For example if I bet $5 and get a blackjack that pays 3:2, this means that I should get payed 7.5.
The problem is that the there is no $0.5 dollar chip. How this situation is handled in the casinos?
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$2.50 chips are mostly used for blackjacktables, since a "natural" (a 21 on the first two cards dealt to a player) typically pays 3:2 and most wagers are in increments of $5. However, the Tropicana Casino and Borgatain Atlantic City, New Jersey, and others, have used $2.50 (pink) chips in $7.50 to $15 and $10 to $20 poker games.
They have $2.50 chips especially for the case you're describing.
I've been to casinos in Las Vegas and Wisconsin and I think they have all had 50-cent chips at the blackjack table. If they don't, you can work around the problem by betting an even amount. For example, playing 6 dollars a hand at a table with a 5-dollar minimum won't have a significant impact on how much you win or lose.