[{"data":1,"prerenderedAt":534},["ShallowReactive",2],{"post-en-poker-combinations-explained":3},{"item":4},{"id":5,"title":6,"body":7,"description":495,"extension":496,"meta":497,"navigation":529,"path":530,"seo":531,"stem":532,"__hash__":533},"content/en/blog/poker-combinations-explained.md","Poker Combos: Count the Hands, Not the Labels",{"type":8,"value":9,"toc":483},"minimark",[10,14,17,23,26,29,37,42,45,48,51,56,59,74,78,83,86,92,95,101,106,113,118,121,130,136,139,143,146,151,179,182,187,193,199,205,209,212,233,239,242,260,263,268,271,275,278,309,312,317,328,331,343,347,350,357,362,365,370,373,379,386,389,396,400,405,408,413,422,427,430,436,440,443,463,469,472,478],[11,12,13],"p",{},"“They could have AA, KK, or an AQ bluff.”",[11,15,16],{},"Three options. You beat one. Does that mean you win one-third of the time?",[11,18,19],{},[20,21,22],"strong",{},"Not necessarily. Three hand labels do not mean three equal probabilities.",[11,24,25],{},"AA can contain six distinct holdings. AQ can contain more than a dozen. More importantly, your opponent may not reach this decision and bet with all of them equally often.",[11,27,28],{},"Counting combinations turns a vague “they could have it” into specific hands you can check.",[30,31,32],"blockquote",{},[11,33,34],{},[20,35,36],{},"Count the cards. Consider how they get played. Then compare the range with the price.",[38,39,41],"h2",{"id":40},"_1-a-combo-is-two-specific-cards","1. A Combo Is Two Specific Cards",[11,43,44],{},"AA is a hand class. A♠ A♥ is one combination; A♦ A♣ is another.",[11,46,47],{},"Order does not matter. A♠ A♥ and A♥ A♠ are the same holding.",[11,49,50],{},"Choose two cards from a standard 52-card deck, without counting reversed orders twice:",[11,52,53],{},[20,54,55],{},"52 × 51 ÷ 2 = 1,326 starting-hand combinations.",[11,57,58],{},"The familiar 169-cell starting-hand chart groups those combinations into 169 classes. It does not make every cell equally likely.",[11,60,61,62,65,66,73],{},"Start with four numbers: ",[20,63,64],{},"six combinations per pocket pair; for any two different ranks, four suited, twelve offsuit, and sixteen total combinations."," These are baseline counts before relevant cards are known. The ",[67,68,72],"a",{"href":69,"rel":70},"https://pokercoaching.com/blog/wp-content/uploads/2025/10/Poker-Combinations-PDF-Guide.pdf",[71],"nofollow","PokerCoaching combinations reference"," uses the same basic counts.",[38,75,77],{"id":76},"_2-where-do-6-4-12-and-16-come-from","2. Where Do 6, 4, 12, and 16 Come From?",[11,79,80],{},[20,81,82],{},"Pocket pairs: why six combinations of AA?",[11,84,85],{},"Four aces can be paired in just six distinct ways:",[87,88],"article-illustration",{"alt":89,"caption":90,"src":91},"The six AA combinations: spade-heart, spade-diamond, spade-club, heart-diamond, heart-club, and diamond-club","Six possible holdings, not six hands dealt simultaneously from one deck. Reversing the two cards does not create another combination.","/images/poker-combinations/six-ace-pairs.webp",[11,93,94],{},"There are four choices for the first ace and three for the second. That gives twelve ordered selections, but every pair appears twice. So:",[11,96,97,100],{},[20,98,99],{},"4 × 3 ÷ 2 = 6."," The same reasoning applies to KK, QQ, and every other pocket pair.",[11,102,103],{},[20,104,105],{},"Suited hands: why four combinations of AKs?",[11,107,108,109,112],{},"They are A♠ K♠, A♥ K♥, A♦ K♦, and A♣ K♣. One per suit, four in total. The ",[20,110,111],{},"s stands for suited",".",[11,114,115],{},[20,116,117],{},"Offsuit hands: why twelve combinations of AKo?",[11,119,120],{},"Each ace can pair with three kings of a different suit. A♠, for example, can go with K♥, K♦, or K♣. Four aces, three choices each:",[11,122,123,126,127,112],{},[20,124,125],{},"4 × 3 = 12."," The ",[20,128,129],{},"o stands for offsuit",[11,131,132,133],{},"If we write AK without restricting the