lucky dip (US English = grab bag)
noun phrase

- a game in which you pay to pick a wrapped object out of a container, which is filled with wrapped objects of various different values, hoping to get something of higher value than the amount you have paid

(Cambridge Advanced Learner's Dictionary)

- figuratively speaking, a purely random or miscellaneous selection or decision

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WORD ORIGIN

The term lucky dip refers to taking a chance on winning something (try your luck), and dip, as in "dipping" your hand into a container like a jar to retrieve something. Parties and festive occasions often include lucky dip games. Many non-profit organisations have lucky dip games to raise money for themselves or for charity.

The UK National Lottery offers a feature called Lucky Dip, in which players can have the ticketing machines randomly generate six numbers for them. Statistics show that around 40% of the millionaire winners use this method.

Where the winners safeguard their tickets provides interesting insight into human nature:

24% chose a bag, purse or wallet, 14% kept it under the pillow, 10% put it in their underwear and around 2% sought the ultimate protection in the Bible. According to the UK National Lottery web site, "an additional 2% have kept it under a bird cage - an interesting variation on the traditional guard dog."

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SMUGGLE OWAD into a conversation:
say something like:

"In Brussels we couldn't decide which restaurant to try, so we just selected one out of a telephone book LUCKY DIP style. It was one of the best dining experiences we ever had!"