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Message: [QUOTE="aliengenius, post: 733407, member: 11924"] [URL="http://www.blackjackforumonline.com/content/Poker_Tournament_Strategy_True_M.htm"]Your M is lower than you think:[/URL] [B]"True M" versus Harrington's M: Critical Flaws in Harrington's M Theory, And Why Tournament Structure Matters[/B] [B]By Arnold Snyder (From [I]Blackjack Forum[/I] Vol. XXVI #1, Spring 2007) © Blackjack Forum Online 2007[/B] [B]Critical Flaws in the Theory and Use of "M" in Poker Tournaments [/B] In this article, I will address critical flaws in the concept of “M” as a measure of player viability in poker tournaments. I will specifically be addressing the concept of M as put forth by Dan Harrington in [I]Harrington on Hold’em II [/I](HOH II). My book, [I]The Poker Tournament Formula[/I] (PTF), has been criticized by some poker writers who contend that my strategies for fast tournaments must be wrong, since they violate strategies based on Harrington’s M. I will show that it is instead Harrington’s theory and advice that are wrong. I will explain in this article exactly where Harrington made his errors, why Harrington’s strategies are incorrect not only for fast tournaments, but for slow blind structures as well, and why poker tournament structure, which Harrington ignores, is the key factor in devising optimal tournament strategies. This article will also address a common error in the thinking of players who are using a combination of PTF and HOH strategies in tournaments. Specifically, some of the players who are using the strategies from my book, and acknowledge that structure is a crucial factor in any poker tournament, tell me they still calculate M at the tables because they believe it provides a “more accurate” assessment of a player’s current chip stack status than the simpler way I propose—gauging your current stack as a multiple of the big blind. But M, in fact, is a less accurate number, and this article will explain why. There is a way to calculate what I call “True M,” that would provide the information that Harrington’s false M is purported to provide, but I do not believe there is any real strategic value in calculating this number, and I will explain the reason for that too. [B]The Basics of Harrington’s M Strategy[/B] Harrington uses a zone system to categorize a player’s current chip position. In the “green zone,” a player’s chip stack is very healthy and the player can use a full range of poker skills. As a player’s chip stack diminishes, the player goes through the yellow zone, the orange zone, the red zone, and finally the dead zone. The zones are identified by a simple rating number Harrington calls “M.” [B]What Is “M”?[/B] In HOH II, on page 125, Dan Harrington defines M as: “…the ratio of your stack to the current total of blinds and antes.” For example, if your chip stack totals 3000, and the blinds are 100-200 (with no ante), then you find your M by dividing 3000 / 300 = 10. On page 126, Harrington expounds on the meaning of M to a tournament player: “What M tells you is the number of rounds of the table that you can survive before being blinded off, assuming you play no pots in the meantime.” In other words, Harrington describes M as a player’s [I]survival indicator[/I]. If your M = 5, then Harrington is saying you will survive for five more rounds of the table (five circuits of the blinds) if you do not play a hand. At a 10-handed table, this would mean you have about 50 hands until you would be blinded off. All of Harrington’s zone strategies are based on this understanding of how to calculate M, and what M means to your current chances of tournament survival. Amateur tournament players tend to tighten up their play as their chip stacks diminish. They tend to become overly protective of their remaining chips. This is due to the natural survival instinct of players. They know that they cannot purchase more chips if they lose their whole stack, so they try to hold on to the precious few chips that are keeping them alive. If they have read a few books on the subject of tournament play, they may also have been influenced by the unfortunate writings of Mason Malmuth and David Sklansky, who for many years have promulgated the misguided theory that the fewer chips you have in a tournament, the more each chip is worth. (This fallacious notion has been addressed in other articles in our online Library, including: [URL="http://www.blackjackforumonline.com/content/reverse_chip_value_theory.htm"]Reverse Chip Value for Poker Tournaments: Good Math, Bad Logid (A Reply to David Sklansky[/URL].) But in HOH II, Harrington explains that as your M diminishes, which is to say as your stack size becomes smaller in relation to the cost of the blinds and antes, “…the blinds are starting to catch you, so you have to loosen your play… you have to start making moves with hands weaker than those a conservative player would elect to play.” I agree with Harrington on this point, and I also concur with his explanation of why looser play is correct as a player’s chip