I don't think your scissors actually did anything given that your rock also lost, as have the half dozen rocks in a row before it...Scissors.
I just lost against myself. But on the other hand, I just won against myself. Fascinating.
ok. 5) If they beat the person directly below them, they get 1 win.Interesting question. Just a quick mistake in point 4 before tackling it. You forgot to mention that they also gain a win if they beat the person below them. In the statement it says they win if they draw and every other combination apart from a draw is a loss.
Well, you've done the most so far. It's actually quite a hard problem. If you want, you could try and figure out the case when you compare to people above you as well (e.g if you beat the person above you and the person below you, above you there were k draws, below you l draws, then you win k+l+2 times). For the expected value questions this is actually easier, but for the maximum win question, not so much.My usual Maths work: a few examples, thinking a bit about the results, relating the results to my current knowledge and trying to use knowledge I already have (not too much!).
I noticed the summation from 1 to n in the results here, used that formula, and then that's it.
Sorry for poor non-mathematical explanation. Hope I get a prize for my answer by the way.
Ah, but if your opponent is aware of all that, they will specifically pick the OTHER choice so as to confuse you.
Although if he is aware that you are aware that he is aware, then perhaps he will pick the choice that he should traditionally pick because you expect him not to pick it!
^^ dizzying intellect