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Season Break Points for R00t

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Season Break Points for R00t

Post by Dudest on Tue Feb 02, 2010 9:31 pm

Thought it might be useful for the people who have just started speed-looping to have a thread with some of the math for fighting phases. I have found that the break points where it takes one less focus to defeat a phase are pretty important, because although the first 3-4 focuses are pretty cheap, the 5th and 6th mean a huge jump in costs. I can get the 1400 stamina needed for 4 focuses with little bit of planning or consumables, the 2000 stamina for a 5th focus is a big deal, and at the 2700 needed for a 6th push I'd rather just use an Overture.

I'm going to assume that
-you are buying as much Drain & Tonic as you can
-you are using both Core boosts
-you are using the Detective Duo team.
-your village has the Skull Throne and the Drain Amplifier
-you have Tri-Edge, Aromatic Grass, Boomstick, r00t rank, and Epitaph of the Twilight.
For any Phase past the 9k ones I'll assume you are have Lycoris, but I'll calculate some numbers for both in case you want to go back and farm kaiju drops/LWs.

I haven't found Pink Skull to make a significant difference compared to number of buy-ins. Being in Billy Club or having Crystal Tumblers let you buy two more Drain & Tonic which makes you effectively one season higher for the price of some extra Ryo. The bigger game changers which not everyone will have are the Pink Taser and Wired Reflexes. Science 4 also makes a difference but you can't count on it being active. I'm not sure yet whether or not one can farm Bits efficiently enough to make R00t Fu and Digitial Endurance worth using. I'll do the numbers for a couple different set ups, and maybe add more as I find the time.

The first four phases have 6k health for their kaiju drops and 9k if you want to drain them. With the basic setup I've described above, you'll be doing an average of 1.2*(Season+15)*8 damage per attack at maximum push. We'll take Season 10 as our baseline, which gives 240 damage, enough to do 6k in 3 focuses and 9k in 4 focuses. These are both reasonable numbers of focuses for our first time through, but suppose we want to come back with Lycoris and farm them. Now we'll do 1.2*(Season+20)*8 damage, or 288 at season 10, which isn't quite enough to do them in less focuses. But suppose we were season 12, we'd do 307.2 damage per attack, enough to kill a 6k phase in two focuses and a 9k phase in three focuses.
To kill that 6k phase in only one push we'd need to be S44, and to kill a 9k phase in two pushes we'd need to be S27, which isn't really reasonable for our first time through.
How do things change with the Pink Taser? Now we get 12 attacks per focus instead of 10, which helps a lot. We're much closer to be able to do 6k in 2 focuses and 9k in 3 focuses before we get Lycoris- S12 should do it in both cases. Wired Reflexes aren't quite as strong as the Pink Taser (although they do help with death chances, which I'm ignoring in this post) you'd need to be S14 to do the 6k in 2 focuses and the 9k in 3 focuses. Lycoris effectively gives us 5 seasons so we can do it at S7/9 with it, and I'd recommend going to at least S10 for the Awesome, so with Lycoris and either of these you should be fine.

I'm finding my season becomes a much bigger factor as I get ready to fight the 10/15k Phases. At S10 doing 288 damage, it'll take 4 focuses to kill the 10k version of these phases, and 6 focuses (!) to kill the 15k versions. This is a big deal because it takes a lot of resources to get the 2700 Stamina you need for 6 focuses in one day, or even the 2000 Stamina for 5 focuses, and splitting the fight over several days means storm favors and a second round of hacking. It's at the point where I'm probably better served by spending a half million on an Overture, which will significantly slow down my progress. It would be much easier if I could kill them in only 4 or 5 focuses, so let's see what those break points are. S12 would be enough to bring it down to 5 focuses, and S20 to bring it down to 4 focuses. For farming purposes, I'll mention S15 is enough to do the 10k version in 3 focuses instead of 4, but again the jump from 4 to 5 and 5 to 6 are the really important ones.
Pink Taser would help enormously here. S7 would be enough to do 15k in 5 focuses, and S13 enough to do it in 4 focuses. S9 and S17 with Wired Reflexes instead.

The last pair of Phases have 14/21k health. The 21k version you'll probably need to Overture, but it's worth checking whether or not we can get the 14k version down to 4/5 pushes since we'll want a lot of those for PW- I'm thinking you'll want to fight each eight times if you need one to upgrade for R00t, one to upgrade for PW, five for PW, and one to loop with for the theme. S10 is just enough to do the 14k fights in 5 pushes, S17 to do them in 4 pushes. (Yuck.) The 21k probably need to be Overtured- S17 just to get them down to 6 pushes, S24 for 5 pushes.
If we have the Pink Taser, S11 is enough to the 14k version in 4 pushes and the 21k in 6. Wired Reflexes S14 for the same results.

