Suuji de Sukuu! Jyakushou Kokka - Vol. 1 Ch. 4

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This is hilarious. The math is so incredibly simplistic that it fooled the tls into thinking it was wrong. The lottery problem in the chapter assumes you draw once. It's the simplest possible expected value problem: pay 1 coin, 20% chance to get a return of 10 coins; the net return for the single draw is -1 + 2 = +1. On the other hand if the return is 4 coins, the net return is -1 + 0.8 = -0.2. For multiple draws with a small pool of lottery tickets, the calculation for the true/exact expected value is more complicated, as shown on the first page of tl note (an unstated application of the law of total expectation, which applies here but should not be taken for granted).

As the second page of the tl note points out, our resident high school hotshot is missing the part where you sum over the expected value for all events to get the total expectation. The equation he states is kinda correct, kinda strange in many ways, like for example the (1-P) term is artificial and could easily cause mistakes when for a different calculation we don't mean to negate a probability. There need only be one letter to represent the probability of some event, straight-out: P itself. Another rookie mistake: writing out × for (regular) multiplication, especially since he is already using a script x...

Other commenters hit the nail on the head with the combat strength "laws", as they are clearly nothing more than a vague estimation.

This kid would be better off using his rudimentary math skills to reinvent calculus or linalg or optimization or rocketry or something, in the service of engineering better weapons if he's interested in winning a war. I was gonna say that I was irrationally ticked off by this chuugakusei 'A in algebra 2' wannabe genius chessmaster, but I CAN rationalize it: I don't like the treatment of mathematics in this manga. This kid has done nothing but regurgitate formulas without proof since the start of the manga, and acted like he knows something because of it. ESPECIALLY if you found yourself transported to a backwards ass other world, it would be critically important to explain math from the ground up. Whoever that was telling the queen/princess to be more skeptical was right. For one thing she has not verified how the calculator works, or if/why it gives correct results. And for the rest of this assorted trivia he is introducing, if you can't justify to the rightfully skeptic academic court your calculations, aaaall the way down, your mathematical point should be as good as moot.

What I'm trying to say is that although this manga offers math, rather than magic, as the protagonist's main boon in the parallel world, we might as well have a lameo main character who only knows how to use magic through cringy chants anyway. The most critical and interesting part of math (in this manga at least), the reasoning for its applicability across time and space, has been totally crippled by the author's shabby presentation of modern mathematics to a world that does not know it. Or maybe the author is just playing up the short sightedness of the main character to build him up as a kind of heel, I dunno.
 
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my brain has simply started filtering out all forms of math ever since that cursed 6 years of my life.
 

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