{"id":3399,"date":"2024-02-11T18:41:56","date_gmt":"2024-02-11T18:41:56","guid":{"rendered":"https:\/\/crashxbet.com\/?p=3399"},"modified":"2026-01-08T23:43:47","modified_gmt":"2026-01-08T23:43:47","slug":"kelly-criterion-crash-gambling","status":"publish","type":"post","link":"https:\/\/crashxbet.com\/pl\/kelly-criterion-crash-gambling\/","title":{"rendered":"The Kelly Criterion in Crash Gambling"},"content":{"rendered":"<p class=\"wp-block-paragraph\">Kryterium Kelly&#039;ego to sprytny spos\u00f3b na podj\u0119cie decyzji, ile pieni\u0119dzy postawi\u0107. Pomaga obstawi\u0107 odpowiedni\u0105 kwot\u0119, aby stale zwi\u0119ksza\u0107 swoje pieni\u0105dze bez ryzyka utraty wszystkiego. Potraktuj to jako przewodnik po m\u0105drym obstawianiu zak\u0142ad\u00f3w. Jest bardzo popularny w\u015br\u00f3d lepszych i inwestor\u00f3w ze wzgl\u0119du na utrzymywanie ryzyka na niskim poziomie.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Podstawowy wz\u00f3r kryterium Kelly&#039;ego to:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud835\udc53\u2217=(\ud835\udc4f*\ud835\udc5d\u2212\ud835\udc5e)\/\ud835\udc4f<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Gdzie:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud835\udc53\u2217 to u\u0142amek bankrolla, kt\u00f3ry nale\u017cy postawi\u0107;<\/li>\n\n\n\n<li>\ud835\udc4f to kurs netto otrzymany na zak\u0142ad;<\/li>\n\n\n\n<li>\ud835\udc5d to prawdopodobie\u0144stwo wygranej;<\/li>\n\n\n\n<li>\ud835\udc5e to prawdopodobie\u0144stwo przegranej, kt\u00f3re wynosi 1\u2212\ud835\udc5d.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-interpretation\">Interpretation<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud835\udc53\u2217: Reprezentuje optymaln\u0105 cz\u0119\u015b\u0107 Twojego bankrolla, kt\u00f3r\u0105 powiniene\u015b obstawi\u0107, aby zmaksymalizowa\u0107 oczekiwany wzrost. Je\u015bli na przyk\u0142ad wynik wynosi 0,25, sugeruje to, \u017ce powiniene\u015b postawi\u0107 25% swojego bankrolla.<\/li>\n\n\n\n<li><strong>\ud835\udc4f<\/strong>: Mno\u017cnik powi\u0105zany z zak\u0142adem minus 1. Na przyk\u0142ad, je\u015bli mo\u017cesz podwoi\u0107 swoje pieni\u0105dze w przypadku wygranej (2 $ zwrotu za ka\u017cdego 1 $ zak\u0142adu, \u0142\u0105cznie z pierwotnym zak\u0142adem), \ud835\udc4f wyniesie 1.<\/li>\n\n\n\n<li><strong>\ud835\udc5d<\/strong>: Twoje oszacowane prawdopodobie\u0144stwo wygranej zak\u0142adu. Musi to by\u0107 warto\u015b\u0107 z zakresu od 0 do 1, gdzie 0,5 oznacza 50% szans na wygran\u0105.<\/li>\n\n\n\n<li><strong>\ud835\udc5e<\/strong>: Prawdopodobie\u0144stwo przegranej zak\u0142adu, obliczane jako 1\u2212\ud835\udc5d.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Kelly Bet Calculator<\/h2>\n\n\n\n<div style=\"max-width: 400px; margin-left: 0;\">\n        <label for=\"probability\">Probability of a Win (0 to 1):<\/label>\n        <input type=\"number\" id=\"probability\" placeholder=\"e.g., 0.6\" step=\"0.01\" min=\"0\" max=\"1\" style=\"width: 100%; margin: 5px 0\">\n\n        <label for=\"proportion\">Proportion of the Bet Gained with a Win:<\/label>\n        <input type=\"number\" id=\"proportion\" placeholder=\"e.g., 2\" step=\"0.01\" min=\"0\" style=\"width: 100%; margin: 5px 0\">\n        <div style=\"margin: 3px 0 10px 0; font-size: 12px; line-height: 1.2;\">\n            E.g., if betting $100 on a 2-to-1 odds bet (upon win you are returned $300, winning you $200), then b=$200\/$100=2.