Interesting approach by the riot balancing team: make a borderline overpowered item but getting the charged auto attack is so satisfying that it causes players to int for it
@@Esodum played against it , was a bit annoying yeah but I had a heartsteel tank too so it was ok ornn on the other hand, ornn passive+grasp+heartsteel is like 50% hp on a squishy its legit unfair
@@voidroad i mean, yeah. I was thinking about the "The more health you have, the more stacks you get" part, since even lethality sion has quite a bit of HP.
@@Esodum I should try to go on a new account and try this build out lol, im just so shit on sion that if I went on a normal game I would be smashed lmao
I normally don't follow YTers, but honestly xpetu your stuff is so enjoyable to watch. I enjoy how you analyze situations outloud and break down your actions. I've been sending shen top every time I play. He will be my next mastery 7.
I'm so glad I actually remember to spend time to watch your most *Forbidden* Techs-You make every video I watch enjoyable and not just because of your undeniable ability-But also the way you portray every single move. And, above all, the fact you legitimately have fun on League of Legends, out of all rage-inducing games it could've been... X'D... You made stacking Heartsteel look *so easy* that I realise now, I haven't unleashed its full might just yet... Whenever I use it. I've been experimenting with Item Haste on Moonstone with very little to no success on most champions, but now that you do remind us what Heartsteel is... _The Bastard child of Grasp of the Undying and Duskblade of Draktharr,_ I now understand. Once again, your superior intellect comes in clutch when I didn't even know I needed help. I owe you my thanks yet again, Petu! You... *Inspire me.*
when getting around 30 HP/stack, its the same as getting 80gold/stack. when hitting the 40HP every stack, its worth 100 gold of stats. So basically, if you use the item 20 or 30 times(not that much), it means you can get 1500-3000 gold back from the item converted in HP and even more on longer games.
Just watching xPetu play has made me way more chill in my own games. Thank you xPetu for being you! And I'm also expecting a forbidden jungle Shen technologies video soon,
i have discovered a new good shem build. Purple shen is now a thing after the release of new items the build goes like this: jak'sho, boots, witts end, demonic embrace, randuins omen and maw of malmortious, as u can see its mostly for when ur playing against a primarily ap team but is super fun to build
I feel like the ingenious hunter doesnt matter because you only get 1 chonk per person per fight like 90% of the time, so maybe ultimate or relentless for more roaming for more fights for more chonks is better
He actually got in this game 2 stacks from more than 1 champion in 2 extented teamfights. Now think about in terms of pro play were fights can take crazy long up to 2 minutes.
I need more xPetu Heartsteel Shen in my life!!! Actually so excited for the absolute GOOFINESS that's going to be S13. So much fun to be had! More please!
Hey Petu, I've tried Shen for a several games, first at mid and then as a support, I wanted to thank you for showing us this meta with Shen, next season I'll be pushing to plat with Shen support boeacuse of you, this champ is so op!!
I don't think Heartsteel will be nerfed or hotfixed, but rather Shen and Sejuani will be nerfed. Heartsteel has negative winrate on most of the tanks building it, is just that these 2 early game is strong enough to get away into building a 3200 gold item that provides no defensive status. Specially because these 2 can force procs easly.
I loved the idea of infinite health scaling off of grasp… and now this item just works so well with it and also has infinite health scaling. My new favorite item
thx petu for sticking with shen. I played him myself in season 3- 6 at a high rank somewhere like diamond and masters. I dropped league entirely for about 6 long years and well never go back to. BUT youtube algorithm thought otherwise! and I found this great channel and content. I see alot of plays of myself where I got reported for, banned for and even flamed for. Till this day I think old shen- the old old shen is better than the warden shen but thats just my opinion :) thanks for the content- keep it up and Please more of uncut games :) its just fun to hear you have fun and doing crazy stuff :)
Nothing to do with this.... But, new xPetu video, had an amazing day and things seemed to have turned "the right way" in my life.... man how good I'm feeling. This new video, ans the new ones to come with the new items and the new Shenanigans promise a lot!
