With 23 people, some shared birthday often exceeds 50%. That is “some pair.” Lotto first prize is “this exact 6-set.” birthday-bias-lottery is the 1–31 crowding bias. This essay splits the paradox from the ticket cell.
Some pair collides versus my birthday collides versus this 6-set hits.
365 and 45 are different urns. Do not copy-paste the formula.
birthday-bias-lottery.
No classroom-to-jackpot table.
For entertainment and arithmetic. Combinatorics, bias, and expected value are not a winning tip or investment advice. Draws are random.