Local Play on Bomberman Live is gaming without being online You can verse other computer characters, or you can play with other people who may be in your home. Local Play allows users to unlock certain achievements in the game that would only be available on Local Play, so if you are into collecting all of the games achievements than you can unlock a few here in Local Play.
For those new to the game, it is a good idea to play solo for awhile just to get a feel for the game. Although it is set up in a very similar way to Bomberman Land for the Nintendo Wii, Bomberman Live includes a few new spin-offs in the arenas.

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One for instance, which is a personal favorite of mine is painting tiles with your bombs. For instance, instead of running around trying to blow up other players, you will also- run around trying to blow up players, but with each bomb that goes off of yours, you will also be painting tiles. The player who paints the most tiles will win the game.
Another form of playing is an arena that will include quicksand. The quicksand tiles can stop your character dead in it's tracks. It's relatively simple though to spot which tiles have quicksand on them, so unless you purposely want to sink I don't see why else you'd end up in the sand.
There are quite a few fun arenas, but frankly most Bomberman fans will stick to the original classic version arena, which is basically a blow em' all up, before they blow you up.
In local play you have the option to customize how your game is played. If you want power downs to not be included in the game, feel free. If you want every item to be used during game play, you have that option as well. You also have the option to pick how many wins one must accomplish before the game is over.
All in all local play is fun, but if you don't have another player to go head to head with in the room, the fun gets old fast. Versing other human players is what really charges up game play into the fun zone.