Combos, ranges and equity:
think beyond your own hand

You know the hand rankings: a flush beats a straight, a full house beats a flush. That ranking describes your best five-card hand at showdown. To make a decision before seeing your opponent’s cards, you need to add another question: which hands can the other player still have?

Here, a combo means two specific hole cards. A♠ K♥ is one combo; A♦ K♣ is another. Both belong to AKo: ace-king offsuit. AKs means ace-king suited, with two cards of the same suit. AK includes both families. A range is the set of combos assigned to a player in a situation.

With no known cards, four aces form six distinct pairs: 4 × 3 ÷ 2. We divide by two because A♠ A♥ and A♥ A♠ represent the same hand. For AK, each of the four aces can accompany each of the four kings: 4 × 4 = 16. Four combinations are suited; the other twelve are offsuit.

So do not simply count squares in a range chart. An AKo square carries three times as many combos as an AKs square if every combo is included at the same frequency. A grid of 169 hand families therefore represents 1 326 distinct starting hands.

Suppose only A♠ is removed from the deck: no king or other ace is known. Three aces remain. AA falls to 3 combos and AK to 12: 3 suited and 9 offsuit. The module below isolates this effect. In a real hand, also remove your second hole card and every board card.

A card that reduces some opposing hands is a blocker. Its strategic effect depends on what it removes: strong hands, hands likely to call or possible bluffs. Holding an ace therefore does not, by itself, justify bluffing. Examine the relevant range and the actions that led to the spot.

Start with context: positions, effective stacks, the initial raise, any re-raise and then postflop actions. A starting range provides a base. After each action, ask which hands continue and how often. Keeping every initial hand through to the river ignores information supplied by earlier decisions.

Here is a deliberately simplified assumption without blockers: JJ is included at 100 % and AQs at 50 %. The six JJ combos contribute a weight of 6; the four AQs combos contribute a weight of 2. AQs therefore represents 2 out of 8, or 25 % of this weighted range. The 50 % weight means each relevant combo is included half the time in the model; it is not its final share of the range.

These frequencies are working assumptions. Compare a conservative version with a wider one when information is missing. Displaying a percentage to two decimal places does not make the opponent-range assumption more certain.

Equity measures the average share of the pot you receive if players reach showdown without further betting, accounting for remaining cards and the ranges entered. It includes split pots. Heads-up, it equals the probability of winning plus half the probability of an equal split.

A purely hypothetical example: a hand wins outright in 30 % of cases, splits in 10 % and loses in 60 %. Its equity is 30 % + 10 % ÷ 2 = 35 %. This number illustrates the formula; it is not from a simulation of a real spot. With multiple players, each split contributes according to the fraction of the pot actually received.

Your equity against a specific hand differs from your equity against a range. To prepare a decision, test plausible hands before looking at the game’s result. Calculating only against the cards eventually shown turns information unknown at decision time into a certainty.

Heads-up on the river, the pot contains 100 chips before your opponent’s bet. They bet 50. You must call 50; the final pot will be 200. The equity threshold is therefore 50 ÷ 200 = 25 %. Using 50 ÷ 150 would omit your own call from the final pot.

In this model, the EV of calling relative to folding is: equity × 200 − 50. With hypothetical equity of 30 %, that gives +10 chips. At 20 %, it gives −10. At 25 %, both options have the same expected value. These results assume the call closes the action, with no rake or ICM effect; amounts already invested do not change the cost of the present decision.

On the flop or turn, future bets complicate the comparison. You may have to fold before showdown or invest more. Position and how each range continues influence the value actually obtained. Equity above the immediate threshold therefore does not automatically validate a call.

Start by choosing a heads-up river decision. You can then work on ranges and the price of calling without having to model another card or a new bet.

Manual calculation is enough to learn combos and pot odds. Software becomes useful when you repeat the exercise with multiple ranges, weights or boards. Flopzilla presents the distribution of made hands and draws in a range on a board, along with equity calculations. GrindLab presents weighted-range work and analysis of hands from compatible histories.

Before paying, check that the tool lets you reproduce your exercise: enter cards, change a range, adjust frequencies and find the result. For importing, check your own history’s format. A higher plan becomes useful when its features address a task repeated in your study sessions.