That's a lot of text, so let me sum up what I'm taking away from this
-I'm going to get Wired Reflexes ASAP, and assume one has it in further calculations.
-Being higher season with Wired Reflexes or Pink Taser makes the first four phases cheaper the first time through, but not enough to worry about. S10+Lycoris+Wired Reflexes is enough to farm them efficiently so you really don't need to worry about it for these fights. Likewise the 10k fights can be done in 4 focuses, 3 with Pink Taser, so not really worth worrying about. (S13 worth it to 3 focus them without Taser?)
-If I had the Pink Taser I would seriously consider looping a couple seasons higher than 10 for the 15k fights. With Wired Reflexes and Pink Taser, they can be done in 4 focuses instead of 5 at S11. At 5 focuses you'd probably be better off buying overtures and fighting them two at a time, but at 4 focuses you could much more reasonably fight them one at a time. Looping to S17 to do this without Pink Taser probably isn't worthwhile, but you might disagree.
-S10 is enough for beat the 14k spirit fights in 4 focuses with Pink Taser, but without it you'd need S14. Again debatable, but you'll want to fight those phases many times, and an extra 4 seasons isn't as bad as 7 seasons.
-No real way to beat 21k Phases without Overtures at any reasonable season.

I'd be happy to show more details of my calculations or do them for a different set of assumptions if anyone is interested. Also, remember you'll lose a couple attacks to deaths, and that sometimes you need a weak push to get in the 0-100 when draining a phase, so being a season higher than the values listed here is a good idea. Also, remember being in Billy Club or having Crystal Tumblers is like having an effective extra season.

Dudest

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Re: Season Break Points for R00t

Post by Lear on Wed Feb 03, 2010 3:07 am

An interesting read, I must say. I've never really looked too in depth into what Seasons are most advantageous to fight a phase at.

Anyway, I actually have written a program to help calculate things like the number of buy ins (attacks actually, but its the same thing) that would be needed to fight a phase. It calculates success rate (original intent) and average # of deaths as well, but for the purposes of this, I'll leave those aside.

Anyway, testing a few things to compare your numbers to my program's. Keep in mind, my program runs with a slightly different set of assumptions than yours, which are explained after the numbers:

Situations where our numbers disagree are in bold, along with the breakpoint Season that my calculator finds. Assuming no Pink Kitten whats-it-called.

Season 10:

6k phase = 23.19 attacks => 3 focuses
9k phases = 34.83 attacks => 4 focuses
10k phases = 38.79 attacks => 4 focuses
14k phases = 54.47 attacks => 6 focuses (becomes 5 @ Season 12)
15 phases = 58.47 attacks => 6 focuses

Season 12:

6k phases = 21.18 attacks => 3 focuses (becomes 2 @ Season 15)
9k phases = 31.74 attacks => 4 focuses (becomes 3 @ Season 15)
15k phases = 53.28 attacks => 6 focuses (becomes 5 @ Season 15)

Season 15:
10k phases = 32.90 attacks => 4 focuses (becomes 3 @ Season 18)

Season 17:
14k phases: = 42.72 attacks => 5 focuses (becomes 4 @ Season 21)

------------

Now, there are three two big reasons why my calculator may disagree with yours.

First is that it adjusts for deaths. If the player dies, the phase takes no damage but it still counts as an attack. My calculator takes this into consideration. This makes a difference of about 0.75-2.25 attacks per phase, depending on difficulty.

Second, my calculator automatically assumes you switch your team to Offline Romance when you have 1 life left. Since you will do less damage per hit with Offline Romance, this brings up the average number of attacks against some phases. This difference ranges from almost non-existant (< 0.1) to about 1.75 attacks per phase, depending on difficulty. (I should point out that, while you do need 6 LW to use Offline Romance, I left it in for all calculations, as the intent of this seemed to be Phase farming, rather than for beating them for the first time.)

Third, my calculator runs simulations, rather than doing straight math. As a result, this could lead to an outlier result, which isn't representative of what the numbers should actually be. Nevermind. After testing this, I've found the number of attacks to be remarkably stable, with a variance of less than 0.02*. (Win chance on the other hand tends to fluctuate a bit (about 1% in either direction).)

