I opened a Kasikorn account at the branch on Mittraphap Road about a month ago with a Non O visa. I had a Thai friend to help but there were no problems it was just a bit long winded. Passport, certificate of residence from immigration, Thai mobile number. I took along my visa as well although they may have just taken a photocopy of the stamp in my passport rather than the visa itself. I think it was 300 Baht for the passbook and ATM card.
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I've since tried to open a second account at SCB and GSB in Central Plaza but they both refused saying I had to have a 'year visa' presumably meaning an OA or whatever so I'll be trying other branches next week.