Life In 19x19

I know the full-size game of Go is played on a 19x19 board and comes with 181 black stones and 180 white stones. This is to accommodate filling every spot on the board with a stone. I want to know if there are suggestions for (much) smaller boards.

While for other typical board sizes (9x9 and 13x13), I'm guessing we could adopt a similar rule for the number of stones to include (41/41 and 85/84, respectively), but what about very small boards?

I made this 3x3 novelty board for a friend, and I'm not sure how many stones to include with it.



Because of the size, I am certain many games could involve a lot of capturing, and I wouldn't want him to run out of stones. He doesn't own a full-size game, so he has no pieces to use with this little board (we have been playing on my full-size board).

For folks who have played on small boards, how many pieces do you think I should include?

Extended Question: Do you have suggestions for other small sizes -- say, the 5x5 "capture go", or some irregular sizes?

For a 19x19 board, 180+181=361 stones are not always enough: https://homepages.cwi.nl/~aeb/go/misc/gostat.html but if you run out of stones, you can exchange prisoners. So I suppose that for a nxn board, if you allow to exchange prisoners then nxn stones are enough, and if not I suppose that adding 30% more stones is safe, unless players make very stupid moves, in which case you need a larger safety margin.

On a 9x9 board, 40+41 stones are often not enough for beginners, even reusing prisoners, because one player might live on more than half the board, and prove it.
In any way, 80+80 stones are always enough, since it is not allowed to put more of the same colour on the board.

For very small nxn boards, I would provide n2-1 stone of each colour.
For a 3x3 board : 8 black and 8 white stones.
For a 5x5 board : 24 black and 24 white stones.
For a 7x7 board, maybe it is not necessary to have that many.

Hi,
at this link there is the product from Kuroki Go Ishi store http://shop.kurokigoishi.co.jp/en/item/1912
For their very basic gift set of pink and green coloured stones (Sakura Go), they offer 42 + 42 stones for the 9x9 board.
Still it happened to me that 42+42 are not enough to close the game as Pio2001 suggested.
btw: your 3x3 goban looks VERY nice!
Galation