*I should point out, this is over 25,000 trials, not just 1. So this is NOT the same as saying that the amount of attacks it will actually take is stable. Over just one trial, the number of attacks needed is actually EXTREMELY variable, varying by as much as 15% of its expected value in either direction. (So if you're expecting to need 50 attacks, it could range anywhere from 43 to 57, and I wouldn't be surprised.) Over 25,000 trials, however, this tends to dissapear.

------------

All in all Dudest, your numbers seem good, and it's very nice that you brought this up (or I'd have never thought of it). However, your numbers seem to underestimate (for reasons explained above) the number of attacks needed by about 1-4 attacks per phase. I'd keep that in mind if you're expecting to just barely be able to kill it in X number of focuses. You'll probably need an extra focus. (Also, if you're draining, expect to use another 2-3 attacks to get it down to the right amount of hp.)

Edit: Of course, this is assuming that my simulator actually produces correct results. I think I've got everything right, but I do have a habit of making some very stupid errors when I'm programming.

Side note: As a result of an input error, I can say that a theoretical phase with 140k hp would result in the player's death >99.99% of the time and would take 43 buy ins to kill at Season 15. (To be honest, I was rather surprised that my simulator actually managed to beat it once out of its 25k fights.)

Lear

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Re: Season Break Points for R00t

Post by Dudest on Wed Feb 03, 2010 6:16 am

Thanks for doing these calculations Lear, I found your results very interesting. I'm a little disappointed to see how overly-optimistic I was- I knew I was leaving out deaths but forgot about how switching to Offline Romance would hurt, and that seemed to be a big effect.

A couple of questions/ requests for calculations, if you don't mind...
1. Did you assume Wired Reflexes or not for your numbers? It looks like not. I think the calculations including Wired Reflexes may be more useful, since it's looking to me like it's definitely worth getting. I'd be interested in seeing the numbers with Wired Reflexes but both with and without Pink Taser.
2. You mention a variance of .02, is that in units of number of attacks? Also, is that the variance of the mean number of attacks? Because that will depend upon how many trials you run, and so may not be as useful as the single run variance.
3. When I did some back of the envelope calculations I determined that my chance of winning Phase fights only changed by about 1% per season, so I decided it wasn't worth my time to loop for a better chance of winning. Does your simulator bear that out? I'm curious how your chance of victory changes for various fights from, say, S10 to S11 or S11 to S12, and it might be interesting to the future speed loopers who inspired me to look at this.
4. Beyond chance of victory, my main concern in picking a season to do R00t is being able to farm the spirits efficiently, so the break points where the 14K fights are doable with 5 or 4 focuses instead of 6 are important. But it occurs to me that having a mean number of attacks of 40 or 50 is probably not the best value to find out- what I'd really want is the season where I can do succeed within 40 attacks or 50 attacks say 90% of the time. How hard would it be to use your simulator to figure out what season you'd need to be so that 90% of your fights were victories, and took 50/40 attacks or less?

Dudest

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Re: Season Break Points for R00t

Post by Lear on Wed Feb 03, 2010 3:09 pm

Okay, let me first explain how my calculator works. Then I'll get to the questions.

The calculator (simulator, really) basically runs out a phase fight, just as though it would play out if you were actually fighting the phase. It fights with perfect strategy (ie. guardian at 1 life, then favor, then Offline Romance, as needed) until either the phase is killed (not drained, killed. Programming it to get within drain range wouldn't be worth the effort.) or the player runs out of lives. If the player won, it records 1 win, the number of attacks used to kill it, and the number of times the player died. It then runs 24,999 more simulations, each time adding to the number of successes, attacks, and deaths. After all of the trials, it divides the successes by the total number of fights, and the deaths and attacks by the number of successes and prints them out. Specifically, I get this:

XX.XX%
XX.XX attacks (XX.XX successful)
X.XX deaths

So, what I can test:
Wired Reflexes
Science 4
max push vs. min push
Changing to Offline Romance vs. staying at Detective Duo
Legacy vs. not-Legacy
Boomstick
Lycoris
Purchasing drain power (from fields)
Purchasing edge power (from fields)
Bullet Time
Spear of Wotan
Root Fu
Tri-edge
Drain Amplifier
Aromatic Grass
# of Drain & Tonics
Season
Base Death Chance (# of days alive)
# of lives lost per death (for 11 tails)
Phase health
Any combination of the above

What I cannot test:
Hacking anything less than the phase difficulty (on the to-do list)
Teams other than Offline Romance or Detective Duo
Win chance if you DONT use Twilight Guardian
Win chance if you DONT use a favor (on the to-do list)
Switching to Offline Romance before using a favor (on the to-do list)
Fights over several days (ie. increasing days alive/death chance)
Additional attacks needed to drain, rather than kill
The fact that you cannot (I believe) die on the last attack of a drain
Chances of 0/1/2/etc. deaths (on the to-do list)
Edit: Also, Time Reversal Cube and K-belt. The K-belt is new, but I completely forgot about the Time Reversal Cube (mostly because I don't have it). I will add it before running more calculations

