This is a magic trick that has a formula which I don't understand. 5 cards are used 3 black 2 red, so N = 5 (total cards) k=2 (red cards) and N-k=3 (black cards) and the magician always bets that the card drawn will be red for any shuffled combination of BBBRR cards. He multiplies his initial bet by y=3/2 for a loss and x=1/2 for a win. And he always bets 16$. The formula is 
which gives 5/16 for the given values of x and y. I think this has something to do with a geometric series but am not sure, does anyone know how to explain this formula or derive it?
2026-04-29 09:18:29.1777454309
Explain this formula of geometric series/math magic
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