Why is a queen worth 9 and not 8?

If a queen is a rook+bishop combo, why is it worth 9 and not 8?

Three minor pieces (2xBishops+1 Knight or 2x Knights and 1 Bishop) or a Rook+Bishop+Pawn.

A queen isn't a combination of a rook and a bishop. It has the same moves but when you think beyond the current move, it can do much more than both combined, but also less because it's only one piece. There isn't any formula which can be derived the the value of each piece. The values have been empirically determined over many years.

A queen can draw by repetition and save a losing game, thus the additional point value.

Funny, when I started playing (back when I was 5) a Queen was considered 10 points.

The point system gives you a rough estimate of how you're doing, but a rough estimate is all it is. In actual practice, a poorly placed queen might be worth a lot less than 9 points, while a good queen may be worth a lot more. But in typical positions, valuing it at 9 points will give you a reasonably good estimate of how you're doing.

In the end, points don't matter. You win games by checkmate or resignation, not by arguing that your queen should be counted as 10 instead of 8 or whatever.

So a queen was equal to two rooks? Honestly doesn't seem too far-fetched 

the two rooks are slightly better because:

two rooks can checkmate by themselves; a queen cannot.

two rooks can back each other up; a queen cannot.

two rooks cover 28 squares, not counting overlaps or the square they are on, in the center; a queen covers 27 when in the center.

If  a bishop could move one square sideways and thus change color,
then it would be worth 4 pawns.
So a queen (9 pawns) is worth a rook (5 pawns) and a super-bishop (4 pawns).
5 + 4 = 9

The whole is greater than the sum of its parts

- Aristotle

So now why 9 but not 8.25?

But what if the bishop was secretly worth 3.75? Or ...

My 2¢ or is it 2.05 with inflation?

Is a queen in the hand with two on the board?

#14
"why 9 but not 8.25"
AlphaZero:
Q = 9.5 P, R = 5.63 P, B = 3.33 P, N = 3.05 P
Table 6
https://arxiv.org/pdf/2009.04374.pdf

Every decimal place matters. Don't let anyone tell you otherwise

Inflation.

I do know that two rooks these days are considered slightly better than a queen, hence the queen being 9 instead of 10.

Bishop can only control 1 color diagonally when a queen controls bother colors diagonally. Pretty simple. The extra point value is being able to control both colors. Now 2 bishops and 1 rook is stronger than a queen ( by 2 points) because the bishops control both colors at the same time when a single queen controls 1 color at a time but can switch color per turn. Rook + bishop = 8. If a queen moved like a rook and bishop but can’t change colors it would be worth 8 instead of 9. Like tygxc said up above a bishop that could change color would be worth 4 instead of 3. In my custom chess game I made in real like I have a red bishop that can switch color. I made it 5 points instead of 4 cuz it has a special move. But without the special move it would be worth 4 points. A queen is basically a rook and a red bishop combined together. 1 Rook + 1 bishop = 8. 1 Rook + 1 RedBishop = 9. 4 + 5 = 9. Pretty simple.

Not the way you described it.