Man, I'm sorry to tell you that, but you can't reduce Heartsteel's cooldown with item haste. I've tested it on the practice tool and live games with both Ingenious Hunter and Cosmic Insight (for a total of 60 item haste) and the cooldown was always 30 seconds. It actually work just as Night Harvester, both items are not affected by item haste. It seems that for a item to be affected by item haste it needs to actually 'go on cooldown' on some of your item slots.
whats interesting, if you have a champion that naturally has health stacks already like sion, swain or Chonk'gath, you get an insane amount of gold value just of that item paired with tytanic hydra or demonic embrace. on Sion i got 80 bonus ad from hydra passive alone with 3 items (warmogs 2nd to stay longer in lane).
sooooo, i did hunter aswell but i just noticed in the vid that it doesnt do much with heartsteel. if you look at silas at 12:25 videotime which is 12:54 in game time, yo proc it once and it only comes back up at 12:50 vid time aka 13:18 in game. its roughly 6 seconds less and with full stacks about 7 seconds i assume. dont know how much that counts tho. it would only really be wort it if you were going to get more items that scale down with itemhaste. like a ga or as tank gargoyle or such. and that only provided you dont die instantly in late game, making you having less cd wasted if you are dead longer than that
I love the concept of Ingenious hunter with heartsteel, but there was not ONCE in the video where it mattered. You hit the same timings as a default heartsteel would hit. There was one instance at 12:22 when you could've hit heartsteel twice which you didn't get due to multiple cc's. From there on, there was another chance against sej at 22:43 BUT never hits it due to sej running away. The concept only works for very extended team fights otherwise you would have higher chances by starting more fights and running away using literately any other "hunter rune" BUT Ingenious hunter would work more often if it was against 2 tanks (jungle and top). I can see it working if that is the condition; quite often as well. SO against only one tank, i would recommend you run any other hunter rune.
There is a crazy thing with that tech that is to get: Heartsteel + Titanic Hydra + Demonic Embrace + Sunfire Aegis + Gargoyle Stoneplate More Health = More DoT damage, more AD, more AP and more barrier Infinite scaling, infinite growth.
I know it's cheesy and dumb but when you said "No I'm not bad, I played poorly. I don't associate my gameplay with myself" that really spoke to me. I have definitely been thinking about video games and performance in an incredibly toxic and negative way and that really did help to hear.
i wanna se how many stats one can gain from this, grasp + Ingenious Hunter + overgrowth with heartsteel for infinity HP. now titanic for AD, demonic for AP and sunfire for AOE AP damage on hit, all scaling with stacking HP. lets get the strongest hybrid shen ever just from stacking HP
When I saw Heartsteel I immediately thought the item cd rune. The only problem is how do you proc it multiple times in 1 team fight? Isn't the cooldown still ~20seconds per target?
Petu, I've tried and found something great with Shen; Grasp, Heartsteel, Titanic, Demonic; the rest is up to you, this means infinite health, AD and AP scaling
It would be interesting to have a guardian angel paired with heartsteel, and ingenius. i mean, reduced cooldown of items, hp procs, and a second life all coming back on a tanky, shielded, and max hp hitter... Sounds interesting
holy baby yisus Petu man, today I play my first time with shen TOP with this build against a mordekaiser, and i followed your way of playing, again i never played SHEN before i ended 12/0/5 and literally carry my team that was loosing hard.
Xpetu, think about the mathematics of how to stack this item the fastest. I have determined the formula for you health at minute t as approx: H(t) = (b*gpm+10+a*H_0)*t/(1-at) b is the price of hp per unit gold, H_0 is your hp when buying heartsteel. a is more complicated, its 0.06*0.1*other_stuff. the numbers are the amount of hp you gain every time you hit something based off of your own max hp (10% of 6% of your max hp), the other stuff is dependant on what assumptions/simplifications you use in your model. Derivation: You have 2 variables, your hp and how often you proc heartsteel. Your hp determines how much you gain per proc, and each proc gives you more hp. However, when you have low hp, a proc does not give you much. I postulate that you actually want to rush bami's cinder first item and FARM to gain hp. ofc go to every fight you can but at 20 minutes if you dont just run at people and instead hit creeps you could have like 150+cs instead of 86. You use that gold to buy MORE HP, which then is used to print more hp by pepega running at people for heartsteel procs. Approximating HP as a function of time such that: H(t) = hp gained from farming/kills + hp gained from mythic procs H(t) = A*gpm(t,B)+B(t)*(0.06*H(t)+125)*D A = representative cost of health per gold, which is either 150/400 (ruby crystal stats) or something smaller when you account for finite inventory space and gold lost to non-hp stats of items. B = number of hits at minute t divided by 10, note hitting more people means hitting less creeps but also means more kills/objectives. C = scaling factor to account for the fact that you gain hp by hitting people, so the hp you have gained from the mythic accumulates as H increases. D = Scaling factor to account for your health changing over time. The (naive) time averaged health is (H+H_0)/2 where H_0 is your health when you buy the item. Using data from this game, H_0 = 2388. Let A be some representative cost of HP, I've chosen it to be the HP of (heartsteel+bamis)/cost which is 11/42, approx 0.25. At 20 minutes you had 16 procs, so lets set hits per minute/minutes to be 16/20 or 0.8, so set B=0.8*t/10, where t is the current minute. Two potential improvements: 1) The cost of Hp is really fucking wrong, it would probably be best to look at a representative set of item choices at the end of shen games and see how much gold was spent and how much bonus HP then costs. 2) Instead of taking the arithmetic mean of H and H_0, we could integrate from t'=0 to t'=t H(t), if you call this F(t) then H(t)=F'(t) and you obtain a differential equation in F(t) F' = gold + constant*t + factor*F. Should be solvable using integrating factor if you assume the number of hits you make per minute is some fixed number (in our case 0.8). Anyway, once youve done ALL of this you can find the maximum of the function and from there infer whats most important I've made a mistake, this function is monotonically increasing so only has a 0 derivative
Interesting approach by the riot balancing team: make a borderline overpowered item but getting the charged auto attack is so satisfying that it causes players to int for it
Sion is going to be a problem right now, i can feel it
@@Esodum Sions W will work overtime!
