I almost never use battlemaps and when I do, it's more a way to provide some decorum and structure informations rather than as a tool for battle. I don't really get how so many people online are obsessed by the idea of battlemap. Looks like kids this days have it too easy and didn't started playing at the time where RPG magazine was publishing 3 scenario a month, with sometimes one for a game they play, and had to do without map in general.
A few idea pointers,
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I played Ryutama only once, but remember their concept of battle egg which just tell whether you're in contact, second-line, ranged distance or away using a few circle. Nobody care about your exact distance, but just use some adjective to describe your position.
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As usual, PBTA and forged in the dark, can use consequences to generate danger, like you open a chest but choose one : Someone has seen you/ A trap trips/ Move to a worse position
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Even in traditional game, you can describe the dungeon with a few adjectives, and by thinking what it's for and answer the players question when they ask-it rather than in advance: Can we enter by the sewage ? Well there is a garnison in this castle, it's near a river, people need to piss and shit, so most-likely there is a pipe going directly to the river, let's say yes. However people are not stupid so there is some metal bar to block the access, the player can try to break them works as well as doing a map and thinking about the 5 possible way to enter while the player will use only one.