Hurst exponent: Difference between revisions

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In [[betting (poker)|no-limit or pot-limit]] [[poker]], a player's '''M-ratio''' (also called "M number", "M factor"<ref name="pokergreed">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</ref> 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 high number of rounds before making a move. The concept applies primarily in [[poker tournament|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]].
==Calculation==
The M-ratio is calculated by the formula:
 
:<math>M = \frac{\mbox{stack}}{\mbox{small blind} + \mbox{big blind} + \mbox{total antes}}</math>  
 
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:
 
:<math>M = \frac{2300}{50 + 100 + (10 \times 8)} = \frac{2300}{230} = 10</math>
 
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'', <ref>[http://www.blindbetpoker.com/books/harrington-holdem-2.html Harrington on Holdem: The Endgame - Poker Book Reviews<!-- Bot generated title -->]</ref> defining several "zones" in which the M-ratio may fall:<ref>[http://www.pokerlistings.com/tournament-nolimit-holdem-harringtons-zone-system-5475 Tournament No-Limit Hold'em: Harrington's Zone System - Poker Strategy - PokerListings.com<!-- Bot generated title -->]</ref>
 
{| class="wikitable"
! M-ratio
! Zone name
! "Optimal" strategy
|-
| M ≥ 20
| Green zone
| Most desirable situation, freedom to play conservatively or aggressively as you choose<ref>''Harrington on Holdem'', Volume II, p129</ref>
|-
| {{nowrap|10 ≤ M < 20}}
| Yellow zone
| Must take more risks (see reference #3), hands containing small pairs and small suited connectors lose value
|-
| 6 ≤ M < 10
| Orange zone
| Main focus is to be first-in whatever you decide to play, important to preserve chips
|-
| 1 ≤ M < 6
| Red zone
| Your only move is to move [[all in (poker)|all-in]] or fold
|-
| M < 1
| Dead zone
| You are completely dependent on luck to survive, the only strategy is to push all-in into an empty pot
|}
 
==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".
 
:<math>M_{\mbox{Effective}} = M \times \left( \frac{\mbox{Players}}{10} \right)</math>
 
Therefore, for a player with a "simple M ratio" of 9 at a five player table, the effective M is 4.5:
 
:<math>M_{\mbox{Effective}} = 9 \times \left( \frac{5}{10} \right) = 4.5</math>
 
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.
 
== See also ==
* [[Q-ratio]]
 
== References ==
{{reflist}}
 
[[Category:Heuristics]]
[[Category:Poker strategy]]

Latest revision as of 10:21, 17 September 2014

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