@@Esodum played against it , was a bit annoying yeah but I had a heartsteel tank too so it was ok
ornn on the other hand, ornn passive+grasp+heartsteel is like 50% hp on a squishy its legit unfair
@@voidroad i mean, yeah. I was thinking about the "The more health you have, the more stacks you get" part, since even lethality sion has quite a bit of HP.
@@Esodum I should try to go on a new account and try this build out lol, im just so shit on sion that if I went on a normal game I would be smashed lmao
I loved the part where petu said it's chonkin time and started chonkin all over the enemies. Truly a petu moment thanking them after
That was quite a petu moment. I loved it when Petu scream "IM GONNA SHEN" and Shen'd all-over the enemy team.
it do be chonkn time tho
let the meme die please dont bring petu into this
Got cat named chonk
@@YSleepish make us
I love when Petu says “Forbidden _____” it never fails to get a laugh out of me, even if it goes poorly
Kind of reminds me of WhiteRa's special tactics.
3:00
Thank you all for donating to Shen's HP Chonk Foundation!
Just listening petu laugh and seeing him have fun is kinda wholesome lol
"The faster we get to higher HPs, the higher we're gonna get to faster HPs" - Petu 2022
😂😂😂
MOR CHONK MOR GUD
moar chonk moar good
It´s true tho.
Petu slowly losing his mind as he gains stacks is hilarious lmao
You can already hear him smiling only seconds into the video, such a happy environment
Riot should add xPetu’s giggle to Shen’s next skin. If you get a q e q combo kill.
xpetu should just get his own skin
@@UninstalledLeague Sauna shen in nothing but a towel.
@@badgeholder6122 Q would be a ladle, W is a tub, E should have soap bubbles during dash, then R has water splash
I normally don't follow YTers, but honestly xpetu your stuff is so enjoyable to watch. I enjoy how you analyze situations outloud and break down your actions. I've been sending shen top every time I play. He will be my next mastery 7.
Switch to Shen mid to really emulate xPetu ;)
We all congregate here to watch the King make wonders
I'm so glad I actually remember to spend time to watch your most *Forbidden* Techs-You make every video I watch enjoyable and not just because of your undeniable ability-But also the way you portray every single move. And, above all, the fact you legitimately have fun on League of Legends, out of all rage-inducing games it could've been... X'D...
You made stacking Heartsteel look *so easy* that I realise now, I haven't unleashed its full might just yet... Whenever I use it. I've been experimenting with Item Haste on Moonstone with very little to no success on most champions, but now that you do remind us what Heartsteel is... _The Bastard child of Grasp of the Undying and Duskblade of Draktharr,_ I now understand. Once again, your superior intellect comes in clutch when I didn't even know I needed help. I owe you my thanks yet again, Petu! You... *Inspire me.*
petu joyfully laughing and saying "I'm going to have so much fun" soothes my soul
19:30 that is the only time I’ve EVER heard “exponential growth” outside of school
Genial empezar el dia aprendiendo nuevas tecnologias de shen⚔
when getting around 30 HP/stack, its the same as getting 80gold/stack. when hitting the 40HP every stack, its worth 100 gold of stats.
