Blocker Effects
How holding a card moves your opponent's frequencies. One blocker is worth a few points at most - a tiebreaker, not a read.
How often they actually have it
Game
How often a random hand holds it, as copies die on the board or in your hand.
They hold a King
K♠K♥K♦K♣ 4 liveon Q♦9♠6♥ 29.7%
K♠K♥K♦K♣ 3 liveon K♦9♠6♥ 23.0%
K♠K♥K♦K♣ 2 liveon K♦K♠9♥ 15.8%
K♠K♥K♦K♣ 1 liveon K♦K♠K♥ 8.2%
They hold both ranks
Board 9♠8♥7♦
J♠J♥J♦J♣+T♠T♥T♦T♣ none 7.2%
J♠J♥J♦J♣+T♠T♥T♦T♣ one 5.7%
J♠J♥J♦J♣+T♠T♥T♦T♣ J-J 4.1%
J♠J♥J♦J♣+T♠T♥T♦T♣ J-T 4.6%
J♠J♥J♦J♣+T♠T♥T♦T♣ J-J-T 3.2%
J♠J♥J♦J♣+T♠T♥T♦T♣ J-J-T-T 2.3%
Methodology
- Exact closed-form card-removal combinatorics: binomial ratios over the hole-card counts (PLO4-PLO8 = 4-8 cards), zero simulation. The opponent draws from the deck minus the board minus any named blockers.
- A King = holds ≥1 King; KK = holds ≥2; flush = holds ≥2 spades on the monotone flop; nut straight and top two = holds ≥1 of each of the two ranks they need.
- What a King makes depends on the row's board: no pair on Q-9-6, top pair on K-9-6, trips on K-K-9, quads on K-K-K. Same for KK: overpair, set, quads, then impossible with one King left.
- The rank ladder fixes the rank and changes only the board: 0, 1, 2 or 3 copies buried. The flush and two-card ladders fix the board and remove the cards you hold.
Unblocked baselines (what a random hand holds on every texture) live at Board & Hand Probabilities. How played ranges bend these numbers: PLO Range Frequencies and PLO Range Advantage. What a frequency edge lets you do with sizing: Bet sizing & MDF.