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Im fine with promoting the free stuff, but i will always prefer the domain name to be

bingobonus
bingorooms
bingoclub
bingo whatever

over free bingo.

But im no expert, i just dont like...

I deffo vote for going with a NON "free" domain :)

Number 3, but none of them would be best. You can find a better bingo domain unregistered in 5min imo.