This is an interview question I found online, yet I am still uncertain about how it works
Two player A, B are playing a game. A throws three fair 6-sided dice (each one has face values from 1 to 6), while B throws a fair 20-sided die (each one has face values from 1 to 20). Whoever gets a bigger number (or sum of numbers for A) wins the game. Is this a fair game?
So I have read a few people's answer on the net, and still not knowing how it works. But I have one approach here (very native) and would love to see whether it is a way out.
As the expected value of 3 dice $= 3 * 7/2 = 10.5$ = the expected value of the 20 sided dice. Therefore we may conclude that they are the same and hence a fair game? Seems too good to be true. And later proven wrong in the variant question.
And then a variant of the question:
Now another player C joins, also with a 20 sided dice. Is the game now fair?
From other's answer: it is now unfair. Somehow adding another 20 sided dice makes the game being unfair. I can't get the intuition for the whole set of question.
Appreciate if anyone can help me with getting some intuitive explanation for this question, as I don't really understand the logic behind the whole set. (Perhaps some idea on the original question but proven wrong)