this small numbers. But keep in mind that the ratio shots-hits is relevant here, so with different shots/hits ratio results could be different.

I really want to finish the combat simulator, but dunno when.

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Re: Anybody knows how chaff scale the bouts?

#25 Post by Oberlus » Thu Dec 05, 2019 3:59 pm

Ophiuchus wrote:
Tue Dec 03, 2019 1:45 pm
Did you try in the your simulator?
I'm about to finish a real simulator.
It still has many inconvenients, but it seems I'm starting to get real results.

I'm testing right now the following:

Fleet A:
2 x Robo with 2 laser (11 damage) and 2 zortrium (+22 structure), so total 47 structure and 2 shots of 11 damage.

Fleet B:
1 x Robo with 2 laser (11 damage) and 2 zortrium (+22 structure).
N chaff.

The results are rather variable, more than I expected from the half-theoretical calculations, but mutual annihilation seems more frequent with 12 chaff:
RepetitionA ships aliveA HP leftB ships aliveB HP left
#100217
#200114
#300114
#41300
#50026
#611400
#71300
#80000
#90000
#100000
This results all needed 5 bouts.


Edit: This was using current implementation of targeting.

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Re: Anybody knows how chaff scale the bouts?

#26 Post by Oberlus » Wed Dec 11, 2019 11:08 am

Update.

The combat simulator works nicer now, at least without fighters, that needs testing. Still needs some polishing, like calculating the statistics itself, instead of copying the raw data into a spreadsheet to compute them there.
Oberlus wrote:
Thu Dec 05, 2019 3:59 pm
Fleet A:
2 x Robo with 2 laser (11 damage) and 2 zortrium (+22 structure), so total 47 structure and 2 shots of 11 damage.

Fleet B:
1 x Robo with 2 laser (11 damage) and 2 zortrium (+22 structure).
N chaff.
Computing 100 simulations, for mutual annihilation the right chaff number is 10:

Stats after combat:
fleetA-ShipsfleetA-CostfleetA-HPfleetB-ShipsfleetB-CostfleetB-HP
MIN000000
MEDIAN000000
AVG0.4550.43.440.433.143.07
MAX222428211836
STDEV0.68777.06.220.56951.16.11

With 11 or 12 chances are that at least some chaff or the B-robo will survive.
With 9 chaff, more than 50% of the repetitions one A-robo survives.

Note: for statistics here, these chaff are comsats of cost 6 PPs.


Edit2: Following is the (hopefully) definitive statistics table format, I've discarded average and std. dev. stats because they seem to convey little information with these kind of data (not normal), and I've added instead more percentiles. Ophiuchus, let me know if you'd like something different once I begin calculating more fleet scenarios.
MINP10P25MEDP75P90MAX
fleetA-ships00.000.000.001.001.002
fleetA-cost00.000.000.00112.00112.00224
fleetA-HP00.000.000.004.5014.0028
fleetA-fighters00.000.000.000.000.000
fleetB-ships00.000.000.000.001.003
fleetB-cost00.000.000.000.00112.00124
fleetB-HP00.000.000.000.006.0025
fleetB-fighters00.000.000.000.000.000
PS: So the actual optimal chaff for mutual annihilation is somewhere around 10.5. Chaff 10 has an small advantage for fleet A (non-chaff) as seen in the better P75 (Q3) values.

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