Side note: To-do list = stuff I would like to do, but may not ever get around to

Anyway, on to your questions:

1.) Those were all without Wired Reflexes. I tried to make the exact same assumptions as you. I will run a few comparison trials with Wired Reflexes in a bit to test. Also, my simulator does not take Pink Taser into account simply because it calculates # of attacks, not # of focuses, so the Taser becomes irrelevant (which is why it's not listed in either list above). I'll give you the attack #s (and win chance, since it becomes relevant now) and you can do the math for with/without the Taser.

2.) I suppose I wasn't quite clear on what I meant. I'll give an example. Say I calculate that the # of attacks needed to be 46.66. What I mean is that if I run the same trial again, I consistantly get between 46.64 and 46.68 attacks (where 46.66 is the median).

This does NOT mean that individual trials are stable. They're not. It means that the average over 25000 trials is stable. I simply mentioned this to say that the simulator won't return wildly different if I run it twice.

I may add a function to calculate the standard deviation in the # of attacks, but I haven't yet.

3.) I haven't tested it at length, but I've generally found a single season to be worth only a few percent. I'll test it a bit more thoroughly in a bit.

4.) With a little bit of trial and error, very easy. I'd actually considered adding a function to automate it, but at the moment, I wouldn't use it enough to justify the time to add it.

Posting this part now. Will update with numbers in a bit.

----------------

Testing stuff:
Base = same assumptions as before. No bit shop 2 stuff or Science.
Stuff listed is additional to the base. Things are listed for each individual trial and do not carry over. (So stuff in above trials is not included unless specifically listed.)
Important breakpoints,etc. are bolded.
Billy Club and Tumblers are not included, but if you have them, you can just assume your Season is 1/2 higher than it is and go with those numbers.
Each trial is run separately, so the same setup ran different times may yield slightly different results.

@ Season 12 - 15k phase:

Base: 90.78% win rate; 53.22 attacks
Wired: 92.59% win rate; 49.37 attacks
Root Fu: 92.14% win rate; 50.57 attacks
Root Fu + Bullet Time: 96.97% win rate; 49.73 attacks
Science 4: 93.82% win rate; 47.12 attacks
Wired + Root Fu + Bullet Time: 97.88% win rate; 46.29 attacks
Science 4 + Root Fu + Bullet Time + Wired: 98.55% win rate; 41.04 attacks

I'll test more of these later. These are just a bit time consuming to do.
-------

Testing the value of a single Season at Base.
14k phases aren't tested since they're nearly the same as 15k.

9k phase:
Season 10: 97.51% win rate; 34.83 attacks
Season 11: 98.26% win rate; 32.60 attacks
Season 12: 98.32% win rate; 31.75 attacks
Season 13: 98.50% win rate; 31.04 attacks
Season 14: 98.59% win rate; 30.36 attacks
Season 15: 98.65% win rate; 29.59 attacks

15k phase:
Season 09: 86.81% win rate; 60.11 attacks
Season 10: 87.94% win rate; 58.45 attacks
Season 11: 89.91% win rate; 54.62 attacks
Season 12: 90.65% win rate; 53.26 attacks
Season 13: 91.38% win rate; 52.02 attacks
Season 14: 91.80% win rate; 50.75 attacks
Season 15: 92.50% win rate; 49.60 attacks


21k phase:
Season 10: 70.88% win rate; 82.36 attacks
Season 11: 75.48% win rate; 76.91 attacks
Season 12: 76.55% win rate; 74.97 attacks
Season 13: 78.02% win rate; 73.22 attacks
Season 14: 79.34% win rate; 71.48 attacks
Season 15: 80.79% win rate; 69.84 attacks
Season 19: 86.00% win rate; 61.93 attacks
Season 21: 88.01% win rate; 57.89 attacks
Season 24: 90.06% win rate; 54.53 attacks

Conclusion: Season matters against the 21k phases, although not much. The others are easy enough that you shouldn't have much trouble assuming you have all the appropriate bonuses.

Also, I should point out, if you use the bit shop 2 powers against the 21k phases, your chances go up enormously. Bullet time alone increases your win chance by 13% at Season 12, the rough equivilant of doubling your Season.

But yes, it comes out to about +1% win chance per Season against the 15k and 21k.

Lear

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Re: Season Break Points for R00t

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