In the NAS anime Gozaburo didn't allow Seto to
play and forced him to study the whole day, while in the manga the game
particular isn't stated (in the Toei version Seto and Mokuba backstory
is totally missing. Also, Seto's revenge comes from the humiliation of
having been defeated, and not from the punishment game - Yami Yugi
hasn't the time to inflict it on him, Seto is able to escape before the
other can do anything). And, as you noticed, how could have Seto became
a giant game nerd a great gamer in such few time, even if he was able to rig a chess game when he was 10.
About my theory, I basically threw it together because, according to the
manga canon, it's plausible. Given what he had to endure, it's likely
that Seto would have given the middle finger to his stepfather anytime
soon, but the idea he took the company just to have the means to carry
on his revenge on Yugi could be very plausible, if you think that
accoring to him, to get the BEWD cards he needs to defeat Sugoroku he
doesn't have problem in using mafia connections and pushing one of the
former owners to commit suicide. But if this happened between Yugi and
Seto's first meeting and Death T, this would make Seto words when
Gozaburo commits suicide (more on this under the spoiler tag) something
vague.
Seto shows his problems to deal with defeat everytime he appears, but
his Death T revenge against Yugi was given mostly by the mind screw he
had to live with, or simply the fact that he was defeated and one
important weakness of his had been exposed?
Also, wall of text:
Spoiler: About the Kaibas backstory
In the manga, Gozaburo jumped off the window of the office he, Seto and
the other KC actionists were right after his stepson told him he had
control of the company. Gozaburo tells Seto that losers face one and
only one unavoidable fate, and then commits suicide. Seto thinks "Defeat
is the same thing as death? I'll remember this other thing you taught
me".
In the anime Seto endures the life Gozaburo imposed him for Mokuba, only
to snap when he discovers he's using the game techology he developed to
build weapons (accoring to Mokuba, that was the last time Seto called
Gozaburo 'father'). Some time later, as a birthday present (it's not
stated which, but it's likely to be around Seto's 12th or 15th year)
Gozaburo gives Seto and Mokuba a huge amount of money and 2% of KC
actions each, and challenges Seto to multiply 100 times (if I remember
well) the money he got in a year. Seto does that by taking over
gradually the Corporation. Later Gozaburo discovers that someone is
trying to take over the company and takes precautions, apprently thanks
to some leaked informations. Seto blames Mokuba for this and drives him
out, while keeping on his takeover plans. Mokuba has no other solution
than go back to Gozaburo.
One year later, Seto has 49% of the stocks, and his stepfather the 51%.
Gozaburo is about to proclaim himself winner, when Mokuba sides with
Seto and tells he isn't going to leave his brother, no matter what.
According to one of the Big 5, Gozaburo committs suicide some days
later. Then it turns out that the secret informations that apparently
'leaked' were spread by Seto himself, in a plan reminescen of Light Yagami's, trying to test how much Mokuba was ready to endure for him.
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