suits, each ace can pair with any of four kings: ",[20,134,135],{},"4 × 4 = 16, or four AKs plus twelve AKo combinations.",[11,137,138],{},"There is no division by two here. We consistently choose an ace first and a king second, rather than counting the same selection again as king-ace.",[38,140,142],{"id":141},"_3-known-cards-change-the-count","3. Known Cards Change the Count",[11,144,145],{},"Your cards, the board, and any other cards genuinely known to be unavailable to the opponent must be removed. This is where blockers begin.",[11,147,148],{},[20,149,150],{},"For a pocket pair, count how many cards of that rank remain.",[152,153,154,161,167,173],"ul",{},[155,156,157,158,112],"li",{},"Four remain: 4 × 3 ÷ 2 = ",[20,159,160],{},"6 combos",[155,162,163,164,112],{},"Three remain: 3 × 2 ÷ 2 = ",[20,165,166],{},"3 combos",[155,168,169,170,112],{},"Two remain: 2 × 1 ÷ 2 = ",[20,171,172],{},"1 combo",[155,174,175,176,112],{},"One or none remain: ",[20,177,178],{},"0 combos",[11,180,181],{},"With K♠ K♥ on the board, the opponent has only one possible KK holding: K♦ K♣. Not six.",[11,183,184],{},[20,185,186],{},"For two different ranks without a suit restriction, multiply the remaining counts.",[11,188,189,190,112],{},"Suppose A♠ and K♥ are known to be unavailable. Three aces and three kings remain, giving ",[20,191,192],{},"3 × 3 = 9 AK combinations",[11,194,195,196,112],{},"Do not divide nine by four to estimate AKs. Spades are missing their ace, and hearts their king. Only A♦ K♦ and A♣ K♣ survive as suited combinations. That leaves ",[20,197,198],{},"9 − 2 = 7 AKo combos",[11,200,201,204],{},[20,202,203],{},"Count suited hands suit by suit, checking that both cards remain."," And avoid overlapping totals: AK already includes AKs and AKo. You cannot add four AKs to sixteen AK and call it twenty.",[38,206,208],{"id":207},"_4-turn-aa-kk-and-aq-into-a-range","4. Turn AA, KK, and AQ Into a Range",[11,210,211],{},"Consider a simplified river exercise, not an actual hand history:",[152,213,214,220,226],{},[155,215,216,217,112],{},"Your hand: ",[20,218,219],{},"Q♥ J♥",[155,221,222,223,112],{},"Board: ",[20,224,225],{},"J♣ 9♦ 6♠ 3♥ 2♣",[155,227,228,229,232],{},"Assume the opponent bets only ",[20,230,231],{},"AA, KK, and AQ",", with AQ including suited and offsuit hands.",[11,234,235,236,112],{},"This is a range chosen to teach the calculation, ",[20,237,238],{},"not a claim about what a real opponent must hold",[11,240,241],{},"Your pair of jacks loses to AA and KK, but beats AQ's ace-high. Count each class:",[152,243,244,249,254],{},[155,245,246,247,112],{},"AA: no known aces removed, so ",[20,248,160],{},[155,250,251,252,112],{},"KK: no known kings removed, so ",[20,253,160],{},[155,255,256,257,112],{},"AQ: four aces remain, but your Q♥ leaves three queens, so ",[20,258,259],{},"4 × 3 = 12 combos",[11,261,262],{},"If every available combination has the same weight for reaching this point and making this bet:",[11,264,265],{},[20,266,267],{},"12 winning combos ÷ (6 + 6 + 12) total combos = 12 ÷ 24 = 50%.",[11,269,270],{},"Beating one of three labels does not make this a one-third chance. What matters is the combinations behind those labels.",[38,272,274],{"id":273},"_5-can-you-call-with-50-check-the-price","5. Can You Call With 50%? Check the Price.",[11,276,277],{},"Continue the exercise. This is a heads-up river with no rake or ties. Compare calling with folding only, without a raise option. All amounts are demonstration points:",[279,280,281,287,294,303],"ol",{},[155,282,283,284,112],{},"The pot before the bet is ",[20,285,286],{},"100",[155,288,289,290,293],{},"The opponent bets ",[20,291,292],{},"200",", twice the pot.",[155,295,296,297,300,301,112],{},"There is now ",[20,298,299],{},"100 + 200 = 300"," available, and you must call ",[20,302,292],{},[155,304,305,306,112],{},"After your call, the final pot would be ",[20,307,308],{},"300 + 200 = 500",[11,310,311],{},"You