So basically, if you use the item 20 or 30 times(not that much), it means you can get 1500-3000 gold back from the item converted in HP and even more on longer games.
xPetu's personality transition into Spear Shot's is underway
17:14 Secret Shen technique - "The beastmaster's gift"
Just watching xPetu play has made me way more chill in my own games. Thank you xPetu for being you! And I'm also expecting a forbidden jungle Shen technologies video soon,
i have discovered a new good shem build. Purple shen is now a thing after the release of new items the build goes like this: jak'sho, boots, witts end, demonic embrace, randuins omen and maw of malmortious, as u can see its mostly for when ur playing against a primarily ap team but is super fun to build
Bro doesnt even take a break, preseason out, petu is out here
"The faster we get to higher hp's, the higher we're gonna get to faster hp's."
In other words:
"More *chonk,* more good."
19:35
I feel like the ingenious hunter doesnt matter because you only get 1 chonk per person per fight like 90% of the time, so maybe ultimate or relentless for more roaming for more fights for more chonks is better
He actually got in this game 2 stacks from more than 1 champion in 2 extented teamfights. Now think about in terms of pro play were fights can take crazy long up to 2 minutes.
while that seems true, there is a huge difference between 30s and 26s (unstacked) - 22s(5 stacks).
Congratulations on the Chime Noises feature! 🎉🎉🎉
love to see someone else think about this rune as well. i was doing it with tear and support items since day 1 of the rune rework
It's funny how no other mythic item gives permanent stats other than the mythic passive, only Heartsteel, while doing more damage than assassin items.
I think that Titanic Hydra makes for a good combo with Heartsteel.
23:47 daaamn he sounds like viktor,
"Thank you for your contribution"
I need more xPetu Heartsteel Shen in my life!!!
Actually so excited for the absolute GOOFINESS that's going to be S13. So much fun to be had! More please!
3:10 lmao the "payayay" xd, greetings from Honduras master river shen
Grrreatings dear Petu :3
The wolf kill was the best thing I've seen in league for a long time, excluding all of your videos of course. They're all masterpieces
I didn't even know those two had a synergy, this is BEYOND broken!
Hey Petu, I've tried Shen for a several games, first at mid and then as a support, I wanted to thank you for showing us this meta with Shen, next season I'll be pushing to plat with Shen support boeacuse of you, this champ is so op!!
I don't think Heartsteel will be nerfed or hotfixed, but rather Shen and Sejuani will be nerfed.
Heartsteel has negative winrate on most of the tanks building it, is just that these 2 early game is strong enough to get away into building a 3200 gold item that provides no defensive status.
Specially because these 2 can force procs easly.
Thanks to all the people who contributed for the Shen HP Farming Foundation, all the help its appreciated.
I loved the idea of infinite health scaling off of grasp… and now this item just works so well with it and also has infinite health scaling. My new favorite item
There is mathematical genius Petu and then there is big chonk Petu today we saw the collab, and it was glorious
Petu is an wise old man and an 8 year old child getting along in the same body and I can't get enough of it
thx petu for sticking with shen. I played him myself in season 3- 6 at a high rank somewhere like diamond and masters. I dropped league entirely for about 6 long years and well never go back to. BUT youtube algorithm thought otherwise! and I found this great channel and content. I see alot of plays of myself where I got reported for, banned for and even flamed for. Till this day I think old shen- the old old shen is better than the warden shen but thats just my opinion :) thanks for the content- keep it up and Please more of uncut games :) its just fun to hear you have fun and doing crazy stuff :)
I really love your energy and fun! i wish i could have this much fun when i play :D
first time I have you on my recommended, loved you voice and vibe from the very first sentence. Great video!
Nothing to do with this....
But, new xPetu video, had an amazing day and things seemed to have turned "the right way" in my life.... man how good I'm feeling. This new video, ans the new ones to come with the new items and the new Shenanigans promise a lot!
lmao petu chonking the heartsteel and grasp stacks is so fun to watch for some reason. And the talk about donations was hilarious.
Riftmaker Shen and Divine Sunderer Shen are back on the menu, and not even troll anymore...
you should try riftmaker/sunfire/demonic. the ultimate sustain build, add a spirit visage and deathsdance and you become litteraly immortal.
Man, I'm sorry to tell you that, but you can't reduce Heartsteel's cooldown with item haste. I've tested it on the practice tool and live games with both Ingenious Hunter and Cosmic Insight (for a total of 60 item haste) and the cooldown was always 30 seconds. It actually work just as Night Harvester, both items are not affected by item haste. It seems that for a item to be affected by item haste it needs to actually 'go on cooldown' on some of your item slots.
