Quaffing from fountains in NetHack

https://nethackwiki.com/wiki/Fountain describes the mechanics of
quaffing and dipping in fountains, which are only reproduced here
where they are directly relevant.

1/7 of the fountains in NetHack are magic. If you quaff repeatedly
from a magic fountain with non-negative Luck, you will eventually get
a stat increase; if your Luck is 4 or more, you will get an increase
to all your stats.

A possible strategy is, once you can deal with the adverse
consequences and have suitable Luck, to quaff from any fountain you
find until you know it is not magical, either because you got a stat
increase (which turns it non-magical) or because you got a result you
know a magic fountain cannot give.

Doing so does not decrease the expected value of that fountain in
terms of wishes. This is because if it was a magic fountain you now
have a non-magical fountain with the normal odds of giving a wish, and
if it was a non-magical fountain quaffing from it has the same odds of
granting a wish as dipping.

However, quaffing from a non-magical fountain has a chance of cursing
items in your inventory, so you get these stat increases at a cost of
cursed items, assuming you are unwilling to test fountains when
completely naked and unequipped. (The other consequences of quaffing
are either largely trivial or identical to those of dipping, but they
do include hostile monsters.)

If the fountain was magical, you always get the stat increase and you
never get items cursed.

If the fountain was not magical, there is a 9/30 chance of getting
"the cool draught refreshes you", which leaves you still uncertain as
to the fountain's status. However, there is then a 1/3 chance it dries
up, independent of the previous result. Hence there is a 2/3 * 9/30 =
1/5 chance after each quaff that you are still uncertain.

Therefore the expected number of quaffs Q to determine if a fountain is
magical can be found:

Q = 1 + Q * 1/5
Q = 1 + Q/5     (multiply out Q * 1/5)
4Q/5 = 1        (subtract Q/5)
4Q = 5          (multiply by 5)
Q = 5/4         (divide by 4)

You must quaff from a non-magical fountain an average of 5/4 times to
determine that it is non-magical. Each time you do so, there is a 1/30
chance of cursing items. Hence testing a fountain in this fashion
gives a 5/(4*30) = 1/24 chance of cursing items. 1/5 of your items
will be cursed, so i/120 items will be cursed, where i is the number
of items in inventory.

However, you have to test an average of 7 fountains to get one stat
increase, and 6 of them will be non-magical - so for every stat
increase, you will get i/20 items cursed.

In my view this is not, in fact, a lot.

While I try not to get into more general strategy discussion in this
document, it's worth noting that one result of quaffing is to make
pools. They can't be made on your space, so drop your items on the
fountain, not nearby.

(A likely objection to this document is that dipping a wettable object
which is changed (eg, a potion which dilutes) has only a 1/6 chance of
drying up a fountain. However, this also has only half the normal
chance of getting a wish or other special effect. Hence, the expected
number of wishes is not affected by dipping wettable objects, and the
assertion that quaffing does not change the expected number of wishes
is correct.)