Thinking in ranges is the single largest step between casual and serious poker. You do not put an opponent on ace-king; you put them on the set of hands consistent with everything they have done.
The arithmetic behind it is combinatorial. There are six combinations of any pocket pair, four of any suited hand and twelve of any offsuit hand, out of 1,326 total. So "aces or ace-king" is 6 combinations against 16, a much wider gap than the two hand names suggest.
Card removal sharpens it further. Holding an ace cuts an opponent's possible aces from six combinations to three and their ace-king from sixteen to eight. Half of their strongest holdings vanish because of one card in your hand.
Where the numbers come from
Related terms in poker
- Pot odds — The price a call is getting, compared against how often it needs to win.
- Outs — The cards remaining that would improve your hand to a likely winner.
- Equity — Your share of the pot, meaning how often you win it if the hand plays to showdown.
- Implied odds — The money you expect to win later if your draw comes in, beyond what is in the pot now.
- Position — Where you act in the betting order, and the largest structural edge in poker.
- Button — The dealer position, which acts last on every postflop street.
Where an entry quotes a number, that figure comes from the computed sections of this site rather than from another glossary, so the definition and the derivation cannot drift apart. Each entry links to the page where the number is worked out.