Can Alhambra ticket be purchased by cash ?
 

I read about the Caixa. Have they got an office in Madrid ? Can I buy from them direct with cash ?

What is my chance of a ticket if >I just turn up at the Alhambra in the afternoon ?

It is possible just by turning up, but it depends on the particular day, the time of year, and what is going on in Granada. We had our hotel reserve our tickets for us, so we were able to bypass the VERY long line (I mean VERY long line) and get our tickets at the ticket center right away. This was around 9:30 AM.

You'll be taking quite a risk for just turning up in the afternoon @ Alhambra hoping to get in. I would not recommend that unless you won't feel upset if you can't get in.

There is a ServiCaixa machine inside every branch of Caixa, but you need to use your card to reserve Alhambra ticket. You can't use cash, and they don't sell tickets over the counter in bank branches.
I agree with others about booking your ticket in advance, just about any time of the year. Online reservation works very well, and there is no issue, to my knowledge, about using non-Spanish or non-chipped cards.

Thanks. Mine is an Visa Electron, my bank checked and find their website dont work with it.
Looks like I have to try my luck when I arrive a Caixa Branch.