\n        <\/div>\n\n        <button id=\"calculate\">Calculate Bet Size<\/button>\n\n        <div id=\"output\" class=\"output\" style=\"margin: 5px 0\"><\/div>\n    <\/div>\n\n    <script>\n        (function() {\n            document.getElementById('calculate').addEventListener('click', () => {\n                const probability = parseFloat(document.getElementById('probability').value);\n                const proportion = parseFloat(document.getElementById('proportion').value);\n\n                const output = document.getElementById('output');\n\n                if (isNaN(probability) || isNaN(proportion) || probability < 0 || probability > 1 || proportion <= 0) {\n                    output.textContent = 'Please enter valid inputs.';\n                    return;\n                }\n\n                \/\/ Kelly Criterion formula: f* = p - (1 - p) \/ b\n                const optimalFraction = probability - ((1 - probability) \/ proportion);\n\n                if (optimalFraction <= 0) {\n                    output.textContent = 'The Kelly Criterion suggests not to bet in this scenario.';\n                } else {\n                    output.textContent = `Suggested bet size (as a fraction of bankroll): ${(optimalFraction * 100).toFixed(2)}%`;\n                }\n            });    \n        })()\n        \n    <\/script>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-how-to-use-it\">How to Use It<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Uzyskaj dost\u0119p do swoich ostatnich 50 do 100 gier<\/strong>: Bardzo <span data-no-translation=\"\" class=\"cbw-no-translate\">crash<\/span> gry maj\u0105 histori\u0119. Ponadto, <a href=\"https:\/\/bcgame-project.github.io\/verify\/crash.html?hash=9455412a5e4b51b986ba71ab08eddee80678c905ecefc8d0051c79493f0037b2\" target=\"_blank\" rel=\"noreferrer noopener\">udowodnione, \u017ce sprawiedliwe<\/a> games give you full access to the game history and results. For example, third-party scripts are used to verify game on <a href=\"https:\/\/nanogamesio.github.io\/verify\/crash.html?hash=eedf311a3fdfb41cd4259aabf499c35c6131011b9e64117be99c46462d906756\" target=\"_blank\" rel=\"noreferrer noopener\"><span data-no-translation=\"\" class=\"cbw-no-translate\">NanoGames<\/span><\/a>.<\/li>\n\n\n\n<li><strong>Oblicz swoj\u0105 przewag\u0119<\/strong>: Your \"edge\" is \ud835\udc4f*\ud835\udc5d\u2212\ud835\udc5e. If this value is positive, you have an advantage over the house or the market.<\/li>\n\n\n\n<li><strong>Okre\u015bl wielko\u015b\u0107 zak\u0142adu<\/strong>: Formu\u0142a wskazuje optymaln\u0105 cz\u0119\u015b\u0107 Twojego bankrolla, kt\u00f3r\u0105 nale\u017cy obstawi\u0107, aby zmaksymalizowa\u0107 wzrost i zminimalizowa\u0107 ryzyko.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Applying this strategy manually requires diligence in tracking and calculating. But can offer insights into the game's patterns and your betting strategy's effectiveness.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-example\">Przyk\u0142ad:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">If you're betting on a coin toss where you win double your bet for guessing right, and you somehow know the coin has a 51% chance of landing heads (which you bet on):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud835\udc4f=1 (poniewa\u017c podwajasz swoje pieni\u0105dze w przypadku wygranej)<\/li>\n\n\n\n<li>\ud835\udc5d=0,51<\/li>\n\n\n\n<li>\ud835\udc5e=0,49<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Pod\u0142\u0105czenie ich do wzoru Kelly&#039;ego daje:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud835\udc53\u2217=(1)(0,51)\u22120,49=0,02<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Wynik ten sugeruje, \u017ce powiniene\u015b obstawia\u0107 2% swojego bankrolla przy ka\u017cdym rzucie, aby zmaksymalizowa\u0107 wzrost swojego bankrolla w czasie, minimalizuj\u0105c jednocze\u015bnie ryzyko.