I dunno, but I guess presentation and execution are problems which we are having here. From what I've managed to understand the characters, while having exaggerated qualities like in any other fictional work, does have ample clues and crumbs building up to the behavior of which you see. Perhaps its due to theres too much going on the screen, or you got swarmed by the gags and jokes and missed the tiny details, or hell, shiny graphics. Either way from my point of view the show's characters are certainly not as detached from reality as you may think, here are my responses;
1.Rock-paper-scissors was exaggerated
-To be honest here I do not really understand how do you perceive this as silly. Because looking back at this little game at the first-person point of view, this Janken was a rapid Xanatos Chess level mind screw deployed by the male protag. Let us not forget Sora was approached by Steph in the midst of the night, right after waking up. To drive the point home he was even cuddling Shiro in the very bed they were sleeping on a minute earlier, Sora essentially guessed Steph's character (being brash and emotional) from a really short conversation, and determined a game which Steph would happily accept and Sora could swing it in his favour predictably. All this done in probably less than an hour. And again do not forget the biggest trap in the game was that the penalty for Steph whether she lost or tied were the same. This was not realized by Steph beforehand, and intentionally done by Sora. Steph had every reason to assume Sora is a brilliant tactician (which he is).
in a nutshell i don't understand your point so i restated in detail everything that happened minus the boobies in words so hopefully its more understandable this way
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2: Because Sora understood the King's Gambit was easily exploitable he was super dumb to have broken down when magic, which is something foreign to him, being used as an alternative way to cheat
I think the title pretty much held what I wanted to comment on already, you can't deal with what you have no experience in. In the same way you don't expect even a barrister to perform simple surgeon duties or summat. I won't spend time detailing on this since this is a really simple and straightforward concept. The two examples weren't connected at all.
As for the breakdown being exaggerated, we are discussing about the guy who would cower in fear and babble incoherently simply being out of sight with his sister. It is therefore apparent that it is Sora's (the siblings', actually) weaknesses as implied and brought up that they not only must stick to eachother, but cannot afford to have anything to go wrong. From their philosophy regarding playing games ''[] must not lose!'' to ''The world is a crappy game. (because there are no rules and everyone makes their ''moves'' sporadically)'' we can see a great deal into how dedicated and almost dangerously passionate the two are to maintain their ''perfect'' self-image at least in games. The sheer thought of losing and to lose their only emotional comfort zone is unbearable and unimaginable to them, hence breakdowns. The thing is that since the siblings talents compliment each other like Yin and Yang, when one is unsure, chances are that the other is, as you may recall that when Shiro broke down due to things not going her way, Sora reminded her that this was not her field of expertise and it was pointless to be hard on herself. Similarly, it also applied to Sora when he broke down himself due to magic being used. Therefore in my humble point of view I actually see episode 3 as a great way to cap off the character development of the protagonists by being the climax of all the dropped and implied hints at their strengths and weaknesses.
Yeah thats about it. Hopefully you will keep watching the show!