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Is it practical to let a user choose between the USD and EUR balance?
I couldn't care less if it's USD or EUR. They're both fiat.
You always have to deal with price rises and falls, which could turn out to be a disadvantage for a customer.
You just repeated what @DarkStar_ said
I've never seen that in a sportsbook before.
Which tells me you haven't seen enough bookies.
Maybe it's better to just use 1 currency, which the user can choose and then don't let it change. I think there will be some confusion otherwise.
How can you be confuse with just USD or EUR as option?