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-important-considerations\">Wa\u017cne uwagi:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Kryterium Kelly&#039;ego zak\u0142ada, \u017ce \u200b\u200bmo\u017cesz dok\u0142adnie oszacowa\u0107 prawdopodobie\u0144stwa (\ud835\udc5d i \ud835\udc5e). Przeszacowanie mo\u017ce zwi\u0119kszy\u0107 ryzyko du\u017cych strat.<\/li>\n\n\n\n<li>It's a long-term strategy. Short-term volatility can still result in significant drawdowns.<\/li>\n\n\n\n<li>Obstawianie wi\u0119kszych zak\u0142ad\u00f3w, ni\u017c sugeruje kryterium Kelly&#039;ego, zwi\u0119ksza ryzyko utraty wi\u0119kszej cz\u0119\u015bci bankrolla. Obstawianie mniejszych zak\u0142ad\u00f3w zmniejsza ryzyko, ale tak\u017ce spowalnia wzrost bankrolla.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-script-for-bc-game-s-crash\">Skrypt dla gry Crash<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Zbieraj\u0105c dane z 50 gier, mo\u017cesz obliczy\u0107 dok\u0142adniejsze oszacowanie \ud835\udc5d (prawdopodobie\u0144stwo wygranej) i \ud835\udc5e (prawdopodobie\u0144stwo przegranej, kt\u00f3re wynosi 1\u2212\ud835\udc5d). Dane te umo\u017cliwiaj\u0105 udoskonalenie strategii obstawiania w oparciu o wyniki historyczne, potencjalnie poprawiaj\u0105c precyzj\u0119 zak\u0142ad\u00f3w i optymalizuj\u0105c zarz\u0105dzanie bankrollem.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Krok 1: Zbierz dane gry<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Zacz\u0105\u0142by\u015b od zebrania wynik\u00f3w z ostatnich 50 gier (parametr konfigurowalny). Ta faza gromadzenia danych obejmuje \u015bledzenie, czy ka\u017cda gra osi\u0105ga docelowy mno\u017cnik przed awari\u0105.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Krok 2: Oblicz prawdopodobie\u0144stwa<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Gdy ju\u017c b\u0119dziesz mie\u0107 dane dotycz\u0105ce gry, oblicz prawdopodobie\u0144stwo wygranej (\ud835\udc5d), dziel\u0105c liczb\u0119 gier, w kt\u00f3rych osi\u0105gni\u0119to lub przekroczy\u0142e\u015b docelowy mno\u017cnik, przez ca\u0142kowit\u0105 liczb\u0119 zaobserwowanych gier (w tym przypadku 50).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Krok 3: Zastosuj kryterium Kelly&#039;ego<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Maj\u0105c \ud835\udc5d obliczone na podstawie danych i wiedz\u0105c, \u017ce \ud835\udc5e=1\u2212\ud835\udc5d, zastosuj wz\u00f3r na kryterium Kelly\u2019ego, aby okre\u015bli\u0107 optymaln\u0105 cz\u0119\u015b\u0107 swojego bankrolla do obstawiania.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Script for Crash game on Nanogames<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">We collect game data during the game session. This approach takes some time but is more suitable if you're confident in the game's stability and wish to maximize the data available for analysis.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\ud83d\udd17 <a href=\"\/go\/download-script\/\" target=\"_blank\" rel=\"noreferrer noopener\">Pobierz skrypt<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aby u\u017cy\u0107 <span data-no-translation=\"\" class=\"cbw-no-translate\">Crash<\/span> w\u0142\u0105czony skrypt gry <a href=\"\/go\/nanogames\/\" target=\"_blank\" rel=\"noreferrer noopener nofollow\">Nanogames<\/a>wykonaj nast\u0119puj\u0105ce kroki:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Go to Advanced Betting Mode: In the Crash, switch to \u201cAdvanced\u201d to see different <span data-no-translation=\"\" class=\"cbw-no-translate\">crash<\/span> skrypty gier.