M-ratio

In no-limit or pot-limit poker, a player's M-ratio (also called "M number", "M factor"PokerGreed.com: Understand what hands to play in a tournament [http://www.pokergreed.com/articles/understand_what_hands_to_play_in_a_tournament.html] . Accessed 2008-03-25] 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 calculated 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:

:$M\; =\; frac\{2300\}\{50\; +\; 100\; +\; (10\; imes\; 8)\}\; =\; frac\{2300\}\{230\}\; =\; 10$

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", [ [http://www.blindbetpoker.com/books/harrington-holdem-2.html Harrington on Holdem: The Endgame - Poker Book Reviews ] ] defining several "zones" in which the M-ratio may fall: [ [http://www.pokerlistings.com/tournament-nolimit-holdem-harringtons-zone-system-5475 Tournament No-Limit Hold'em: Harrington's Zone System - Poker Strategy - PokerListings.com ] ]

Effective M

Harrington further develops the concept to account for shortening tables, as is seen at the closing stages of multi-table tournaments. The M-ratio is simply multiplied by the percentage of players remaining at the table, assuming a ten-player table to be "full".

:$M\_\{mbox\{Effective\; =\; M\; imes\; left(\; frac\{mbox\{Players\{10\}\; ight)$

Therefore, for a player with an "simple M ratio" of 9 at a five player table, the effective M is 4.5:

:$M\_\{mbox\{Effective\; =\; 9\; imes\; left(\; frac\{5\}\{10\}\; ight)\; =\; 4.5$

This means that although the player's simple M value places him in the orange zone, his effective M dictates a shift in playing style appropriate for the red zone. In essence, ten times the effective M denotes the expected number of hands a player can let pass before running out of chips.

References