Victor the Vicious Final Boss Optimization

[ZBest]

I've been struggling with the best way to deal with the VtV boss camp.

Asipak's simulator Hall-of-Fame comes up with a suggestion, based upon the unit values used, of:
1: 122R 128C (V)
2: 47M 22S 1E 55C 125K (V)

With a max loss of 3340 barracks-minutes

I've come up with:
1: 106R 44S 100C (V)
2: 83R 15S 1E 27C 124K (V)

With a max loss of only 3075 barracks-minutes (53 minutes less to replace in a lv5 barracks)

And also:
1: 78R 22S 100C
2: 77S 1E 73C 99K (V)

With a max loss of only 3222 barracks-minutes (23.6 minutes less to replace in a lv5 barracks and only 1 vet required)

It's an interesting optimization problem because the first wave, only the cavalry are doing any damage. The other troops are just there to keep the cavalry alive. The minimum you should ever consider is 72C, which would defeat all of the rangers in round 1 so they never have any chance to deal damage.

It will always be better to tailor the 2nd wave to the remaining troops. I think the optimal 1st wave will need to at least bring the count under 79 scavangers. 141s 1e 108k is able to deal with that. I'm coming up with 103s 21e 126k when I try to take on 80 scavangers.

The problem becomes trying to balance the increasing cost of keeping the cavalry alive in the 1st wave against the savings gained in the 2nd wave. The 80R 46S 124C (V) 1st wave solution that guarentees zero scavangers remaining seems a bit wasteful splashing all the extra damage onto Mary -- and the combined 3252 barracks-minute max loss is obviously far from optimal. Both of the 100-cav waves I came up with above target a range of remaining troops -- the veteran targeting 23 remaining scavangers or less (with some chance of zero) -- the normal (200-troop) tuned to have all 100 cavalry survive 3 rounds -- resulting in 46 to 60 remaining scavengers. If the 2nd wave is tailored to the remaining troops, the savings increase.

Just wondering if anybody else has ever spent the effort on this problem, before I start spending my time on it.

[ZBest]

Well, when I try a few combinations of 1st wave, I get the following curve -- the more I spend, the number of scavangers goes down linearly:



Optimizing a few 2nd waves, I find that the curve isn't linear, it's exponential, with it getting increasingly expensive with more scavangers:



The statistics dictate that I should try looking to have an average of 42 scavangers remaining --- when I add the cost of the two waves together:



So --- in the simulator, I came up with a 1st wave that has 30-50 scavangers remaining -- with an average of 42. And a 2nd wave to deal with the worst-case 50-scavangers:

1: 145r 27s 78c (v) 2: 6r 65s 1e 52c 126k (v)

Bringing the grand total down to a maximum of 2961 barracks-minutes -- which is 11.3% less than the best result in the hall-of-fame.

[ZBest]

If I interpreted the optimization wrong -- and I should have a max of 42 scavangers remaining -- I end up with:

1: 142r 20s 88c (v) 2: 18r 51s 1e 54c 126k (v) --- 22 to 42 scavangers remaining -- average 37

Which is able to buy me another 2% of optimization -- and drop the max to 2916 barracks-minutes.

[YeOldeMan]

LOL, nice work. Now do this for gold chain production so no one ever has to ask which building(s) to buf again.

Also - give that propeller on your hat an extra big spin.

[ZBest]

Simming out a bunch of different first wave battles with a 200-gen, I come up with:



There's some low-hanging fruit on there:
30r 75s 95c (4 rounds of 95c - max 36 scavs remain)
35r 75s 90c (4 rounds of 90c - max 40 scavs remain)
40r 75s 85c (4 rounds of 85c - max 44 scavs remain)
50r 70s 80c (4 rounds of 80c - max 48 scavs remain)
60r 65s 75c (4 rounds of 75c - max 53 scavs remain)

So that says with a 200-general, we want enough meat-shield to keep the cavalry alive for 4 rounds.

The same goes for the 250-general -- the 4 round battles are the low-hanging fruit:


130r 25s 95c - 35 scavs
140r 20s 90c - 41 scavs
145r 20s 85c - 44 scavs
150r 20s 80c - 49 scavs

[ZBest]

Adjusting for the low-lying fruit, I get:

1: 167r 11s 72c (v) 2: 77s 1e 73c 99k (v)

Coming in at 2853 barracks-minutes maximum -- getting it down another 2%

And for those without cannons:

1: 152r 18s 80c (v) 2: 88s 1e 50c 111a (v)

Coming in at 3186 barracks-minutes

[ZBest]

For those that insist on efficiency -- you can lose 1R 1G instead of 31R ave 34R max by using a triple (cannon & vet only):



It's tight, but there's a few seconds to spare:

[Asipak]

Morning,

I've read your interesting thread and I implemented a new tab for the Hall of Fame that is ordered by the max. barracks times. Only the dead units are used for the calculation of the time. Is this the way you did your calculation?

The times refer to a level 1 barrack, so if you want to know the time for a level 5 barrack, you just need to divide the time by 5.

If you do not see any results for certain camps, you need to delete the cache file first.

Do you want me to change anything?

Regards

[ZBest]

I'm a numbers / stats fanatic, so I'd like to see a distribution plot for the losses, so I can judge how rare the max loss occurs.

The max loss is down to a 0.05% chance and ultra-conservative -- I'd like to be able to sort loss value at the 50th, 90th, or 95th percentile instead.