A friend told me that he would like to try playing a gridless game next - still on tabletop, but without the gridlines. Is there any difference in the game except for movement? There are some things I don't know how to go about like line of sight, flanking, and traps and invisible enemies. Any help?
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If you absolutely must play 4e gridless
First, mapping squares to feet is quite possible. Once you do that, you can absolutely play it as a proper wargame. Break out some cloth rulers and enjoy a "natural terrain." This could actually be a fascinating look at a more "realistic" D&D. Be prepared for the relative power of quite a few abilities to change. Be sure to rule about how to calculate the radius of area effects in the squares-to-feet game.
I would strongly recommend to play with essentials only. Measuring will consume non-trivial amounts of time, and you'll want to use a simpler set of powers to compensate.
I would also recommend bending wires to default areas. They are quite standardized zones of 3x3 to 11x11. Having a metal template you can plop down (and having transparent overlays you can leave on the map) will make things much much much faster.
You also need to rule about flanking and the number of people who can be adjacent to someone. I would recommend making a "melee" circle sufficient to fit 8 minies around someone, and paint the circle with different colours of nail polish to show flanking matches.
It sounds like the friend in question is suggesting a system which is designed to be run without a grid, which definitely does not describe D&D 4e. Plenty of games have no use whatsoever for a grid, and plenty that do can be made to work without one even if they’d usually use one, but 4e is going to make it very difficult for you. As @SevenSidedDie mentions, though, some groups have managed to do it.
DM Scotty had good videos about gridless D&D play. You may want to check it out:
Videos are really informative and done by guy that actually play gridless all the time. If you search his channel you also find session recording played gridless. HTH.
In our group we play gridless dnd-3.5e without any problems. It does require buy-in from the party, and rules-lawyery people might run afoul of this variant.
It works best if the DM is a little bit generous in favour of the party when estimating distances, so a PC might be able to move/reach 2.5 feet further (if that's what's needed to get into cover, hit their charge, land the fireball), and an NPC might be able to move/reach 2.5 feet less.
We've found the following easy-to-come-by implements can be helpful when estimating distances:
We have been doing this in our 4e campaigns, and it's not a problem. My experience started with a grid but shortly moved to whiteboards, and occasionally the DM (me) prepares a map in advance with a program like Photoshop(painting) or Inkscape(drawing).
In practice, rules and number values do not need to be refactored. For context, this is the consensus of a gaming group consisting entirely of hardcore Computer Science students: obsessed with numbers, algorithms and game mechanics. In fact, the mathematics of the game become more consistent. Unlike the original grid system, diagonals will not make distance vs. time path dependent.
What changes? Instead of measuring by 1 square you've got 1 unit distance. To remain consistent with the grid mechanics, close blast powers have a 180-degree arc. That's it!
For measuring distances, you can set a token or miniature to be 1 unit in diameter (bonus if their base is round), or if you have no such tokens just draw a letter or symbol and estimate from there. In the interest of keeping up the game's pace, if your ruler's most prominent markings do not match the width of your mini's/tokens, don't use it.