contribute 200 to contest a final pot of 500. With no ties in this exercise, equity equals the probability of winning. The minimum required is:",[11,313,314],{},[20,315,316],{},"200 ÷ 500 = 0.4 = 40%.",[11,318,319,320,323,324,112],{},"Written as pot odds, that is 200 : 300, or 2 : 3. The percentage conversion is ",[20,321,322],{},"2 ÷ (2 + 3)",", not 2 ÷ 3. See the ",[67,325,327],{"href":326},"/pot-odds-calculation-complete-guide","full pot-odds walkthrough",[11,329,330],{},"Under the equal-weight range assumption, 50% exceeds 40%, so calling has positive chip expected value. Check it through outcomes: winning adds 300 relative to folding now; losing costs 200.",[11,332,333,336,337,342],{},[20,334,335],{},"Call EV = 50% × 300 − 50% × 200 = +50."," Expected value is not a prediction of the next result. ",[67,338,341],{"href":339,"rel":340},"https://blog.gtowizard.com/how-to-solve-toy-games/",[71],"GTO Wizard's simplified river games"," also explain decisions through the relationship between equity, betting ranges, and price.",[38,344,346],{"id":345},"_6-twelve-aq-combos-but-do-they-all-bet","6. Twelve AQ Combos. But Do They All Bet?",[11,348,349],{},"Now change one assumption. AA and KK always reach this point and bet, while AQ does so only half as often. Hold the other arrival conditions equal for comparison.",[11,351,352,353,356],{},"AQ still has twelve physically available combinations, but its ",[20,354,355],{},"weighted combo count"," in the betting range becomes:",[11,358,359],{},[20,360,361],{},"12 × 50% = 6.",[11,363,364],{},"You beat a weight of six out of a total weight of 6 + 6 + 6 = 18:",[11,366,367],{},[20,368,369],{},"6 ÷ 18 = 1/3, approximately 33.3%.",[11,371,372],{},"The price still requires 40%. Under this new assumption:",[11,374,375,378],{},[20,376,377],{},"Call EV = 1/3 × 300 − 2/3 × 200 ≈ −33.3."," Folding now beats calling.",[11,380,381,382,385],{},"Same board. Same hand. Different conclusion. You face ",[20,383,384],{},"the range that actually chooses to bet",", not every hand that could physically have been dealt.",[11,387,388],{},"“Weighted combos = available combos × relevant action frequency” is a shortcut. Real analysis also needs arrival frequencies through earlier streets, and different suit combinations within one hand class may follow different strategies. A fractional weight does not mean that half a physical hand exists.",[30,390,391],{},[11,392,393],{},[20,394,395],{},"Combinations count the possibilities. Action frequencies determine their relative weight.",[38,397,399],{"id":398},"_7-what-changes-in-calls-bluffs-and-value-bets","7. What Changes in Calls, Bluffs, and Value Bets?",[11,401,402],{},[20,403,404],{},"Calling: count more than the hands that beat you.",[11,406,407],{},"Count the hands you beat, then ask whether they really bet. In our exercise, Q♥ removes AQ combinations. If AQ supplies the bluffs in that model, your queen blocks some of the hands you want to see.",[11,409,410],{},[20,411,412],{},"Bluffing: blocking strength is not automatic permission to bet.",[11,414,415,416,421],{},"Check whether you also remove hands that would have folded, and whether this opponent folds them at all. GTO Wizard's ",[67,417,420],{"href":418,"rel":419},"https://blog.gtowizard.com/blockers-unblockers-the-secret-to-picking-great-bluffs/",[71],"blocker and unblocker discussion"," examines both sides together.",[11,423,424],{},[20,425,426],{},"Value betting: count the worse hands that can continue.",[11,428,429],{},"If your cards remove many of the opponent's worse calling hands, “they have plenty to pay me with” deserves another look. Conversely, do not focus on a few combinations that beat you while ignoring the worse calls.",[11,431,432,433],{},"None of these is an automatic action rule. ",[20,434,435],{},"A blocker is evidence for adjusting a range, not a command to call or