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The rules on "Using Different Speeds" state (emphasis mine):

[...] Whenever you switch, subtract the distance you've already moved from the new speed. The result determines how much farther you can move. If the result is 0 or less, you can't use the new speed during the current move. [...]

However, I'm unsure what the rules mean when they say "the distance you've already moved" especially when difficult terrain is thrown into the mix. The very next section is on "Difficult Terrain" and it states:

[...] Every foot of movement in difficult terrain costs 1 extra foot. This rule is true even if multiple things in a space count as difficult terrain. [...]

So what happens if a creature with a Walking Speed of 30 and a Climbing Speed of 20 begins their turn by walking through 15 feet of difficult terrain to the nearest wall (which is not difficult terrain)? Their remaining Walking movement will be 0, but will their remaining Climbing movement be 5 or 0?

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You subtract the movement you have used in a turn from your speed.

Page 190 of the PHB states the rules for using different kinds of speed in a turn:

If you have more than one speed, such as your walking speed and a flying speed, you can switch back and forth between your speeds during your move. Whenever you switch, subtract the distance you've already moved from the new speed. The result determines how much farther you can move. If the result is 0 or less, you can't use the new speed during the current move.

This remains true with difficult terrain, in the section right below the previous one:

Every foot of movement in difficult terrain costs 1 extra foot.

Even if you did not actually move 30 feet in difficult terrain, you are still considered as if you had used 30 feet of movement.

In your example, the character would move 15 feet in difficult terrain, which would count as 30 feet of movement from their walking speed. Then that character would be next to the wall, but cannot use their climbing speed, because they have already used 30 feet worth of movement, and their climbing speed is only 20 feet. Subtracting the amount of movement they've used so far from their climb speed results in a value below 0; at that point, that character cannot use their climbing speed that turn since they have no available movement left.

If said character used the Dash action, it would increase their available movement for the turn by an amount equal to their speeds: an extra 30 ft. walking / 20 ft. climbing. Then, subtracting the movement they've already used, the character could climb 10 feet or walk an additional 30 feet.

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Subtract the equivalent number of feet from all your speeds.

The rules that you quoted say the distance you've already moved, but you should reason in terms of equivalent distance you've already moved.

Take the example in the "Using Different Speeds" rule:

For example, if you have a speed of 30 and a flying speed of 60 because a wizard cast the fly spell on you, you could fly 20 feet, then walk 10 feet, and then leap into the air to fly 30 feet more.

You can think of your available movement for the turn (without Dashing or anything) as 30 ft. (walk) / 60 ft. (fly). As you move, you subtract the feet you've moved from both amounts:

  1. You firstly fly for 20 ft.
    The remaining amount you can move is: 10 ft. (walk) / 40 ft. (fly)
  2. Then you walk for 10 ft.
    Remaining movement: 0 ft. (walk) / 30 ft. (fly)
  3. You can still fly for another 30 ft.
    Remaining movement: -30 ft. (walk) / 0 ft. (fly)

You can fly after step 2 because you still have available movement of this kind, but you can not walk since the available movement is less than 0.

In your example, you can think of your available movement for the turn as 30 ft. (walk) / 20 ft. (climb). Then, working through your movement for the turn:

  1. You walk on difficult terrain to get 15 ft. from where you started, which costs 30 ft. of your movement. Remaining movement: 0 ft. (walk) / -10 ft. (climb)
  2. After that, you cannot climb the wall, since your remaining climbing movement (from your climb speed) is less than 0, and you don't have any walking speed to climb with (at extra cost) either.
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  • \$\begingroup\$ I feel like adding an additional term is not productive, and I think 'distance budget' is misleading. Distance budget sounds like you add your distances together (which you demonstrate is not the case) and also sounds like it doesn't matter which speeds you use to achieve the speed (which you don't necessarily demonstrate nor avoid). For example, if I was told I had 30ft movement budget from my 30ft of land speed and something gave me only 20ft of climb speed, I would think I could Climb 30ft because it's 'within budget'. \$\endgroup\$ – Ifusaso Nov 1 '20 at 16:08
  • \$\begingroup\$ @Ifusaso You are right, it was indeed confusing. I modified my answer and tried to clarify it. \$\endgroup\$ – Eddymage Nov 1 '20 at 17:40
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“Every foot of movement in difficult terrain costs 1 extra foot”

When you move through 1 foot of difficult terrain, the "distance you have moved" (for movement calculation) is 1 + 1 = 2 feet, since that's how much movement you spent to get there. If you move through 15 feet of difficult terrain, you have spent 30 feet of movement - you have no walking or climbing speed unused.

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