I love how you took the concept of using the Zhonya's tech and applying it to the uber-broken mythic.
how did I not even think of getting ingenious with this. that's genius
PETU! We need a full guide for the new items 😭
your pfp is so damn good, loveless - mbv what an album
whats interesting, if you have a champion that naturally has health stacks already like sion, swain or Chonk'gath, you get an insane amount of gold value just of that item paired with tytanic hydra or demonic embrace. on Sion i got 80 bonus ad from hydra passive alone with 3 items (warmogs 2nd to stay longer in lane).
Looks like the wolves wanted to get in on all the *chonkin'* action.
sooooo, i did hunter aswell but i just noticed in the vid that it doesnt do much with heartsteel. if you look at silas at 12:25 videotime which is 12:54 in game time, yo proc it once and it only comes back up at 12:50 vid time aka 13:18 in game. its roughly 6 seconds less and with full stacks about 7 seconds i assume. dont know how much that counts tho. it would only really be wort it if you were going to get more items that scale down with itemhaste. like a ga or as tank gargoyle or such. and that only provided you dont die instantly in late game, making you having less cd wasted if you are dead longer than that
Ingenious Hunter + overgrowth + grasp proc= Chunky Boi!~
3:10-3:15 Ai ai ai what is that reaction was so funny I exhaled trough my nose spilling my seeds on the ground
Hi master, it would be nice if you could do a video with all the new mythic items on shen and wich one is the best. Greetings
Another 10 hour video incoming? 👀👀👀
3:11 This shit made me laugh so fucking hard, that delayed jumpscare lmfao
I love the concept of Ingenious hunter with heartsteel, but there was not ONCE in the video where it mattered.
You hit the same timings as a default heartsteel would hit. There was one instance at 12:22 when you could've hit heartsteel twice which you didn't get due to multiple cc's. From there on, there was another chance against sej at 22:43 BUT never hits it due to sej running away.
The concept only works for very extended team fights otherwise you would have higher chances by starting more fights and running away using literately any other "hunter rune" BUT Ingenious hunter would work more often if it was against 2 tanks (jungle and top). I can see it working if that is the condition; quite often as well. SO against only one tank, i would recommend you run any other hunter rune.
0:03:08 "you see how I calculated - BIEYIEYIE!" 🤣😂🤣😂
If you die, but you proc it 3 times, it's almost worth goldwise. They get 450, you get about 150ish hp, that's like 400 gold.
1st vid I've seen from u. Absurdly entertaining! 10/10
There is a crazy thing with that tech that is to get:
Heartsteel + Titanic Hydra + Demonic Embrace + Sunfire Aegis + Gargoyle Stoneplate
More Health = More DoT damage, more AD, more AP and more barrier
Infinite scaling, infinite growth.
3:11 got me laughing very hard 😂
This item feels like raid-boss-in-a-can. I can only imagine nasus with a stacked one.
xPetu showing the nordic mastery on commanding dogs at 17:17, mush!
I do love he got his last ingenious hunter stack at 23:25 into the vid
Honestly I have never enjoyed watching league this much.. this man Petu has me crying laughing
at this point i think every Petu video starts with an invade
I just saw a video about you on happychimenoises channel, omg I’m screaming.
I know it's cheesy and dumb but when you said "No I'm not bad, I played poorly. I don't associate my gameplay with myself" that really spoke to me. I have definitely been thinking about video games and performance in an incredibly toxic and negative way and that really did help to hear.
Great vid! Very fun indeed! Loved it!
i wanna se how many stats one can gain from this, grasp + Ingenious Hunter + overgrowth with heartsteel for infinity HP. now titanic for AD, demonic for AP and sunfire for AOE AP damage on hit, all scaling with stacking HP. lets get the strongest hybrid shen ever just from stacking HP
New heartsteel is making tank players look like crack fiends the way they constantly look for the stacks
3:11 made me subscribed to you instantly !
3:17 it was at this moment Petu knew he fked up
Hey Petu if you run around collecting their blood donations, you might want to play with the surgeon skin!
The best part of this item is watching xPetu go crazy for those chonks
Petu: greeting dear viewer
me all the time: greetings father
17:16 ah YES the wolfs AA tecnology at its finest
3:10 you see how i calculate that ....
Enemy jg :Say no more 😂
17:16 his assertive, dominant order for the wolves to kill seraphine...
dude i watched 3 mins of your commentary and i am in love... great content....
