If (a) it sends to the server "I want to use the MAX" and then the amount is fetched server side or (b) it sends the exact amount itself as previewed in the input box.
This is what I just answered above. When you click max you get a popup saying "Are you sure you wish to bet the maximum amount? Click OK if you would like to proceed else click CANCEL.". At this point, the input box still shows your last input or the default 1 Sat because the max value is only filled in if/when you click OK. Then after the amount is filled in you still have to enter all the other roll parameters and then either click BET HI or BET LO.