Hayate no Gotoku! Ch. 515


It is time for the boss fight!

Why do recent chapters touch on so many things that Doughnut Gunso does not have a clue about?

Not long ago we had a chapter on investment, of which I only do the most basic of stock purchasing. Then we have this chapter which touches on the technical details about gambling – and of all games in the world, they have to choose roulette, which I have never played before… As such, let’s see what I can do.

On paper, the entire point of Nagi vs. Maria appears to be a battle between the two factors in gambling: luck and technique. We all know some people who can win money without knowing what has been going on, and we would conclude that they are being lucky. We also have read numerous cases that there are techniques you can employ in gambling so to increase your odds of winning. Nagi is an incredibly lucky person, while Maria has techniques so refined that she could pick red or black to throw with 100% accuracy. As such, this looks like the best of luck vs. the best of techniques.


The problem here is that you know full well she is telling the truth.

There is one problem with this theory, which Nagi certainly realises: luck is simply favourable probabilities, but there is no probability when things are 100% certain. If Maria really can pull off a 100% accuracy in picking a colour, then Nagi can only be doomed because her luck would not make any difference. You would not be able to do anything with a 0% chance – just ask any player of Super Robot Wars.

As such, we should be glad to see that Nagi does not blindly bet on her luck; instead, she develops a strategy that not only make room for at least 1% chance of winning, but she actually tries to maximise her probability of winning, which ends up being about 5.6%. Compared to some other odds out there (e.g. “3,720 to 1” in successfully navigating an asteroid field), this is very acceptable.


A case study of Exact Words, huh?

One may still wonder why Nagi doesn’t just stick to the colour and bargain for a 50% chance of winning either red or black. However, one must remember that Maria (the dealer) is not so generous to them. The rules after all the negotiations would still give Maria absolute control over the colour; in other words, if Nagi bets on the colour, her odds of winning will be 0%.

Here, Nagi successfully strikers at a mental blind spot of Maria, and creates a loophole in the rules which she could then exploit. Maria requests Nagi to “change your bet” once she touches the coin, by which she assumes that Nagi would change the colour she bets on. What she overlooks here is that Nagi can choose to change the number she bets on. Should Maria specifically say that you have to change the colour you bet, Nagi would not be able to pull this trick off.



So, why would Maria – someone this ridiculously clever – overlook such a simple detail? I think that it may simply be that Maria has fallen prey to the game of odds. As mentioned above, if we talk about maximising our odds, the most reasonable thing to do is to bargain for that 50% on colours. Maria simply overlooks the possibility that Nagi would settle for 5.6% of odds on betting a colour and number combination.

This way, Maria thinks that she can throw to any number of red because she expects Nagi to settle on betting black. This “any number” has Maria unwittingly leave the number to luck, for which even a 5.6% chance of winning is good enough for Nagi. As a result, Nagi does end up winning with odds at 5.6.% against someone whose winning percentage is 100% by default. Brilliant.


You have to complicate things.

So, everyone is saved from the debt of 18 billion yen. Nagi has promised to give Yukiji (and perhaps the others as well?) an 18% share of her prize money (which is 36 billion yen), and that would be about 6.5 billion. Everyone should be happy, but Hayate is not: somehow he has developed an existential crisis as he doubts his purpose around Nagi. Does she really need him?

It seems that Hayate thinks his worth is his ability to save Nagi when she is in trouble. Hayate’s logic in this chapter is probably that Nagi would not be in any trouble at all because of her luck. If he is not needed to save her from any troubles, then he is not needed for anything else. Right?

Well, I don’t even think I need to address his dilemma.

22 comments on “Hayate no Gotoku! Ch. 515

    • What concerned me was not Nagi’s strategy. Of course Nagi wanted Maria to fall for it, but I wanted to explore just why Maria would fall for it. To me, she is cleverer than this.

      I can only conclude that she is being too clever in guessing what Nagi was after. She went for a more proactive strike in order to ensure her 100% chance of winning, while accidentally leaving some other options off guard.

  1. As much as I don’t want it to end with Nagi winning the harem game, Hayate’s reaction caught me off guard because it felt a bit out of the blue… I just hope Hata won’t rush things too much.

    • As things go, it seems that the Hayate-Nagi relationship is suffering from all kinds of insecurities.

      From a shipping point of view this is a sign that they are trying to change the status quo: moving out of an employment and into something more intimate. From a non-shipping point of view this shows how fragile their employment relationship actually is: after about a year of such relationship, they still can’t figure out what could actually bond them together in a prolonged relationship.

    • hayate does not want to leave nagi because after his hellish experience with his parents life as nagi’s butler has been much better and if he is longer needed he is beginning to think he is lacking purpose. poor hayate.

    • Makes it even sadder that he never figured that his job has a purpose.

