Suuji de Sukuu! Jyakushou Kokka

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Ch. 1
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1 chapter in and we've already confused the TL with the math, a good start.
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@NeoSmile I plugged the equation into an online graphing calculator and got it to look exactly like breasts with nipples. The drawing might be misrepresenting some symbols when entered, keep in mind the symbols surrounding x are not 1's but absolute value signs. Try plugging:

y=sqrt(1-(|x|-1)^2)
y=sqrt(0.01-(|x|-1)^2)+1
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the math equation in the beginning is incorrect (i used an graph-calculator to check and they became 2 lines pretty much on top of one another (which is actually a pretty easy to see error) )

the closest i got with a working pattern was:

and this looks barely like the picture
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Not sure if this was answered already but this is how the math checks out:

The probability they're trying to define here that's not well translated is "the probability of at least 1 success in gacha." So this might mean 1 win, or 2 prize wins or 3 prize wins, up to 20 prize wins since he's doing gacha total of 20 times. The number of attempts can be defined as 20 attempts (n=20). The easiest way to calculate the probability of "1 win chance"+"2 win chance"+"3 win chance"...+"20 win chance" is by taking the total probability of everything (the two outcomes are win and lose, simply put the formula 'all outcome'='win chance'+'lose chance'=100%=1) subtracted by the chance of losing. 100%-lose=win or 1-lose=win, where we define win as at least 1 success and losing as a total of 0 successes out of 20 tries.

To calculate the probability of losing, multiply each outcome by each other. Let's say you're trying to flip a coin and we consider tails to be loss and heads to be win. To calculate 3 losses, we do (0.5)*(0.5)*(0.5)=1/8. Another way to look at this is (1/2)^3 or ('chance of loss')^n where n=3 in this example since we flip the coin 3 times. Applying this to gacha, the chance of losing is (0.95)^20=0.358 or rounded to 36%.

Thus, the protagonist is stating that since he gets 0 wins 36% of the time, he will get at least 1 win (up to 20 wins) 64% of the time. He is pointing out that 5% * 20 is not the correct way to applying probability of outcomes in this situation. This is also why +5 atk or +15 atk work gloves were worth so fucking much in maplestory
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Come on, elevators don't just "fall". There are physical mechanisms in place to prevent that.
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isn't that lift jumping myth debunked already?
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Pages 26 and 27.

Is this... it cannot be!

Is this MISMARCA?

YESSSSSSSSSS!
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I am more interested in Rito fall probability. Just how?
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@stal2walk it only gets worse the lower the success rate is too
50% rate: pull 2 times, 75% success probability
33% rate: pull 3 times, 70% success probability
20% rate: pull 5 times, 67% success probability
5% rate: pull 20 times, 64% success probability
1% rate: pull 100 times, 63.4% success probability
0.01% rate: pull 10000 times, 63.2% success probability!
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This guy destroyed the concept of gacha. That's a very impressive first impression.

The rational hero and princess. I am so down. Here's hoping the ecchi is downplayed.
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a bit ecchi... but I love this manga already
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4 stars not more. Do they really listen to childrens? They just kill them and put on throne some puppet.
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RNG is root of evil....

beware of gacha addiction.....
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this guy ruin my illusion theory about gacha
SHIT NOW I CAN'T LIE TO MYSELF ANYMORE
RIP 1% x 100 = 100% dreamlike theory
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"Wait that girl looks like ekakibit's doujin chara, who's the artist"

*checks

"Oh it is ekakibit"
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@Yahagai Yea at the times I didn't understand the logic/concept behind the calculations, but now I know. But thanks anyway.
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@Nullify You simply calculate 1-(1-0,05)^20 and you get 64%. In other words 100% - (chance of failure)^(amount of tries).
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Man, I don't understand how it becomes a 64%. Like personally probability was never a Strong point for me in math, but I just can't conceptually find it to be a 64% chance. The only explanation they give is the rate of success = 1 - rate of failure (well Duh) which does not help at all. Can someone explain to me the concept or logic behind this?

Ok looking at the picture it seems that he does 0.95^20 which is ~0.36 which comes explains why 64%. But it still doesn't give info on why the equation is rate^turns.

Ok, so I drew some pictures for myself and now I made sense of it.
So lets say H = hit or gacha win and M = miss or lose so the probabilities or P is P(M) = 0.95 and P(H) = 0.05. 20 draws is too much to write so I'll first show what the percent is to win if 2 draws were made
So in 2 draws the sequences are HH, HM, MH, or MM. Their goal is to get at least 1 hit so the probability of getting their goal is P(MM) which is equal to 0.95^2 = 0.90. This means that if they have a 5% chance to win SSR and they draw 2 times then they would only have a 10% chance of getting at least 1 SSR.

Since each subsequent draw gives a lower increment chance of winning at least 1 SSR then to approach 100% they would need infinity draws.
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@YuriM You sure? if it was realistic to real life in that time period I'd agree to an extent but based on the fact there seems to be guns and other little details I'm not even 100% sure what time period it's goin' for. It just seems to be an under developed fantasy world.
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I hope he can prove her mathematically, that the war is not a women's place. At least in the medieval.
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