<\/li>\n\n\n\n<li>Dodaj skrypt: Naci\u015bnij przycisk Dodaj skrypt, wpisz kod skryptu, od kt\u00f3rego chcesz rozpocz\u0105\u0107 automatyczne obstawianie, nadaj mu nazw\u0119 i naci\u015bnij przycisk Zapisz.<\/li>\n\n\n\n<li>Uruchom skrypt: W\u0142\u0105cz skrypt, aby automatycznie obstawia\u0107 i ewentualnie zwi\u0119ksza\u0107 swoj\u0105 kryptowalut\u0119.<\/li>\n<\/ol>\n\n\n\n<details>\n  <summary><span style=\"text-decoration-style: dashed; text-decoration-line: underline; cursor: pointer;\">Learn how to add and use scripts<\/span><\/summary>\n  <figure class=\"wp-block-image size-large\"><a href=\"\/go\/nanogames\/\"><img decoding=\"async\" src=\"https:\/\/crashxbet.com\/wp-content\/uploads\/2023\/11\/bcgame-script-screencast-original.gif\" alt=\"How to add and use scripts\" class=\"wp-image-1276\" data-no-translation=\"\"\/><\/a><\/figure>\n<\/details>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-fe48e5de wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"\/go\/nanogames\/\" style=\"background-color:#17a10d\" target=\"_blank\" rel=\"noreferrer noopener nofollow\">PLAY CRASH<\/a><\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Wa\u017cne uwagi:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Dok\u0142adno\u015b\u0107 \ud835\udc5d<\/strong>: Dok\u0142adno\u015b\u0107 prawdopodobie\u0144stwa wygranej (\ud835\udc5d) wp\u0142ywa bezpo\u015brednio na skuteczno\u015b\u0107 kryterium Kelly&#039;ego w optymalizacji wielko\u015bci zak\u0142adu. Upewnij si\u0119, \u017ce gromadzenie i analiza danych s\u0105 tak dok\u0142adne, jak to mo\u017cliwe.<\/li>\n\n\n\n<li><strong>Zmiana dynamiki<\/strong>: <span data-no-translation=\"\" class=\"cbw-no-translate\">crash<\/span> game's dynamics might change over time. Regularly update your data and recalibrate your strategy accordingly.<\/li>\n\n\n\n<li><strong>Zarz\u0105dzanie ryzykiem<\/strong>: The Kelly Criterion helps manage risk, but it's based on the accuracy of your inputs (\ud835\udc5d and \ud835\udc5e). Always be cautious and consider setting aside a portion of your bankroll that is not at risk.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-summary\">Streszczenie<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Podsumowuj\u0105c dyskusj\u0119 na temat stosowania kryterium Kelly&#039;ego i analizuj\u0105c histori\u0119 gier pod k\u0105tem zak\u0142ad\u00f3w w a <span data-no-translation=\"\" class=\"cbw-no-translate\">crash<\/span> game, the strategy indeed focuses on identifying situations where the probability of winning is deemed favorable based on historical data. By calculating the win probability (\ud835\udc5d) from recent game outcomes and applying the Kelly Criterion, the strategy aims to optimize bet sizes in scenarios where there's a perceived edge\u2014that is, where the chances of winning are higher relative to losses. Here's how it works:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Zrozumienie strategii<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Zbieraj dane historyczne<\/strong>: You accumulate outcomes from a certain number of recent games to analyze the game's behavior. This dataset helps you understand the frequency of winning versus losing at your target multiplier.<\/li>\n\n\n\n<li><strong>Oblicz prawdopodobie\u0144stwo wygranej (\ud835\udc5d)<\/strong>: Analizuj\u0105c zebrane dane, szacujesz prawdopodobie\u0144stwo, \u017ce gra osi\u0105gnie lub przekroczy docelowy mno\u017cnik. To prawdopodobie\u0144stwo wygranej ma kluczowe znaczenie dla ustalenia, czy masz przewag\u0119 w zak\u0142adach.