Poker odds, answered
Odds of being dealt pocket aces (and other starting hands)
You are dealt pocket aces 0.45% of the time, 1 hand in 221. Any pocket pair: 5.9% (1 in 17). Ace-king: 1.21% (1 in 82.9). Two suited cards: 23.5%.
Exact counts, not simulations.
How it is counted
There are C(52,2) = 1,326 two-card hands. Six of them are aces (choose 2 of the 4), 78 are pairs of any rank (13 × 6), 16 are ace-king (4 × 4) and 312 are suited (4 suits × C(13,2)).
Aces: 6 ÷ 1,326 = 1 ÷ 221 Any pair: 78 ÷ 1,326 = 1 ÷ 17 Ace-king: 16 ÷ 1,326