{"id":449,"date":"2026-03-26T21:00:33","date_gmt":"2026-03-26T21:00:33","guid":{"rendered":"https:\/\/winneronline.net\/au\/?page_id=449"},"modified":"2026-09-30T06:19:02","modified_gmt":"2026-09-30T06:19:02","slug":"craps-odds-probability","status":"publish","type":"page","link":"https:\/\/winneronline.net\/ca\/casino-games\/craps\/craps-bets-odds\/craps-odds-probability\/","title":{"rendered":"Craps Odds &amp; Probability"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">Craps Odds and Probability: The 36 Dice Combinations<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Two fair independent six-sided dice have 36 equally likely ordered outcomes. Totals are not equally likely: 7 has six combinations, while 2 and 12 have one each. This guide distinguishes a one-roll probability from a multi-roll settlement and a profit payout.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">One-Roll Combination Table<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The last column expresses a probability as \u201c1 in X,\u201d not odds against. For example, 1 in 36 corresponds to 35:1 odds against, not 36:1. Percentages are rounded.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><td><strong>Total<\/strong><\/td><td><strong>Combinations<\/strong><\/td><td><strong>Probability (%)<\/strong><\/td><td><strong>Probability expressed as 1 in X<\/strong><\/td><\/tr><\/thead><tbody><tr><td><strong>2<\/strong><\/td><td>1-1<\/td><td>2.78%<\/td><td>1 in 36<\/td><\/tr><tr><td><strong>3<\/strong><\/td><td>1-2, 2-1<\/td><td>5.56%<\/td><td>1 in 18<\/td><\/tr><tr><td><strong>4<\/strong><\/td><td>1-3, 2-2, 3-1<\/td><td>8.33%<\/td><td>1 in 12<\/td><\/tr><tr><td><strong>5<\/strong><\/td><td>1-4, 2-3, 3-2, 4-1<\/td><td>11.11%<\/td><td>1 in 9<\/td><\/tr><tr><td><strong>6<\/strong><\/td><td>1-5, 2-4, 3-3, 4-2, 5-1<\/td><td>13.89%<\/td><td>1 in 7.2<\/td><\/tr><tr><td><strong>7<\/strong><\/td><td>1-6, 2-5, 3-4, 4-3, 5-2, 6-1<\/td><td>16.67%<\/td><td>1 in 6<\/td><\/tr><tr><td><strong>8<\/strong><\/td><td>2-6, 3-5, 4-4, 5-3, 6-2<\/td><td>13.89%<\/td><td>1 in 7.2<\/td><\/tr><tr><td><strong>9<\/strong><\/td><td>3-6, 4-5, 5-4, 6-3<\/td><td>11.11%<\/td><td>1 in 9<\/td><\/tr><tr><td><strong>10<\/strong><\/td><td>4-6, 5-5, 6-4<\/td><td>8.33%<\/td><td>1 in 12<\/td><\/tr><tr><td><strong>11<\/strong><\/td><td>5-6, 6-5<\/td><td>5.56%<\/td><td>1 in 18<\/td><\/tr><tr><td><strong>12<\/strong><\/td><td>6-6<\/td><td>2.78%<\/td><td>1 in 36<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">The Distribution Is Triangular<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Combination counts rise from one at total 2 to six at total 7, then fall symmetrically to one at 12. This is a discrete triangular distribution, not a bell-shaped normal distribution.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">A Point Before Seven Is a Different Event<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">For a point of 4, three combinations produce 4 and six produce 7. Other totals leave the wager unresolved. The probability that 4 appears before 7 is therefore 3\/(3+6) = 1\/3. That is different from the one-roll probability of 4, which is 3\/36.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The corresponding before-seven probabilities are 4\/10 = 40% for 5 or 9, and 5\/11 \u2248 45.45% for 6 or 8. These describe a race until one of the two relevant totals occurs, not the chance of winning on the immediately next roll.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">True Odds and Paid Odds<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A one-unit wager with probability 1\/3 needs a 2:1 profit payout to have zero expected gain or loss: a win returns three units including the stake. If the payout is instead 9:5 profit, expected loss is 1\/15, approximately 6.67%, per resolved stake.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The <a href=\"https:\/\/winneronline.net\/ca\/casino-games\/craps\/craps-bets-odds\/taking-laying-odds\/\">taking and laying odds guide<\/a> explains true-odds components. Those components can still lose and require underlying wagers with their own negative expectation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">House Edge Requires a Defined Bet<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Conventional Pass\/Come has approximately 1.41% house edge per initial stake. Don\u2019t Pass\/Don\u2019t Come with bar 12 is approximately 1.36% including initial pushes. Place-bet percentages are usually quoted per resolved wager, while one-roll bets settle immediately. Mixing denominators can make a comparison misleading.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">At 4:1 profit, Any Seven returns five stakes on six of the 36 outcomes: expected return is 30\/36 and house edge is 16.67%. A Field payout change on 2 or 12 changes that wager\u2019s calculation; no single percentage covers every Field paytable.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Independent Rolls and Session Results<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A previous 7, a long point sequence or a \u201ccold\u201d table does not change the next roll\u2019s probabilities under the independent-dice model. Expected return is not a maximum loss or a guarantee that a balance survives a chosen number of rolls.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">See <a href=\"https:\/\/winneronline.net\/ca\/casino-games\/craps\/craps-bets-odds\/\">bets and payout assumptions<\/a>, <a href=\"https:\/\/winneronline.net\/ca\/casino-games\/craps\/craps-bets-odds\/field-bets\/\">Field calculations<\/a> and <a href=\"https:\/\/winneronline.net\/ca\/casino-games\/craps\/craps-bets-odds\/proposition-bets\/\">proposition payout notation<\/a>. WinnerOnline provides information and does not host games.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Related reading: <a href=\"https:\/\/winneronline.net\/ca\/casino-games\/sic-bo\/sic-bo-odds-strategy\/sic-bo-odds-payouts\/\">Sic Bo Odds and Payouts: Probabilities Explained<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Craps Odds and Probability: The 36 Dice Combinations Two fair independent six-sided dice have 36 equally likely ordered outcomes. Totals are not equally likely: 7 has six combinations, while 2 and 12 have one each. This guide distinguishes a one-roll probability from a multi-roll settlement and a profit payout. One-Roll Combination Table The last column [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":435,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-without-title.php","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-449","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Craps Probability: Dice Outcomes and House Edge<\/title>\n<meta name=\"description\" content=\"An explanation of the 36 ordered outcomes of two dice, roll totals, true odds and house edge. 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