A release-checked easy problem for training Exchangeability.
Question
Alice and Bob alternate picking balls without replacement from an urn that has $k$ red balls and $1$ black ball. The winner is the person who draws the black ball. Alice gets to decide the order of drawing. If Alice plays optimally, what is her chance of winning when $k = 25$?
Practice focus
This Games problem is tagged Exchangeability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.