The bingo hall

A hall sells 100 cards at $2 and pays $150 to whoever finishes the first line. It takes in $200 and pays out $150, so it keeps $50 a game. Each card, on average, carries $1.50 of prize for its $2 price: the players get back 75 cents of every dollar they pay.

Nobody in the room is being cheated. The cage is honest and every card has the same chance. The keeping is in the price, decided before a ball is drawn — which is why the numbers belong on the wall where everyone can read them.

Bingo apps keep more quietly. Coins you buy turn into tickets you spend, so the price gets hard to see. A banner shouts SO CLOSE! when one square is missing, though "one away" on a card is ordinary. A daily bonus grows only if you come back. None of these changes the odds; they change how often you play.