Okey petu now listen to my perfect thumbnail idea "Surgeon Shen heart surgery"
*ahem*
"Who Do You Think You Are?//
runnin' around leavin' scars//
filling your jar of hearts"
Man I love this guy. Always with the hidden tech and positive vibes. He's the only league guy i watch and i don't even play league anymore ahha.
When I saw Heartsteel I immediately thought the item cd rune. The only problem is how do you proc it multiple times in 1 team fight? Isn't the cooldown still ~20seconds per target?
5 procs are possible no matter what, and sometimes a fight can be 20 seconds even if relatively rare
Petu be like:
Move over Singed, there's a new mad Scientist on the Rift
A trade offer:
Petu gets: A stack of chonk.
Riot get: A piece of his sanity.
Alright that's it!
Imma build this on senna.
The grasps are going to be plentyful
The "I'm gonna have do much fun" at the end of the vid hahahaha
My boys got 5000 hp with two items
Petu, I've tried and found something great with Shen; Grasp, Heartsteel, Titanic, Demonic; the rest is up to you, this means infinite health, AD and AP scaling
yea and you can get ravenous since that damage scales with HP also. I think second item ravenous into warmogs is the way.
man i would have loved to see a full build to this vid :D
It would be interesting to have a guardian angel paired with heartsteel, and ingenius. i mean, reduced cooldown of items, hp procs, and a second life all coming back on a tanky, shielded, and max hp hitter... Sounds interesting
NEW SHEN TECHNOLOGY LETSGOOO
holy baby yisus Petu man, today I play my first time with shen TOP with this build against a mordekaiser, and i followed your way of playing, again i never played SHEN before i ended 12/0/5 and literally carry my team that was loosing hard.
it's so good to have all those videos, the only lol content I watch
Xpetu, think about the mathematics of how to stack this item the fastest. I have determined the formula for you health at minute t as approx: H(t) = (b*gpm+10+a*H_0)*t/(1-at)
b is the price of hp per unit gold, H_0 is your hp when buying heartsteel. a is more complicated, its 0.06*0.1*other_stuff. the numbers are the amount of hp you gain every time you hit something based off of your own max hp (10% of 6% of your max hp), the other stuff is dependant on what assumptions/simplifications you use in your model.
Derivation:
You have 2 variables, your hp and how often you proc heartsteel. Your hp determines how much you gain per proc, and each proc gives you more hp. However, when you have low hp, a proc does not give you much. I postulate that you actually want to rush bami's cinder first item and FARM to gain hp. ofc go to every fight you can but at 20 minutes if you dont just run at people and instead hit creeps you could have like 150+cs instead of 86. You use that gold to buy MORE HP, which then is used to print more hp by pepega running at people for heartsteel procs.
Approximating HP as a function of time such that: H(t) = hp gained from farming/kills + hp gained from mythic procs H(t) = A*gpm(t,B)+B(t)*(0.06*H(t)+125)*D
A = representative cost of health per gold, which is either 150/400 (ruby crystal stats) or something smaller when you account for finite inventory space and gold lost to non-hp stats of items.
B = number of hits at minute t divided by 10, note hitting more people means hitting less creeps but also means more kills/objectives.
C = scaling factor to account for the fact that you gain hp by hitting people, so the hp you have gained from the mythic accumulates as H increases.
D = Scaling factor to account for your health changing over time.
The (naive) time averaged health is (H+H_0)/2 where H_0 is your health when you buy the item. Using data from this game, H_0 = 2388.
Let A be some representative cost of HP, I've chosen it to be the HP of (heartsteel+bamis)/cost which is 11/42, approx 0.25.
At 20 minutes you had 16 procs, so lets set hits per minute/minutes to be 16/20 or 0.8, so set B=0.8*t/10, where t is the current minute.
Two potential improvements:
1) The cost of Hp is really fucking wrong, it would probably be best to look at a representative set of item choices at the end of shen games and see how much gold was spent and how much bonus HP then costs.
2) Instead of taking the arithmetic mean of H and H_0, we could integrate from t'=0 to t'=t H(t), if you call this F(t) then H(t)=F'(t) and you obtain a differential equation in F(t) F' = gold + constant*t + factor*F. Should be solvable using integrating factor if you assume the number of hits you make per minute is some fixed number (in our case 0.8).
Anyway, once youve done ALL of this you can find the maximum of the function and from there infer whats most important
I've made a mistake, this function is monotonically increasing so only has a 0 derivative
Petu has been driven mad by the shear unlimited power riot has handed him.