      Heck, even serving meals and cleaning the house would be purposes important enough. Why on earth would he think that he, even if only as an employee, is not needed?

    • Sorry this isn’t related to the discussion, but apparently you can’t read the manga anymore at MangaFox because “it’s licensed”. Anyone has an explanation? I have imported every volume released in English so far (1~26), isn’t it a bit late to axe the series from the site?

    • i agree at the end of the day he is there to serve her i dont get it why is he getting so worked up about not being needed by nagi. if he likes his job he should keep at it even if nagi is not dependent on him.

    • Maybe Hata-sensei wanted to show how lucky Nagi is. Or he wanted to create Hayate’s existential crisis. A good story is not all about the plot. It also needs a good character development.

  2. so nagi does have her mother’s luck and what makes her more formidable is that she is not goofy like her mom. i always thought that she had some power that is why isumi was always protecting her from supernatural stuff.
    hayate is now feeling inadequate because he always thought nagi couldn’t survive without him but seeing her managing such a feat has made him feel conscious about his future.
    i get the feeling next chapter will be a filler. at least school trip is over i hope.

  3. the ye old main girl gets everything she want while others get shafted with bad luck. Hata really didn’t tone down Nagi’s win in this one by letting her win the biggest prize but the win became more luck instead of skills even with all that explanation. If the mangaka arc was about nagi being able to achieve something out of hard work and learning the difference between winning through cheap tactics, and winning through working hard for her goal. this arc is literally about reminding everyone and possibly informing new readers that nagi wants, nagi gets through Hata’s will because we can say for sure in a fair world a 1 in 18 chance is like betting the worst horse in a race, not gonna win unless the other horses somehow got the plague(maria being clumsy suddenly even though her character in the series is the perfection that everyone strives to become). my rant is over… bleh….

    • Thing is, Nagi’s blessings are already a given and there is not much we can complain about. My only wish is that Nagi learns not to exploit her luck with brainless decisions and actions, and only utilise her gift as a useful weapon when absolutely needed. Here, I think she has done a decent job.

  4. I was actually very pleased with how Nagi won against Maria. While many would disagree and quickly jump on the “because she’s the MC” mentality, I believe Nagi won in a convincing way.

    She acknowledged Maria as a strong opponent that can’t be underestimated, mentally prepared herself by strengthening her resolve, used teamwork to help even the odds, took advantage of the enemy’s overconfidence and showed full confidence in her decisions. Exactly the kind of formula I love to see when protagonists face an overwhelming foe.

    Its that same confident, resolute and reliable Nagi we saw before in the final episodes of CTMEOY.

    • yup i was amazed by the way she won i thought maria will go easy will easy on her or something but finally hata sensei gave her the spotlight she deserved.
      she is a brilliant analyst and humble enough to she her opponent’s strengths and her weaknesses. for a 13 year old she is very capable and i give her credit for that.

    • Plus, Nagi knows Maria better than anyone else. Only she could have correctly predicted Maria’s habits. If there is anyone who could (and should) beat her, its Nagi and it’d be very fitting since seeing Nagi surpass Maria would be something to be proud of considering their relationship. Had it been Hinagiku or Athena to have challenged and beaten Maria, I would’ve been annoyed since I’d feel no sense of pride or accomplishment in seeing already known over-achievers winning.

      In fact, I had hoped that instead of Hayate, this chapter should have had Maria suddenly feeling that she’s slowly becoming less needed by Nagi. It wouldn’t have felt so rushed if it was Maria instead of Hayate feeling inadequate since there is an actual build up to the sub-plot of Maria feeling less useful to Nagi all the way back to the Mangaka saga.

    • To be fair though, we still haven’t seen Maria’s full reaction to Nagi’s win. We’ll find out in the next chapter. I’m speculating that Maria will also feel a bit insecure. Still, I feel that Hayate’s reaction was also foreshadowed, albeit less convincingly. He did mention that he feels that the time when Nagi might not need him anymore is coming very soon while talking to Ruka.

    • If I remember correctly, when Hayate talked to Ruka about this possibility, he was *expecting* – borderline *accepting* it. In this chapter, he is seen to be *worrying* about this possibility.

      There is a difference, I would say.

      P.S. I almost thought we have all been bored to death by the lack of new chapters, but now… the resurrection!

    • Ah… but that makes Hayate’s reaction more believable for me, though. It’s like how you don’t miss something until it’s actually gone or you are faced with the possibility of it being gone. (shipping lens on).

      Meanwhile, I’ve been staving off boredom by drawing Nagi’s face on the dust accumulated on my car.

    • nice point Doughnut Gunso, hayate is accepting this that he wont be needed but is definitely not looking forward to it .
      he is going through emotional roller coaster and i wanted piece of that action but hata sensei is taking such a loooong break . hope we get new chapter soon even if its not plot related.

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