Expectation

Expectation is the return that can be anticipated from any given wager or proposition after enough bets have been made to normalize the result. All experienced poker players are intimately acquainted with the concepts of both positive and negative fluctuation. Results from any given proposition may vary greatly from a correctly calculated expectation in the short term, but will completely normalize themselves after a sufficient sampling. We know that the odds against drawing an Ace from the top...

Practica Poker Math

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Royal Cards Royal Flush Draw

Odds Flopping Flush Draw

With 2 cards to a Royal in the hole there are only 3 2-card combinations that can appear on the Flop that will make a Royal Flush draw For example, with JVQV in the hole these are the only 3 2-card combinations that can come on the Flop to yield a Royal Flush draw Minus the 2 hole cards and the 2 cards that make the draw, and minus the 1 card that would complete the Royal Flush, there are 47 unseen cards. With the possibility that the Flop will pair either a hole card or a board card, the...

Unpaired Hole Cards Runner Runner Pair

With 2 unpaired cards in the hole there are 6 cards among the remaining 47 that will pair either card. For this calculation we will multiply the probability that the first card will pair either card by the probability that the second card will pair the remaining unpaired card. That probability expressed as a decimal ratio to 1 is With 6 cards of a total of 47 that will pair either hole card, the probability that the first card will pair either hole card is With the first card paired there are 3...

Open Backdoor Straight Flush Runner Runner Straight Flush

Backdoor Straight Flush

With 3 suited and connected cards above 2 and below K in rank, there are 3 2-card combinations that will make a Straight Flush Thus of a possible 1,081 2-card combinations only 3 WILL make the Straight Flush. Knowing that with only 3 of over 1,000 possibilities you can approximate that the odds will be just over 300 to 1 Total Possibilities 1,081 - WILLs 3 WILLNOTs 1,078 Odds of a RR Straight WILLNOTs WILLs 1,078 3 Reduce 1,078 3 3 3 359.3 1