https://apds.ircam.fr/api.php?action=feedcontributions&feedformat=atom&user=42025583562077 2026-04-09T11:59:01Z Contributions de l’utilisateur MediaWiki 1.30.0 https://apds.ircam.fr/index.php?title=Implied_Probability_And_Overround_In_Betting_Markets&diff=372 2026-03-30T08:11:32Z

<p>42025583562077 : Page créée avec « &lt;br&gt;&lt;br&gt;Mathematical Expectation in Gambling&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Mathematical expectation, or expected value (EV), is one of the fundamental concepts in probability theory, wid... »</p> <hr /> <div>&lt;br&gt;&lt;br&gt;Mathematical Expectation in Gambling&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Mathematical expectation, or expected value (EV), is one of the fundamental concepts in probability theory, widely applied in the analysis of gambling games. The expected value of a bet represents the average amount a player can expect to win or lose per unit wagered over a large number of repetitions.&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;In casino games, the expected value is almost always negative for the player, which reflects the built-in house edge. For example, in European roulette, a straight-up bet on a single number pays 35:1, but the actual probability of winning is 1/37 (approximately 2.7%). This creates a house edge of about 2.7%, meaning the expected value of every €1 wagered is approximately −€0.027.&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Understanding expected value allows players to compare different games and bet types objectively. A blackjack player using basic strategy faces a house edge of roughly 0.5%, while certain side bets in the same game may carry edges exceeding 10%. Poker differs from most casino games because players compete against each other rather than the house, making EV calculations dependent on opponent behavior and strategic decisions.&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;The Kelly Criterion, developed by John L. Kelly Jr. in 1956, extends the concept of expected value into bankroll management by determining the optimal fraction of one's bankroll to wager when the bettor believes they have an edge. Various online tools, such as EV calculators and Kelly Criterion calculators available at [https://gamblingcalc.com/ GamblingCalc.com], allow users to compute these values for different game scenarios and betting structures.&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Expected value analysis is also central to advantage play techniques, including card counting in blackjack and identifying mispriced lines in sports betting markets.&lt;br&gt;</div>

42025583562077 https://apds.ircam.fr/index.php?title=Utilisateur:42025583562077&diff=371 2026-03-30T08:11:27Z

<p>42025583562077 : Page créée avec « &lt;br&gt;&lt;br&gt;Variance and Volatility in Gambling&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Variance is a statistical measure of how widely individual outcomes deviate from the expected value. In gambling... »</p> <hr /> <div>&lt;br&gt;&lt;br&gt;Variance and Volatility in Gambling&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Variance is a statistical measure of how widely individual outcomes deviate from the expected value. In gambling, it determines the magnitude of short-term swings a player experiences, even when the long-term mathematical expectation remains constant.&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Two casino games can share the same house edge yet produce vastly different player experiences due to variance. A low-volatility slot machine with a 96% RTP might deliver frequent small payouts, keeping the player's balance relatively stable across a session. A high-volatility slot with the same RTP concentrates its returns into rare large payouts, meaning most sessions end in loss while occasional sessions produce outsized wins. The RTP is identical in both cases; only the distribution of outcomes differs.&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;In poker, variance manifests as extended winning and losing streaks that can span thousands of hands. A skilled cash game player with a win rate of 5 big blinds per 100 hands might experience a downswing of 30 or more buy-ins that lasts tens of thousands of hands — a statistically normal occurrence that feels devastating in practice. Understanding this distinction between short-term results and long-term expectation is essential for maintaining discipline and proper bankroll sizing.&lt;br&gt;&lt;br&gt;&lt;br&gt;&lt;br&gt;Standard deviation, expressed in units relevant to the game, quantifies volatility numerically. For slot machines, this is often measured per spin relative to the bet size. For poker, it is measured in big blinds per 100 hands. Players can use [https://gamblingcalc.com/ [https://gamblingcalc.com/ session simulation tools]] to model likely outcome distributions over a chosen number of sessions, helping to set realistic expectations about the range of results they may encounter.&lt;br&gt;</div>

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