Knowing when to make players roll and when not to roll is a skill for
a Dungeon Master. The scope of the roll is important as well. Do you
roll for every jump when crossing containing a long fall and floating
disks? Or do you roll once for the entire trip across? I hope to give
my advice in this situation as well as provide my argument for why I
like the method I use. I'll need to go into a bit of math: you have
been warned. It's also partially a brainstorming of my thoughts on
the subject matter.

##
**The Problem with Rolling Too Much**

In the example of the floating disks, each jump needs to be
accomplished in order to reach the end. However, the odds of reaching
the end will be the probability of succeeding all of the jumps
multiplied together. This means that if you have a 45% chance of
success (roll 10 or higher) and you need to succeed on three jumps,
the odds of reaching the other side is just under 10%. These odds can
slowly sneak up on you and for that reason you need to be careful
when rolling a lot (I've seen this occur quite often for persuasion
checks). Even if the odds of success of an individual jump are 80%,
there is a 51% chance of succeeding on 3 jumps in row (0.8 * 0.8 *
0.8 * 100 to make it into a percent). This means that if a player
does enough trivial tasks in a row, they will eventually most likely
fail at least once. Depending on how trivial it is, I would say it
isn't even worth the roll.

##
**How to Think
About Rolling**

I tend to think of an activity that is being performed and thinking
about the odds of success. What should the odds of making it across
the room be? Let's say we decide on a DC 12 acrobatics (DEX) check.
This means that the party member with a modifier of 0 has a 45%
chance of success and others most likely a bit more (I'm assuming a
level 1 party). If it's supposed to be dangerous, I'd be perfectly
fine with those odds.

However, the odds of the entire party of 4 making it across are much
worse. For simplicity's sake, let's assume everyone has a modifier of
+0 for the roll. This will give us odds of 0.45 * 0.45 * 0.45 * 0.45
for a final of 4% chance of everyone making it across. This would be
much better if a DC 12 acrobatics check also let a player that misses
the jump to grab the edge and pull themselves up. Doing the math we
get 0.45 + (0.55 * 0.45) for a total of 69.75% or roughly 70%. The
0.55 * 0.45 part calculates the odds of failing the jump check but
succeeding the check to grab the edge. For four players, we get a
final of 24% for everyone to make it across which is much better but
still a bit too low. Redoing the calculation using a DC of 10 (55%
chance of success) we get (0.55 + (0.45 * 0.55))^4 since each player
has 0.55 + (0.45 * 0.55) odds of success, which is about 41% odds of
success. This is close to that 45% chance I thought was fine earlier.

The above example is meant to show a few things. Even a change of a
couple of points of DC can make a huge difference in the odds,
especially when the modifier of the character is low. Having a backup
option, such as grabbing the ledge, greatly increases the odds of
success as well.

##
**How Big a Task?**

I personally would not try to make players roll for every jump. It's
a lot of rolling and even one failure means a bad outcome. Instead,
I'd base the result on the one roll (a really bad roll means they
didn't even land on the first platform though they can try to grab
the ledge, really close means they only ruined the final jump, etc.)
or just describe it without worrying which jump they missed since
they still failed. It's also harder to determine the odds of success
for 4 consecutive checks compared to a single roll and as a result
easier to accidentally make the room harder than intended (“it's
easy, I'll use DC10” results in 9% odds of success).

##
**What Results?**

The fall in the previous example has been deliberately left
ambiguous. A 10 foot fall (1d10 of damage) is more tolerable than a
100 foot fall (10d10 or 55 average damage) for a level one party. The
reason is because the result is a setback and less health in the next
combat instead of outright death. It also means that the odds of a
character dying from the situation is far lower since they can climb
back up and try again (or have a party member drop a rope on the
other side and climb up). The odds are bad for EVERYONE to make it
across on their first attempt. You could also make the odds much
lower and expect that your players will do something else (make a
bridge from disk to disk, have someone try to grab the falling
characters hand, tie everyone together with rope in case they fall,
use a rope to drop to the floor and then have the person who made it
across drop a rope, etc.). In this kind of situation, it is typically
best if your players realize it is dangerous, failure will result in
death (being 100 feet above the ground has that effect) and/or that
they realize odds of success are low.

##
**When Players Almost Always Succeed**

Don't bother rolling when success is almost guaranteed. A 1 still has
a 5% chance of occurring on a d20 which means that even an absurdly
low DC has a chance of failing. A reasonable exception to this is if
the situation is abnormally stressful, such as in combat, since there
is a chance of failure that normally is not present. It can also
result in some very funny situation in comedy games. Like all things,
consider your group. However, I feel usually it's best to just let
the player succeed and move on. It can get annoying quite quickly
even in a comedy game.

##
**Conclussion**

Be aware of stringing together rolls and needing them all to succeed
since the odds of success quickly become low. Don't forget to
consider the results of failure and what your players know (it will
influence their decisions). If the task is so easy that it'll almost
always succeed in normal circumstances, don't roll unless in an
abnormally stressful situation such as combat (a situation where
failure normally nearly impossible becomes possible).