Pairs 73.1 · suited 201.8 · offsuit 262.6
A hand played part of the time counts in proportion: raised half the time, it adds half its combos.
Poker combos are the exact two-card ways a hand can be dealt. A chart shows ace-king as one cell, but at the table it is sixteen different pairs of cards: four aces times four kings. Counting in combos instead of hands is what keeps range maths honest, because some hands are far more likely to be dealt than others.
| Hand type | Hands | Combos each | Combos total | Share of all hands |
|---|---|---|---|---|
| Pocket pairs | 13 | 6 | 78 | 5.9% |
| Suited | 78 | 4 | 312 | 23.5% |
| Offsuit | 78 | 12 | 936 | 70.6% |
| All starting hands | 169 | 1,326 | 100% |
The 1,326 is every way to pick two cards from 52. The 169 is how many different hands a chart needs, once suits that play the same are grouped together.
Combos are not the same thing as “poker combinations” in the sense of a flush or a full house. Those are the five-card hands, and their order is on our poker hand rankings chart.
Because an unpaired hand can use any ace with any king, and a pair has to pick two cards of one rank. Ace-king is 4 × 4 = 16: four of those share a suit (the suited combos) and the other 12 do not. Pocket aces need two of the four aces, and there are only six ways to choose two from four.
So ace-king is dealt 2.7 times as often as aces, and any one offsuit hand three times as often as its suited version. A range that looks mostly suited on a chart can still be mostly offsuit in what actually gets played.
Count the combos of every hand in it, and count a hand played part of the time in proportion: a hand raised half the time adds half its combos. Here are the opening ranges PlusEV drills, 6-max cash at 100 big blinds, counted that way:
| Seat | Opening range | Share of all hands | Pairs | Suited | Offsuit |
|---|---|---|---|---|---|
| Under the gun | 232.1 combos | 17.5% | 27% | 43% | 30% |
| Hijack | 286.4 combos | 21.6% | 24% | 42% | 35% |
| Cutoff | 377.9 combos | 28.5% | 20% | 41% | 39% |
| Button | 537.5 combos | 40.5% | 14% | 38% | 49% |
| Small blind (raises) | 345.7 combos | 26.1% | 13% | 42% | 46% |
Every percentage on our preflop charts comes from this count. When PlusEV’s solver ranges say under the gun opens 17.5% of hands, that is 232 of the 1,326 combos.
The mix shifts as the range widens. Under the gun opens mostly pairs and suited hands, and offsuit hands are under a third of the range. On the button, offsuit hands are the largest group at 49%, because each one that gets added brings 12 combos with it. The small blind also limps another 394 combos on top of the raises above.
The combo counter at the top of this page has each of these ranges as a preset. Load one, tap the cards you hold and watch the count move.
Every card you can see is a card your opponent cannot hold. Your own two cards and the board remove combos from their range, and the effect follows fixed rules:
| Their hand | Normally | You hold one of its cards | You hold two of its cards |
|---|---|---|---|
| A pocket pair, like AA | 6 | 3 | 1 |
| Ace-king, any suits | 16 | 12 | 9 (one ace, one king) |
| Ace-king suited | 4 | 3 | 2 |
| Ace-king offsuit | 12 | 9 | 7 |
This is card removal, and using it on purpose is what blockers in poker are about. In a real range the effect is real but modest. Facing a button open, the big blind’s 3-bet range in PlusEV’s charts is 191 combos, and 34 of them (17.8%) are aces, kings, queens or ace-king. If the button holds the ace of spades, those drop to 27 of 172 combos (15.7%). Holding the ace of spades and the king of diamonds, 21 of 157 (13.4%).
The same counting works on the flop, with the board cards treated as dead, and it shows how few combos a strong hand really is. On K♥ 9♠ 4♦:
By comparing how many combos beat you with how many you beat, then checking the price. This is a worked illustration of standard theory, not solver output.
