Blocker Effects
How the cards in your hand change a random opponent's holding odds. On the 8-card flush example, holding one spade changes the result by several percentage points.
How often they actually have it
Game
The King rows change the board. The flush and two-rank rows condition on your full 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 8.4%
J♠J♥J♦J♣+T♠T♥T♦T♣ one 6.5%
J♠J♥J♦J♣+T♠T♥T♦T♣ J-J 4.4%
J♠J♥J♦J♣+T♠T♥T♦T♣ J-T 5.0%
J♠J♥J♦J♣+T♠T♥T♦T♣ J-J-T 3.4%
J♠J♥J♦J♣+T♠T♥T♦T♣ J-J-T-T 2.3%
Methodology
- Exact closed-form card-removal combinatorics for high-only Omaha with 4-8 hole cards, zero simulation. In the flush and two-rank charts, your full hand is known: unshown hole cards have other suits or ranks. The opponent draws from the 49-card flop deck minus all of your hole cards. The King chart is a separate board-only random-hand baseline.
- A King = holds ≥1 King; KK = holds ≥2; flush = holds ≥2 spades on the monotone flop; nut straight = holds J and T on 9-8-7; Q + 9 = holds both top board ranks on Q-9-4. The last group includes hands that make top set as their best hand.
- 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 your exact count of target cards.
Unblocked baselines (what a random hand holds on every texture) live at Board & Hand Probabilities. How played ranges bend these numbers: Range Frequencies and PLO Range Advantage. What a frequency edge lets you do with sizing: Bet sizing & MDF.