{"id":178,"date":"2026-07-10T11:22:15","date_gmt":"2026-07-10T11:22:15","guid":{"rendered":"https:\/\/freebetrange.com\/academy\/?page_id=178"},"modified":"2026-07-11T11:33:48","modified_gmt":"2026-07-11T11:33:48","slug":"poker-combinatorics-explained-what-it-is-and-how-to-count-combos","status":"publish","type":"page","link":"https:\/\/freebetrange.com\/academy\/poker-combinatorics-explained-what-it-is-and-how-to-count-combos\/","title":{"rendered":"Combinatorics in Poker: What It Is and How to Count Combos"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">You\u2019ve probably heard the word \u201ccombinatorics,\u201d but never quite dug into what it actually means. It\u2019s one of those fundamental concepts that sounds intimidating at first\u2014but is actually very simple. No complicated formulas. Just three numbers to remember and an understanding of how to use them. After reading this article, you\u2019ll start thinking about your opponent\u2019s ranges differently: not \u201cmaybe they have AA, maybe not,\u201d but \u201chow often does AA appear in their range compared to other hands?\u201d That\u2019s real poker thinking.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Let\u2019s start with a simple question<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Imagine you\u2019re looking at your opponent and thinking: \u201cCould they have AA?\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The answer \u201cyes, they could\u201d is too vague. It\u2019s much more useful to evaluate <strong>how likely<\/strong> AA is for your opponent\u2014and how often AA appears compared to other hands.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">That\u2019s exactly what combinatorics is for. Don\u2019t worry\u2014no complex math. You only need to remember three numbers.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">First: what is a \u201chand combination\u201d?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In poker, you have two hole cards. \u201cAA\u201d is not a single specific hand\u2014it\u2019s any two aces out of the four in the deck.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aces come in four suits: \u2660 (spades), \u2665 (hearts), \u2666 (diamonds), \u2663 (clubs).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So \u201cgetting AA\u201d means getting any two of those four aces. And there are exactly 6 such combinations:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>A\u2660 + A\u2665<\/li>\n\n\n\n<li>A\u2660 + A\u2666<\/li>\n\n\n\n<li>A\u2660 + A\u2663<\/li>\n\n\n\n<li>A\u2665 + A\u2666<\/li>\n\n\n\n<li>A\u2665 + A\u2663<\/li>\n\n\n\n<li>A\u2666 + A\u2663<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">These six options are called the <strong>6 combinations of AA<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This rule applies to ANY pair\u2014KK has 6, QQ has 6, 22 has 6. Every rank has exactly 4 suits, and choosing any 2 out of 4 always gives 6 combinations.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Easy to remember:<\/strong> a pair = 6 combinations.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/hand2noteguide.com\/wp-content\/uploads\/2026\/05\/\u0421\u043d\u0438\u043c\u043e\u043a-\u044d\u043a\u0440\u0430\u043d\u0430-2026-05-14-201904-1024x689.jpg\" alt=\"\" class=\"wp-image-16743\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Now let\u2019s look at suited hands<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Take AKs\u2014an ace and a king of the same suit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Same suit means both cards must be spades, or both hearts, and so on. How many combinations are there?<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>A\u2660 + K\u2660<\/li>\n\n\n\n<li>A\u2665 + K\u2665<\/li>\n\n\n\n<li>A\u2666 + K\u2666<\/li>\n\n\n\n<li>A\u2663 + K\u2663<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Exactly <strong>4 combinations<\/strong>\u2014one for each suit.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This works for any suited hand: 76s, QJs, T9s\u2014each has exactly 4 combinations.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/hand2noteguide.com\/wp-content\/uploads\/2026\/05\/\u0421\u043d\u0438\u043c\u043e\u043a-\u044d\u043a\u0440\u0430\u043d\u0430-2026-05-14-202136-1024x710.jpg\" alt=\"\" class=\"wp-image-16746\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">And finally: offsuit hands<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Now AKo\u2014an ace and a king of different suits.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">There are many more possibilities here because the suits can differ:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A\u2660 + K\u2665, A\u2660 + K\u2666, A\u2660 + K\u2663 (3 combinations with the ace of spades)<\/li>\n\n\n\n<li>A\u2665 + K\u2660, A\u2665 + K\u2666, A\u2665 + K\u2663 (3 combinations with the ace of hearts)<\/li>\n\n\n\n<li>A\u2666 + K\u2660, A\u2666 + K\u2665, A\u2666 + K\u2663 (3 combinations with the ace of diamonds)<\/li>\n\n\n\n<li>A\u2663 + K\u2660, A\u2663 + K\u2665, A\u2663 + K\u2666 (3 combinations with the ace of clubs)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Total: 4 \u00d7 3 = <strong>12 combinations<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">An offsuit hand appears <strong>three times more often<\/strong> than the same suited hand!<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/hand2noteguide.com\/wp-content\/uploads\/2026\/05\/\u0421\u043d\u0438\u043c\u043e\u043a-\u044d\u043a\u0440\u0430\u043d\u0430-2026-05-14-202029-1024x701.jpg\" alt=\"\" class=\"wp-image-16745\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">The three numbers you need to know<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Hand type<\/th><th>Example<\/th><th>Number of combinations<\/th><\/tr><\/thead><tbody><tr><td>Pair<\/td><td>AA, KK, 22<\/td><td><strong>6<\/strong><\/td><\/tr><tr><td>Suited<\/td><td>AKs, QTs<\/td><td><strong>4<\/strong><\/td><\/tr><tr><td>Offsuit<\/td><td>AKo, QTo<\/td><td><strong>12<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">That\u2019s it! Everything else is just applying these three numbers.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Why this matters \u2014 a simple example<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Imagine you\u2019re thinking: could your opponent have AA or AK when they make a big bet?