Advanced Poker Concepts

Effective Odds : The ratio of the total amount of money you expect to win if you make your hand to the total amount of bets you will have to call to continue from the present round of betting to the end of the hand. Most generally relevant to a Fixed Limit (FL) betting format.

Eight or better : A common qualifier in High-low split games that use Ace-5 ranking. Only hands where the highest card is an eight or smaller can win the low portion of the pot.

Equity : One's mathematical expected value from the current deal, calculated by multiplying the amount of money in the pot by one's probability of winning. For example, if the pot currently contains $100, and you estimate that you have a one in four chance of winning it, then your equity in the pot is $25. If a split is possible, the equity also includes the probability of winning a split times the size of that split; for example, if the pot has $100, and you have a 1/4 chance of winning and a 1/5 chance of taking a $50 split, your equity is $25 + $10 = $35.

Expectation - Expected Value – EV : The amount you can expect to gain or lose on average for a certain act. Expectation can be applied to a bet, a hand, an hourly rate, a career, etc. For instance, suppose you put $10 into a $50 pot to draw at a hand that you will make 25% of the time, and it will win every time you make it. Three out of four times, you do not make your draw, and lose $10 each time for a total of $30. The fourth time, you will make your draw, winning $50. Your total gain over those four average hands is $50-$30 = $20, an average of $5 per hand. Thus calling the $10 has a positive expectation of $5. Expected Value is often shortened to "EV".

Implied odds : Are calculated the same way as pot odds, but take into consideration estimated future betting. Implied odds are calculated in situations where the player expects to fold in the following round if the draw is missed, thereby losing no additional bets, but expects to gain additional bets when the draw is made. Since the player expects to always gain additional bets in later rounds when the draw is made, and never lose any additional bets when the draw is missed, the extra bets that the player expects to gain, excluding his own, can fairly be added to the current size of the pot. This adjusted pot value is known as the implied pot.

Example:

On the second-to-last betting round, Alice's hand is certainly behind and she faces a $1 call to win a $10 pot against a single opponent. There are four cards remaining in the deck that make her hand a certain winner. Her odds of drawing to one of those cards is 10.5:1 (8.7 percent). Since the pot lays 10:1, Alice will lose money by calling if there is no future betting. Since Alice expects to always make an additional $2 when she makes her draw, and always fold when she misses her draw (lose no additional bets), her implied pot odds are 11:1 ($10 plus the additional $1 bet, to her $1 call). This call now has a positive expectation.

M-ratio : In no-limit or pot-limit poker, a player's M-ratio (also called "M number", "M factor"or just "M") is a measure of the health of his chip stack as a function of the cost to play each round. In simple terms, a player can sit passively in the game, making only compulsory bets, for M laps of the dealer button before running out of chips. A high M means the player can afford to wait a number of rounds before making a move. The concept applies primarily in tournament poker; in a cash game, a player can in principle manipulate his M at will, simply by purchasing more chips.
A player with a low M must act soon or be weakened by the inability to force other players to fold with aggressive raises.
The term was invented and named by Paul Magriel, although the concept was described much earlier by Doyle Brunson in Super/System. Calculation

The M-ratio is caluclated by the formula:
"M = \frac{\mbox{stack}}{\mbox{small blind} + \mbox{big blind} + \mbox{total antes}}""

For example, a player in an eight-player game with blinds of $50/$100, an ante of $10, and a stack of $2,300 has an M-ratio of 10:
"M = \frac{2300}{50 + 100 + (10 \times 8)} = 10"

That is, if the player only makes the compulsory bets, he will be "blinded out" of the game in 10 rounds, or 80 hands.
Dan Harrington studied the concept in great detail in Harrington on Holdem: Volume II The Endgame, defining several "zones" in which the M-ratio may fall: