On Monday, March 14, 2022 at 6:19:16 AM UTC-7, Klaus Kassner wrote:

[...] It is, however, a possibility that this is actually already NH 3.6.x code and that it is erroneously posted under the NH 3.4.3 heading.

In general that's a possibility. In this case, it hasn't happened.

Prior to 3.3.0, being Fast increased hero's movement by 1/3,
being VeryFast doubled the normal speed. Unused movement
points, if any, carried over to the next turn so that the 1/3
increase accumulated enough for an extra move every third
turn.

Starting in 3.3.0, that was changed. Being Fast had a 2/3
chance to get the non-Fast number of movement points and
1/3 chance to get 50% more than normal, for an average
movement allotment of 33% faster than normal. So the
average stayed the same but it was no longer predictable
when you would receive an extra move. At that same time,
VeryFast was changed to have 2/3 chance for 150% movement
and 1/3 chance for 200%, giving an average of 67% more
movement than normal speed. So both less than the doubling
effect it had before and also not predictable.

It stayed that way up through 3.6.0, inclusive. That version
left the hero's movement alone but changed monster
movement so that it was no longer predictable and also
slightly faster on average. For monsters which moved at
normal human speed, sometimes they would lose a turn
relative to a normal speed hero, other times they would
gain a turn and that was a little more likely than the chance
to lose one. So a hero trying to run away from a monster
that nominally had the same speed would sometimes get
caught and hit. Or fighting toe-to-toe, sometimes the
monster would get two hits instead of just one. (Other
times it would get none but players didn't seem to notice
that aspect.) A lot of people complained, or more likely it
was a smaller number of people complaining loudly.

In 3.6.1 the movement system was changed for both the
hero and for monsters. The slight boost for monsters in
3.6.0 was removed. For both hero and monsters, unused
movement no longer carries over but instead gives a
percentage chance for extra moves. Being Fast has 2/3
chance for 1 move and 1/3 chance for 2 moves, so is
still 33% faster than normal speed. VeryFast gives 1/3
chance for 1 move and 2/3 chance for 2 moves, same 67%
increase over normal speed as 3.3.0 through 3.6.0.

An actual move requires 12 points of movement. Anyone
with normal human speed gets 12 points per turn, so
makes 1 move per turn. If a monster gets only 4 points
per turn, its first turn it wouldn't move and 4 points would
carry over. On its second turn it would get 4 new points
and add to the carried over 4 points, it still wouldn't be able
to move but this time 8 not-yet-used points would carry
over. Then on its third turn, it would have 12 points and
make a move, with nothing to carry over. That was the old
system. Starting in 3.6.1, if a monster has 4 movement
points it has a 1/3 (4 out of 12) chance to move. If it
doesn't move, the unused points are thrown away rather
than carried over. On its next turn it will again have a 4/12
chance to move. For a fast monster that gets 18 points
per turn, it will always move at least once, using 12 of the
18 points, and have 50% (6/12) chance to move twice. For
either slower than human or faster, the average movement
is the same as it was prior to 3.6.0 but actual movement
is no longer predictable.

In theory a slow monster could move every single turn
or never move at all but a reasonable RNG should result
in matching the average expected movement over time.

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Am 14.03.2022 um 19:55 schrieb Pat Rankin:

On Monday, March 14, 2022 at 6:19:16 AM UTC-7, Klaus Kassner wrote:

[...] It is, however, a possibility that this is actually already NH 3.6.x >> code and that it is erroneously posted under the NH 3.4.3 heading.

In general that's a possibility. In this case, it hasn't happened.

Yes, I realized that by looking for and finding the corresponding code
part in NH 3.6.1. Since it was different, it was clear that a random
component was already present in the algorithm for moves per turn of NH
3.4.3.

Starting in 3.3.0, that was changed. Being Fast had a 2/3
chance to get the non-Fast number of movement points and
1/3 chance to get 50% more than normal, for an average
movement allotment of 33% faster than normal. So the
average stayed the same but it was no longer predictable
when you would receive an extra move. At that same time,
VeryFast was changed to have 2/3 chance for 150% movement
and 1/3 chance for 200%, giving an average of 67% more
movement than normal speed. So both less than the doubling
effect it had before and also not predictable.

Right. And this allowed to conclude that you were sure to get 2 moves in
a turn, if you had gotten only 1 in the preceding turn, provided you
were very fast and unencumbered. The sequence of moves per turn was a
random sequence with 1/3 ones and 2/3 twos, but it was not an
uncorrelated sequence. Ones were anti-correlated -- i.e. you never had
only one move on two consecutive turns each, and clusters of m times 2
moves per turn (after the occurrence of a single move per turn) had a probability of slightly higher than (2/3)^m for small m. (The exact
formula is prob{m consecutive 2} = prod_k=1^m (2/3 -(-1/3)^k. That can
be derived with the help of recurrence relations.)

In 3.6.1 the movement system was changed for both the
hero and for monsters. The slight boost for monsters in
3.6.0 was removed. For both hero and monsters, unused
movement no longer carries over but instead gives a
percentage chance for extra moves. Being Fast has 2/3
chance for 1 move and 1/3 chance for 2 moves, so is
still 33% faster than normal speed. VeryFast gives 1/3
chance for 1 move and 2/3 chance for 2 moves, same 67%
increase over normal speed as 3.3.0 through 3.6.0.

Yes, now it is as random as it can be with the probabilities 1/3 and
2/3. The number of moves in two consecutive turns is uncorrelated.
Clusters of m times 1 move (after a 2-move occurrence) have probability
(1/3)^m and clusters of m times 2 moves have (2/3)^m.

I must say that I liked the old system better, because it gives you an additional option for improvement of your game via skillful action
rather than by a random decision. It could be a life-saver in situations
where you wish to escape a covetous monster while being on the upstairs.
If you zap it with a wand of teleport in a turn where you are sure to
have 2 moves, you should be able to escape upstairs, before it returns. Provided, of course, the moves are not obtained alternatingly with those
of the monster. I presume, the player first gets his moves and then all
the monsters get theirs and then the turn ends?

An actual move requires 12 points of movement. Anyone
with normal human speed gets 12 points per turn, so
makes 1 move per turn. If a monster gets only 4 points
per turn, its first turn it wouldn't move and 4 points would
carry over. On its second turn it would get 4 new points
and add to the carried over 4 points, it still wouldn't be able
to move but this time 8 not-yet-used points would carry
over. Then on its third turn, it would have 12 points and
make a move, with nothing to carry over. That was the old
system. Starting in 3.6.1, if a monster has 4 movement
points it has a 1/3 (4 out of 12) chance to move. If it
doesn't move, the unused points are thrown away rather
than carried over. On its next turn it will again have a 4/12
chance to move. For a fast monster that gets 18 points
per turn, it will always move at least once, using 12 of the
18 points, and have 50% (6/12) chance to move twice. For
either slower than human or faster, the average movement
is the same as it was prior to 3.6.0 but actual movement
is no longer predictable.

I don't mind that for monsters, but I would prefer the player's moves to
have this extra bit of predictability that would make the above strategy
a viable one.

In theory a slow monster could move every single turn
or never move at all but a reasonable RNG should result
in matching the average expected movement over time.

For a very slow monster, it is certainly better not to have it
predictably stay unmoving a long time...

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