Rock paper scissors
One outcome in 3
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Press the button and get rock, paper or scissors, each exactly a third of the time. Use it to settle something, or to practise against an opponent with no habits to exploit.
How to use it
Against a uniformly random opponent no strategy has an edge; whatever you throw, you win a third, lose a third and draw a third. That sounds like it makes the game pointless and it is actually the reason to use this: human rock paper scissors is a game of reading habits, and people have plenty. Men open with rock noticeably more often than chance; players who just lost tend to switch, and players who just won tend to repeat. World-championship play is entirely about exploiting those tendencies. A random throw has none of them, which is what makes it the fair way to settle something rather than a way to win.
Questions
Not reliably. Against a uniform random throw every strategy wins exactly a third of the time, so there is nothing to learn.
No. Every throw is independent, which is what makes it unexploitable.
A third each of win, lose and draw, regardless of what you pick.
Because human throws are not random. Openers, switch-after-loss and repeat-after-win are all measurable patterns a strong player reads.
Yes. Set the count to three and get all three throws at once.