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# /sci/ - Science & Math

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Gamer math moment
/v/ here, this is a math valuation problem that's been at the back of my head for years.
Say that you deal 100 points of normal damage per atk. If you manage to crit, you deal 2x damage.
Along comes the next upgrade choice: 10% atk increase (deal 110 dmg now) VS 10% crit chance (10% chance to deal 200 dmg). Which do you take?
Textbook stats say they are the same, but are they really?
Also how do you account for the value of burst damage from crits, the fact they might outright take an enemy piece of the board.
For those /sci/bros here that game what are your thoughts?

 >> Anonymous Tue Jan 16 02:15:15 2024 No.15978643 I think you are supposed to learn probability theory in middle school.
 >> Anonymous Tue Jan 16 03:06:40 2024 No.15978698 >>15978643You are also supposed to learn reading comprehension in middle school.
 >> Anonymous Tue Jan 16 03:10:50 2024 No.15978702 >>15978631This board would be so much better if it actually was filled with math and science problems but that would require people to learn math and science
 >> Anonymous Tue Jan 16 03:20:21 2024 No.15978711 >>15978631The answer depends on the exact mechanics and future upgrades. If attack upgrades stack with each or crit chance is additive for example. Yeah it all depends on the game board. If enemy has 150 health on average, crit is better because attack stat increase still requires two attacks to kill it.Have you never played a game or something? Honestly something I would expect from a /v/ poster.
 >> Anonymous Tue Jan 16 03:38:01 2024 No.15978733 >>15978711>The answer depends on the exact mechanics and future upgradesOf course, but for context I'm only looking at opinions on this single decision, aka assuming there is only this one single upgrade to see if I'm missing anything.But why 150 hp been the cutoff here? Shouldn't it be if average goes above 110+? In which case crit would have higher value as it passes the breakpoint.
 >> Anonymous Tue Jan 16 03:44:55 2024 No.15978741 >>15978733>Of course, but for context I'm only looking at opinions on this single decision, aka assuming there is only this one single upgrade to see if I'm missing anything.You're missing intelligence>But why 150 hp been the cutoff here?He was giving an example you nimrod
 >> Anonymous Tue Jan 16 04:01:14 2024 No.15978753   File: 34 KB, 548x251, 16988566766243.jpg [View same] [iqdb] [saucenao] [google] Honestly? You guys are bunch of fucking faggots.Thought I'd visit the math experts on the math board for once to double check if I missed anything on a math related problem. And what do I get for my trouble? Bunch of jarring comments with no real insights, except for maybe >>15978711.Picrel is what I just got in 10sec from an AI.Can't wait until /g/ replace you arrogant retards irl.
 >> Anonymous Tue Jan 16 04:03:13 2024 No.15978756 File: 49 KB, 618x809, 4s6756r75687d.png [View same] [iqdb] [saucenao] [google] Honestly? You guys are bunch of fucking faggots.Thought I'd visit the math experts on the math board for once to double check if I missed anything on a math related problem. And what do I get for my trouble? Bunch of jarring comments with no real insights.Picrel is what I just got in 10sec from an AI.Can't wait until /g/ replace you arrogant retards.
 >> Anonymous Tue Jan 16 04:05:58 2024 No.15978759 >>15978756wouldn't it depend on your base crit chance, chatgpt seems thank you are setting the probability at a definite value
 >> Anonymous Tue Jan 16 04:07:52 2024 No.15978760 >muh video gaymezzzttthhhh!!!grow up
 >> Anonymous Tue Jan 16 04:15:12 2024 No.15978768 >>15978733Over extended period of time, like 10000 hits, they will perform the same, but you probably not going to do that many in a single sitting. Going with flat increase allows you to deterministically predict that you will kill a boss with 1000 health in 9 hits instead of 10. With a crit chance, you achieve the same result if you crit once and you can get it done even in 8 hits if you roll crit twice. But the trade off is that you can roll crit zero times and thus take 10 hits instead. The probability of not critting once on 9 strikes in a row (it doesn't matter if you crit on 10th one) is about 38%.It all depends how important it is for you to kill said enemy as fast as possible and if you are okay with 38% failure chance. Basically it's same as choosing between minimum-maximum damage roll and flat damage value.It just fucking depends, pure mathematics and game theory won't give you an exact answer because you didn't set any parameters at all.>>15978756Wow, chatbot gave you a tutorial response to your question. LLMs sure are wonderful.
 >> Anonymous Tue Jan 16 04:21:10 2024 No.15978785 >>15978760they're the intersection of art and science
 >> Anonymous Tue Jan 16 07:14:30 2024 No.15978997 >>15978631assuming you start with zero crit chance then you are doing 110 all the time for option ain option be you are doing 200 damage 10% of the time and 100 damage 90% of the timeso you expected value is 200*0.1 + 100*0.9 = 110 expected value.The answer is crit because when a difference of more than 10 extra damage matters gambling feels way better when you win.Suppose an enemy is at 200 hp left, either you need to hits or there is a chance it dies immediately. Which makes you cum your pants?
 >> Anonymous Tue Jan 16 07:22:59 2024 No.15979007 If we applied the central limit theorem could we prove that it converges to the constant?We also need to consider than chance will make game play feel artificially dynamic and therefore possibly more fun for some people, regardless of CLT
 >> Anonymous Tue Jan 16 21:13:41 2024 No.15980080 >>15978631No math needed, I'll take the crit chance
 >> Anonymous Wed Jan 17 00:33:29 2024 No.15980356 >>15978631Harm=damage*(1+mul*crit)Making partial derivative, and assume linear growth of crit and raw damage is linear, you should alternate between raw and crit upgrade and be even.However most fun game has non linearity. First crit represented as chance would not exceed 100%, so the surplus isn't used. Second is armor calculation, is it subtractive, cap minimum, cap maximum or has quadratic/exponential(gain for the peak) or sqareroot/ln(x)(gain for consistency) terms.And lastly overkill/ underkill. One shot one kill is just efficient, if getting 110 damage would kill a line of 105 hp enemy, the 200 hp crit is wasted on them and you can't kill enough. Some game may make the rest of the damage has alternative effect, like gibbing the body so no revival and body blocking, debuff enemy more or pass through shots/set off ammo rack than just diabled.