Hayate no Gotoku! Ch. 515

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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.

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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.

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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.

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Wrong!

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.

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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.