There is a phrase you hear from good players on every difficult river: "he just cannot have enough value here." It sounds like intuition, a feel for the opponent built over years. It is not. It is arithmetic, run silently and fast, and it is the single most underrated skill in poker. The best players count combinations mid-hand, on every important decision, and it is why they call and fold correctly in spots that look like coin flips to everyone else.
The count that wins the pot
The decision that combinatorics settles more than any other is the big river call. Someone bets large, and you have a bluff-catcher: a hand that beats their bluffs and loses to their value. Whether you call comes down to a ratio. How many combinations of hands that beat you can they have, against how many combinations of bluffs, compared to the price you are being offered.
Do the count and the decision usually makes itself. Suppose you have decided the villain either got there with a specific draw or is firing a missed one. If the value hand can be made in three or four ways and the missed draws total a dozen combinations, you are being offered a call against a range that is mostly bluffs, and even a modest holding is a clear call. Flip the count, so value outnumbers bluffs, and the same hand is an easy fold. Nothing about how the hand felt changed. The maths did, and the maths is what the pro trusts. The mechanics are laid out in How to Count Poker Combos, and the comparison to your price is the same one you make with pot odds.
Blockers cut the count
The reason your own two cards matter so much is that they remove combinations from the villain's range before you even start. This is the blocker effect, and it is the pro's secret weapon on both sides of a decision.
On the calling side, holding a card that blocks the villain's value makes the bluffs relatively more likely, which pushes a marginal spot toward a call. If you hold a card that makes their most likely value hand harder to have, there is simply less value in their range for the same number of bluffs.
On the betting side, the same logic tells you which hands to bluff with. The best bluff is the one that blocks the value the villain could call with, because it makes their continue less likely. This is exactly why suited wheel aces are favourite four-bet bluffs, a play broken down in Why A5 Suited Is a Favourite Four-Bet Bluff.
Why it has to be real-time
Here is what separates the players who know this from the players who use it. Everyone can count combinations slowly, at home, reviewing a hand. Almost nobody can do it in the four seconds a real river gives you, with a large bet in front of them and a dealer waiting. And a count you cannot run in real time is a count you do not have when it matters.
That is the whole case for drilling it. Not learning that combinatorics exists, which takes an afternoon, but grinding the counts until they arrive automatically under pressure. The Combo Counter drill runs you through combination counts and blocker scenarios against a timer until the numbers come without effort, and the Equity Simulator lets you check how those counts translate into raw equity in specific spots. Folded into the daily routine described in How to Get Better at Poker, it becomes the instinct that makes hard rivers easy.
The habit, not the trick
The temptation is to treat this as a party trick you deploy on the occasional big decision. The players who profit from it do the opposite. They are counting quietly on most streets of most hands, keeping a running sense of what the villain can and cannot have, so that when the big decision arrives the count is already most of the way done. It is a habit, and like every habit worth having in poker it is built by repetition until it stops feeling like work.
The read that looks like a gift is a count you can learn to run. Drill it until it runs itself. Start training free at drills.poker.