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s count:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>AA: 6 combinations<\/li>\n\n\n\n<li>AKs: 4 combinations<\/li>\n\n\n\n<li>AKo: 12 combinations<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Total AK (all versions): 16 combinations.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>So AK appears almost three times as often as AA!<\/strong> This already helps you think more precisely about your opponent\u2019s range.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/hand2noteguide.com\/wp-content\/uploads\/2026\/05\/\u0421\u043d\u0438\u043c\u043e\u043a-\u044d\u043a\u0440\u0430\u043d\u0430-2026-05-14-202306-1024x553.jpg\" alt=\"\" class=\"wp-image-16747\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Blockers: your cards affect your opponent\u2019s range<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Here\u2019s an interesting point. Suppose you hold an ace. That means your opponent <strong>cannot have all 6 combinations of AA<\/strong>\u2014you have one of the aces! They only have 3 combinations of AA available (from the remaining three aces in the deck).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is called a <strong>blocker<\/strong>. Your cards \u201cblock\u201d some of your opponent\u2019s possible hands.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">You hold an ace? Your opponent has half as many AA combinations. You hold the ace of spades? Your opponent has zero suited hands with the ace of spades.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It might sound minor, but professionals constantly use blockers when making decisions\u2014especially when considering whether to bluff.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">How many total starting combinations are there in poker?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">There are 52 cards in the deck, and you choose 2. The total number of unique combinations is <strong>1326<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Why does this matter? Because when we say \u201cthe opponent opens 10% of hands,\u201d that\u2019s about 133 combinations out of 1326. Knowing how many combinations each specific hand has helps you understand what actually makes up that 10%.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">How to use this at the table<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">You don\u2019t need to calculate everything in your head during a hand. First, just get used to thinking in terms of \u201chow many combinations could my opponent have?\u201d<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Three simple questions help:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Is it a pair, suited, or offsuit?<\/strong> \u2192 Instantly: 6, 4, or 12.<\/li>\n\n\n\n<li><strong>Do I have a blocker?<\/strong> \u2192 If yes, reduce the number accordingly.<\/li>\n\n\n\n<li><strong>How many value hands vs. how many bluffs are in the opponent\u2019s range?<\/strong> \u2192 Combinatorics gives a clear answer.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">FreeBetRange does the counting for you<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">When you study ranges using <strong>FreeBetRange<\/strong>, you see the number of combinations automatically. Any selected range immediately shows:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The exact number of combinations<\/li>\n\n\n\n<li>The percentage out of all 1326 possible hands<\/li>\n\n\n\n<li>A visual distribution in the matrix<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-group is-content-justification-center is-nowrap is-layout-flex wp-container-core-group-is-layout-d05cb3ef wp-block-group-is-layout-flex\">\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/hand2noteguide.com\/wp-content\/uploads\/2026\/05\/\u0421\u043d\u0438\u043c\u043e\u043a-\u044d\u043a\u0440\u0430\u043d\u0430-2026-05-14-202436.jpg\" alt=\"\" class=\"wp-image-16748\" style=\"width:450px\" \/><\/figure>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\">This is a great way to learn: open a range, look at a BTN opening range, and immediately see\u2014here are 250 combinations, which is 18.9% of hands. You start to feel how wide or tight a position plays.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Summary<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Combinatorics is simply the ability to count <strong>how many real combinations<\/strong> are behind each \u201chand\u201d in a range.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Pairs: always <strong>6 combinations<\/strong><\/li>\n\n\n\n<li>Suited: always <strong>4 combinations<\/strong><\/li>\n\n\n\n<li>Offsuit: always <strong>12 combinations<\/strong><\/li>\n\n\n\n<li>Total starting combinations: <strong>1326<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">With this knowledge, you\u2019ll stop thinking \u201cmaybe they have AA, maybe not\u201d and start thinking \u201chow likely is AA compared to other hands in their range?\u201d And that\u2019s real poker thinking.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>You\u2019ve probably heard the word \u201ccombinatorics,\u201d but never quite dug into what it actually means. It\u2019s one of those fundamental concepts that sounds intimidating at first\u2014but is actually very simple. No complicated formulas. Just three numbers to remember and an understanding of how to use them. After reading this article, you\u2019ll start thinking about your &hellip; <a href=\"https:\/\/freebetrange.com\/academy\/poker-combinatorics-explained-what-it-is-and-how-to-count-combos\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Combinatorics in Poker: What It Is and How to Count Combos<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":361,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"fbr_academy_topic":"basics","footnotes":""},"class_list":["post-178","page","type-page","status-publish","has-post-thumbnail","hentry"],"translation":{"provider":"WPGlobus","version":"3.0.2","language":"en","enabled_languages":["en","es","de","fr","ru","pt","ja"],"languages":{"en":{"title":true,"content":true,"excerpt":false},"es":{"title":true,"content":true,"excerpt":false},"de":{"title":true,"content":true,"excerpt":false},"fr":{"title":true,"content":true,"excerpt":false},"ru":{"title":true,"content":true,"excerpt":false},"pt":{"title":true,"content":true,"excerpt":false},"ja":{"title":true,"content":true,"excerpt":false}}},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v24.9 - 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