## 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...

## Suited Connectors Open Ended Straight Draw

For this calculation we will consider suited connectors from 45 through TJ. With 7 8 in the hole there are 3 2-card combinations that can appear on the Flop to make a Straight draw From each of these 2-card combinations there are 16 possible combinations. Therefore, there are 48 possible 2-card combinations that can be part of the Flop that will make an open ended Straight draw. This also includes the possibility that the Flop will pair either a hole card or a board card and that the open ended...

## Royal Cards Royal 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...

## Pocket JJ or Better

For JJ through AA there are 24 6 4 possible pair combinations from 1,326 total possible 2-card combinations Possible Pairs JJ or Better WILLs 24 Total Possibilities 1,326 - WILLs 24 WILLNOTs 1,302 WILLNOTs 1,302 WILLs 24 1,302 24 Reduce 1,302 24 24 24 54.25 1 The probability of a pair of Jacks or better in the hole is WILLs On average you will be dealt Pocket Jacks or better once in 55.25 hands or roughly 2 of the time.

## Pocket Pair Quads

To flop Quads with a Pair in the hole, 2 of the three Flop cards must be of the same rank as the Pocket Pair and the third card can be any of the remaining 48 unseen cards. With only 1 2-card combination for the first two cards and 48 possibilities for the third card, the number of possible 3-card Flops that WILL make Quads is We now have all the numbers needed to calculate the odds of flopping 4 of a kind with a Pair in the hole Odds of Flopping Quads with a Pocket Pair WILLNOTs WILLs 19,552...

## 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

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