#### Henri Poincaré, Quanta hypothesis: Thermodynamics and probability

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Let us go back to the kinetic theory of gases; the gases are formed of molecules which circulate in all directions with great velocities; their trajectories would be rectilinear if from time to time they did not collide each other, … Read More

#### Probability in games of chance

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One of the player’s goal is to find an optimal method to win the game. We say that the players play a martingale. It should not be confused with the martingale probability which is a stochastic process such that its … Read More

#### Chen Point Count

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There is a way to compute the Skalansky Malmuth table for those people who have trouble memorizing. The results are almost identical to those generated using the Chen Point Count.[1] To compute the point count the following formula should apply: … Read More

#### Runner-runner outs in Texas hold ’em

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Some outs for a hand require drawing an out on both the turn and the river—making two consecutive outs is called a runner-runner. Examples would be needing two cards to make a straight, flush, or three or four of a … Read More

#### Example of drawing outs

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The unseen cards principle states that to calculate the probability (from the point of view of a player about to act) that the next card dealt will be among a certain set, he must divide the number of cards in … Read More

#### Availability error

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Availability error, related to the gambler’s fallacy, is the distortion of one’s perceptions of reality due to the tendency to remember one alternative outcome of a situation much more easily than another. For example, if surrounded by slot machines people … Read More

#### Flopping overcards when holding a pocket pair

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It is useful to look at the chances different starting hands have of either improving on the flop, or of weakening on the flop. One interesting circumstance concerns pocket pairs. When holding a pocket pair, overcards (cards of higher rank … Read More

#### Probability of the dominated hands in Texas Hold’em

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When evaluating a hand before the flop, it’s useful to have some idea of how likely the hand is dominated. A dominated hand is a hand that is beaten by another hand (the dominant hand) and is extremely unlikely to … Read More

#### Lottery Mathematics – Odds of getting other scores in choosing 6 from 49

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One must calculate the total number of lottery combinations (c(49,6) = 13,983,816, as explained in the section above), and divide it by the number of those combinations which give the desired result – which equates to the number of ways … Read More

#### Probability for starting hands in Texas Hold ’em

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The probability of being dealt various starting hands can be explicitly calculated. In Texas Hold ’em, a player is dealt two down (or hole) cards. The first card can be any one of 52 playing cards in the deck and … Read More

#### Non-examples for gambler’s fallacy

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There are many scenarios where the gambler’s fallacy might superficially seem to apply, where it in fact does not. When the probability of different events is not independent, the probability of future events can change based on the outcome of … Read More

#### Boxcars

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Boxcars is the outcome of rolling the dice in a game of craps and getting a 6 on each die. The pair of 6 pips resembles a pair of box cars on a freight train. In modern parlance, it refers … Read More

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