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I was playing an encounter from the tales from the yawning portal hardcover and in this room every foot of movement is 3 feet of speed. We were bunched up by the door and needed to move through each other. We were not sure what to do for the combination of walking on a slick floor in the same space as an ally. Moving each space in the room was costing 15' of speed. Moving through an allies space would normally cost 10' of speed.

Do you just take the larger of the two effects or stack them?

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No, difficult terrain does not stack

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.

An area is difficult terrain or it is not. But there is no area that is more difficult terrain by virtue of having stacking difficult terrain effects in it.

Regardless of the amount of effects that cause difficult terrain in one area, moment costs 1 extra foot per foot of moment.

Your specific case

In your case specifically, the floor appears to have been a special case of difficult terrain that cost even more movement to get through:

The water in the central area of the floor is 2 feet deep, and the floor is very slippery-moving across this difficult terrain costs 3 feet of speed for every 1 foot traveled.

This is a case where the specific (the adventure module) overrules the general (the PHB difficult terrain rules) and allows difficult terrain to cost 3 feet of moment per 1 foot moved. However, this does not overrule the fact that difficult terrain still does not stack. Thus, the difficulty from walking through another creature's space would not add to the movement penalty.

Though not explicitly stated in the rules, it seems to be the most logical to choose the greater effect (the slippery floor) over the lesser one (moving through occupied space). Not only is the floor effect greater in magnitude, but it is also permanent and effecting the entire area. The penalty for moving through another creature's space is local and conditional.

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  • \$\begingroup\$ But difficult terrain would stack with the optional diagonals rule and the Squeezing into a smaller space rule? So if you were moving diagonally over difficult terrain in a tight space it would cost you 15' for the first square and 20' for the second square? \$\endgroup\$ – Steve Bauer Feb 25 '18 at 6:38
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    \$\begingroup\$ @SteveBauer Personally, I think this might be different enough to ask in its own question. Generally we have a one question one answer policy here. We find it gets better answers. I'd remove that part from this question and make it a new one. I'll gladly answer it there. \$\endgroup\$ – Rubiksmoose Feb 25 '18 at 6:44
  • \$\begingroup\$ Sorry, I will ask it in a separate question, I included the paragraph in my original question as it was adding to our confusion of how to apply difficult terrain to this room in yawning portal but specifically only asked the question about stacking difficult terrain. \$\endgroup\$ – Steve Bauer Feb 25 '18 at 6:59

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