The board runs out K♥ 9♥ 4♦ 2♣ 7♠ and your opponent bets the size of the pot. Calling a pot-sized bet needs you to be right at least a third of the time. Say their betting range is sets of kings, nines and fours, king-nine for two pair, and eight missed heart draws such as A♥Q♥, J♥10♥ and 6♥5♥, one combo each.
You hold Q♦Q♣. Their value is 3 + 3 + 3 combos of sets plus 9 of king-nine: 18. Against 8 bluffs, they are bluffing 8 of 26 times, 30.8%. That is short of the third you need, so it is a fold.
You hold K♦Q♣. Same strength in practice, since you beat only the bluffs. But your king leaves just 1 combo of kings and 6 of king-nine, so their value drops to 13. Now the bluffs are 8 of 21, 38.1%, and the call is profitable.
You hold A♥K♦. Your king removes the same value, but your ace of hearts also removes four of their eight bluffs. They are bluffing 4 of 17 times, 23.5%: a fold. Nothing about the board changed between these three hands. Only the cards you hold, and therefore the combos left in their range. The pot odds guide covers the price side of the same decision.
Offsuit broadway and ace-x hands, by a distance. Across PlusEV’s 1M+ graded training decisions, ace-five suited is the single most misplayed hand: players pick the right action 72.0% of the time. But it is dealt only 4 ways. Ace-jack offsuit is nearly as hard (72.1%) and is dealt 12 ways, so at a real table it produces almost three times as many mistakes.
Weight each hand’s error rate by how often it is dealt and the list turns over:
| Hand | Right answer chosen | Combos | Share of all mistakes | Rank by accuracy alone |
|---|---|---|---|---|
| AJo | 72.1% | 12 | 2.1% | 2nd |
| QJo | 72.4% | 12 | 2.1% | 3rd |
| KJo | 75.0% | 12 | 1.9% | 10th |
| ATo | 75.3% | 12 | 1.9% | 12th |
| A2o | 75.6% | 12 | 1.9% | 13th |
| KTo | 76.3% | 12 | 1.8% | 14th |
| A9o | 76.8% | 12 | 1.8% | 16th |
| AQo | 77.3% | 12 | 1.7% | 20th |
| A5s | 72.0% | 4 | 0.7% | 1st |
All 15 of the costliest hands are offsuit, and offsuit hands make up 59.7% of all mistakes when hands are weighted by how often they are dealt. Players actually get offsuit hands right more often than suited ones (90.1% against 83.8% on average), but there are three times as many of them.
The method, so the figures can be checked: standardised accuracy for all 169 hands, counting only spots with one clear solver answer and weighting every difficulty level equally, with at least 770 answers from 357 players behind each hand. The full list of hard hands is in the worst hands in poker.
Memorise four numbers and two removal rules, then practise until you stop doing arithmetic:
Nobody adds up 537 combos mid-hand. What players actually do is compare blocks: “they have 9 combos of sets and maybe 12 of ace-king, but 30-odd combos of draws”. Knowing the counts and using them in a ten-second decision are different skills, and only repetition closes that gap. For the preflop half of it, the PlusEV trainer deals you real spots until the ranges behind these counts stop needing a chart.
Poker combos come down to one fact: ace-king is 16 hands and aces are 6, and every card you can see changes those numbers. Count your opponent’s range that way and the close calls stop being guesses.
1,326 two-card starting hands, grouped into 169 hand types: 78 combos of pocket pairs, 312 suited and 936 offsuit. Each pocket pair can be dealt 6 ways, each suited hand 4 ways and each offsuit hand 12 ways.
Six. If you hold one ace there are 3 left, and if you hold two aces there is only 1.
Sixteen: 4 suited and 12 offsuit. Holding one ace or one king leaves 12, and holding an ace and a king leaves 9.
5.9%. There are 78 pocket pair combos among the 1,326 starting hands, so you are dealt a pair about once every 17 hands.
Three for each rank on an unpaired flop. On K-9-4 your opponent can hold kings, nines or fours 3 ways each, 9 set combos in all, against 6 for any pocket pair not on the board.
No. Combos count the ways two specific cards can be dealt. Hand rankings order the five-card hands, from high card up to a royal flush.
