Video Poker Glossary: Expectation

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Video Poker Glossary

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Often used in place of the mean or expected value, especially as ""The Expectation"
Involving the mathematical operation equivalent to averaging over some quantity of a distribution, random process or data set. If the quantity is the value itself, the expectation is the mean. If the quantity is the value minus the mean squared, the expectation is the variance.

The first moment of a random process, also known as it's mean or average value, and often given the symbol &micron;. In gambling, the Expected Value can be computed for a game itself (example: JOB video poker has an Expected Value of 99.54% when played with a Max-EV strategy) or a particular instance (example: in PKM video poker, the dealt hand with the highest Expected Value is trips) or the entire playing situation (by including the value of cash back and comps, if any). For video poker, Expected Value is usually expressed in percentage units, whereas a game that is exactly break even has an Expected Value of 100%, and a positive game has an Expected Value of greater than 100%. However, other units may be used, including fractional units, or real currency. Expected Value is generally used interchangeably with Expected Return, Return, and sometimes Expectation and long-term return.

Kelly Betting

a (money management) strategy that sets the wager amount for optimal bankroll growth. Under Kelly Betting, the bet size is chosen based on the game's return and current bankroll size. For video poker, bet sizes are limited to certain common denominations. For that, and other reasons, strict Kelly Betting is not practical with video poker. On the other hand, Kelly Betting can be used to estimate the bankroll requirements for a given positive expectation game or playing situation with a fixed bet size. Kelly Betting does not elucidate the Risk of Ruin, however.

Negative expectation game

A game in which the return (expectation) is less then 100%. Mathematically, if the return is expressed as a fraction, the game has a negative expectation if EV - 1 < 0.

Penalty card

A card, that when discarded from a dealt video poker hand, has a negative effect on the overall expectation of the draw. Achieving the maximum return for most video poker games involves situations (dealt hands) in which one or more Penalty cards can matter.

Positive expectation game

A game in which the return (expectation) is greater then 100%. Mathematically, if the return is expressed as a fraction, the game has a positive expectation if EV - 1 > 0.

Risk of Ruin

The probability that, given a certain bankroll, a gambler will be ruined. For video poker, the Risk of Ruin is generally computed for an infinite number of hands, since the computation easier, though it can also be computed for any number of hands. However, if the number of hands is not specified, it is assumed to be infinite. The (infinite run) Risk of Ruin is always greater then zero for video poker, including positive games, since the variance is always non-zero. For all negative expectation situations, the Risk of Ruin is always 100%. That is, regardless of the bankroll, a gambler who plays a bad game will eventually go broke. The Risk of Ruin decreases as the size of the bankroll in betting units increases. Hence, decreasing game denomination (unit or wager) at a fixed bankroll decreases Risk of Ruin.
See also: Survivability.

Variance

A measure of the variability of a data set or random process. The variance describes how far values lie from the mean (the first moment of the distribution), and is used, along with the mean, and higher moments, to characterize a probability distribution. The Variance is defined as the expectation of (X-µ)^2 where X is value and µ is the expected value or mean. While the combination of the variance and the mean fully describe a normal distribution (gaussian) they are not sufficient to describe the strongly non-normal distribution for video poker. Nonetheless, variance is an important factor to consider and understand in many aspects of video poker. For video poker, typical values of the Variance range roughly from 15 (PKM) to 100 (DBDJ) and is in units of the bet squared.
See also: Standard Deviation, Expectation, Expected Value, PKM, DBDJ.

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