bluff.",[38,437,439],{"id":438},"_8-separate-what-you-count-from-what-you-assume","8. Separate What You Count From What You Assume",[11,441,442],{},"Keep three distinctions clear:",[152,444,445,451,457],{},[155,446,447,450],{},[20,448,449],{},"Combos are not outs."," Combos count possible hole-card holdings. Outs count unseen cards that would give you a winning hand. Merely improving your hand without putting it ahead does not make a card a clean out.",[155,452,453,456],{},[20,454,455],{},"A combo fraction is not always showdown equity."," Our shortcut works on a river where each matchup has a known win or loss and no ties. Earlier streets require future runouts; heads-up ties contribute half the pot.",[155,458,459,462],{},[20,460,461],{},"Accurate arithmetic does not guarantee an accurate range."," Extra value hands, or an opponent who almost never bluffs AQ, can overturn a tidy calculation. Tournament payout pressure, multiway pots, and side pots also require more than this heads-up chip-EV model.",[11,464,465,466],{},"Try a post-session exercise in this order: ",[20,467,468],{},"list a range → remove known cards → count combos → apply action weights → compare the price.",[11,470,471],{},"Give the bluff combinations a conservative weight and a higher one. If that change alone reverses the call, the next thing you need may be evidence about the opponent, not another decimal place.",[473,474,475],"review-principles",{},[11,476,477],{},"Build structure with combinations and price. Calibrate ranges with observed actions. Then notice whether fear makes you count only strong hands, or frustration makes you count every weak hand as a bluff. AI can help check the work; it cannot certify missing evidence.",[11,479,480],{},[20,481,482],{},"Counting combos is not about becoming more certain of a guess. It is about making every “they could have it” specific enough to examine.",{"title":484,"searchDepth":485,"depth":485,"links":486},"",2,[487,488,489,490,491,492,493,494],{"id":40,"depth":485,"text":41},{"id":76,"depth":485,"text":77},{"id":141,"depth":485,"text":142},{"id":207,"depth":485,"text":208},{"id":273,"depth":485,"text":274},{"id":345,"depth":485,"text":346},{"id":398,"depth":485,"text":399},{"id":438,"depth":485,"text":439},"Why does AA have six combos and AK sixteen? Follow a QJ river example through card removal, range weights, a 40% calling threshold, and better reasoning about calls, bluffs, and value bets.","md",{"subtitle":498,"keywords":499,"createdDate":500,"updatedDate":500,"coverImage":501,"ogImage":501,"alt":502,"tags":503,"categories":509,"author":513,"relates":517},"From 6, 4, 12, and 16 to blockers, range weights, and river calls.","poker combinations,poker combos,hand combinations,blockers,weighted ranges,river calls,pot odds,Texas Hold'em basics","2026/10/24","/images/poker-combinations/cover.webp","Original cartoon of an adult poker enthusiast studying four aces of different suits and recording six pairs of counting dots in a notebook",[504,505,506,507,508],"Combinations","Range Thinking","Blockers","Pot Odds","Decision Training",[510,511,512],"Basic Concepts","Poker Mathematics","Strategy Learning",{"name":514,"avatar":515,"description":516},"ZenPoker Coaching Team","/avatars/2.png","Helping poker enthusiasts understand decisions through concrete hands and checkable calculations.",[518,521,525],{"title":519,"href":326,"image":520},"Complete Guide to Pot Odds Calculation","/images/international/pot-odds-calculation-complete-guide.jpg",{"title":522,"href":523,"image":524},"Reading the Hand, or Feeling the Fear?","/reading-the-hand-or-feeling-the-fear","/images/reading-the-hand-or-feeling-the-fear.webp",{"title":526,"href":527,"image":528},"Afraid to Value Bet?","/afraid-to-value-bet","/images/afraid-to-value-bet.webp",true,"/en/blog/poker-combinations-explained",{"title":6,"description":495},"en/blog/poker-combinations-explained","61H5OTzdxnFk1CvbZ9lfn_6AWkVOhR7pKjIxB4UV4fY",1793031536306]