<\/li>\n\n\n\n<li><strong>Zastosuj kryterium Kelly&#039;ego<\/strong>: Maj\u0105c prawdopodobie\u0144stwo wygranej (\ud835\udc5d), u\u017cywasz kryterium Kelly&#039;ego do obliczenia optymalnej cz\u0119\u015bci swojego bankrolla do obstawienia. Kalkulacja ta opiera si\u0119 na logice, \u017ce obstawianie powinno by\u0107 proporcjonalne do Twojej przewagi; wy\u017csze prawdopodobie\u0144stwo wygranej sugeruje wi\u0119kszy rozmiar zak\u0142adu, ale tylko do poziomu, kt\u00f3ry r\u00f3wnowa\u017cy wzrost z ryzykiem.<\/li>\n\n\n\n<li><strong>Poczekaj na pozytywn\u0105 okazj\u0119 do zak\u0142adu<\/strong>: Czekasz, a\u017c obliczone prawdopodobie\u0144stwo wygranej wska\u017ce dodatni\u0105 warto\u015b\u0107 oczekiwan\u0105 \u2014 to znaczy, kiedy liczba zwyci\u0119skich gier w Twoim zestawie danych sugeruje wi\u0119ksz\u0105 szans\u0119 na wygran\u0105 ni\u017c przegran\u0105 przy wybranym docelowym mno\u017cniku. Dopiero wtedy stawiasz zak\u0142ad, a wielko\u015b\u0107 tego zak\u0142adu jest optymalizowana zgodnie z kryterium Kelly&#039;ego, aby zmaksymalizowa\u0107 d\u0142ugoterminowy wzrost Twojego bankrolla przy jednoczesnej minimalizacji ryzyka.<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Kluczowa zaleta<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The primary advantage of this strategy is that it's data-driven and dynamic. It adapts to the current conditions of the game as reflected in the most recent outcomes. By focusing on situations where historical data indicates a higher probability of winning, you align your betting strategy with opportunities that have a statistical edge in your favor.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Wa\u017cne uwagi<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Znaczenie danych<\/strong>: Strategia ta zak\u0142ada, \u017ce \u200b\u200bhistoryczne wyniki gier s\u0105 istotnym predyktorem przysz\u0142ych wynik\u00f3w, co ma zastosowanie w grach o sp\u00f3jnej mechanice i prawdopodobie\u0144stwie.<\/li>\n\n\n\n<li><strong>Wielko\u015b\u0107 pr\u00f3bki i zmienno\u015b\u0107<\/strong>: Dok\u0142adno\u015b\u0107 oszacowania prawdopodobie\u0144stwa wygranej zale\u017cy od rozmiaru i zmienno\u015bci zbioru danych. Wi\u0119ksze zbiory danych mog\u0105 zapewni\u0107 bardziej wiarygodne szacunki, ale wymagaj\u0105 czasu na zebranie danych o grach i ostro\u017cne zarz\u0105dzanie w celu zapewnienia ich przydatno\u015bci.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Podsumowuj\u0105c, strategia ta wykorzystuje kryterium Kelly&#039;ego w po\u0142\u0105czeniu z analiz\u0105 danych historycznych z gier, aby zidentyfikowa\u0107 i wykorzysta\u0107 pozytywne mo\u017cliwo\u015bci obstawiania, maj\u0105c na celu zwi\u0119kszenie szansy na wygran\u0105 poprzez dokonywanie \u015bwiadomych i skalkulowanych zak\u0142ad\u00f3w.<\/p>","protected":false},"excerpt":{"rendered":"<p>The Kelly Criterion is a smart way to decide how much money to bet. It helps you bet just the right amount to grow your money steadily without the risk of losing it all. Think of it as your guide to betting wisely. It&#8217;s very popular among betters and investors for keeping risks low. The [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":5776,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[277],"class_list":["post-3399","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-guides-and-strategies","tag-crash-game-script"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The Kelly Criterion in Crash Gambling<\/title>\n<meta name=\"description\" content=\"Apply the Kelly Criterion with real game data for precise betting strategies in crash games and investment scenarios.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/crashxbet.com\/pl\/kelly-criterion-crash-gambling\/\" \/>\n<meta property=\"og:locale\" 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