stack gets shorter: “Another way of looking at M is to see it as a measure of just how likely you are to get a better hand in a better situation, [I]with a reasonable amount of money left[/I].” (Italics his.) In other words, Harrington devised his looser pot-entering strategy, which begins when your M falls below 20, and goes through four zones as it continues to shrink, based on the likelihood of your being dealt better cards to make chips with than your present starting hand. For example, with an M of 15 (yellow zone according to Harrington), if a player is dealt an 8-3 offsuit in early position (a pretty awful starting hand by anyone’s definition), Harrington’s yellow zone strategy would have the player fold this hand preflop because of the likelihood that he will be dealt a better hand to play while he still has a reasonable amount of money left. By contrast, if the player is dealt an ace-ten offsuit in early position, Harrington’s yellow zone strategy would advise the player to enter the pot with a raise. This play is not advised in Harrington’s green zone strategy (with an M > 20) because he considers ace-ten offsuit to be too weak of a hand to play from early position, since your bigger chip stack means you will be likely to catch a better pot-entering opportunity if you wait. The desperation of your reduced chip stack in the yellow zone, however, has made it necessary for you to take a risk with this hand because with the number of hands remaining before you will be blinded off, you are unlikely “…to get a better hand in a better situation, [I]with a reasonable amount of money left[/I].” Again, I fully agree with the logic of loosening starting hand requirements as a player’s chip stack gets short. In fact, the strategies in [I]The Poker Tournament Formula[/I] are based in part (but not in whole) on the same logic. But despite the similarity of some of the logic behind our strategies, there are big differences between our specific strategies for any specific size of chip stack. For starters, my strategy for entering a pot with what I categorize as a “competitive stack” (a stack size more or less comparable to Harrington’s “green zone”) is far looser and more aggressive than his. And my short-stack strategies are downright maniacal compared to Harrington’s strategies for his yellow, orange, and red zones. There are two major reasons why our strategies are so different, even though we agree on the logic that looser play is required as stacks get shorter. Again, the first is a fundamental difference in our overriding tournament theory, which I will deal with later in this article. The second reason, which I will deal with now, is a serious flaw in Harrington’s method of calculating and interpreting M. Again, what Harrington specifically assumes, as per HOH II, is that: “What M tells you is the number of rounds of the table that you can survive before being blinded off, assuming you play no pots in the meantime.” But that’s simply not correct. The only way M, as defined by Harrington, could indicate the number of rounds a player could survive is [I]by ignoring the tournament structure[/I]. [B]Why Tournament Structure Matters in Devising Optimal Strategy[/B] Let’s look at some sample poker tournaments to show how structure matters, and how it affects the underlying meaning of M, or “the number of rounds of the table that you can survive before being blinded off, assuming you play no pots in the meantime.” Let’s say the blinds are 50-100, and you have 3000 in chips. What is your M, according to Harrington? [CENTER]M = 3000 / 150 = 20[/CENTER] So, according to the explanation of M provided in HOH II, you could survive 20 more rounds of the table before being blinded off, assuming you play no pots in the meantime. This is not correct, however, because the actual number of rounds you can survive before being blinded off is [I]entirely dependent on the tournament’s blind structure[/I]. For example, what if this tournament has 60-minute blind levels? Would you survive 20 rounds with the blinds at 50-100 if you entered no pots? No way. Assuming this is a ten-handed table, you would go through the blinds about once every twenty minutes, which is to say, you would only play [I]three rounds[/I] at this 50-100 level. Then the blinds would go up. If we use the blind structure from the WSOP Circuit events recently played at Caesars Palace in Las Vegas, after 60 minutes the blinds would go from 50-100 to 100-200, then to 100-200 with a 25 ante 60 minutes after that. What is the actual number of rounds you would survive without entering a pot in this tournament from this point? Assuming you go through the blinds at each level three times, 3 x 150 = 450 3 x 300 = 900 3 x 550 = 1650 Add up the blind costs: 450 + 900 + 1650 = 3000. That’s a total of only [I]9 rounds[/I]. This measure of the true “…number of rounds of the table that you can survive before being blinded off, assuming you play no pots in the meantime,” is crucial in evaluating your likelihood of getting “…a better hand in a better situation, with a reasonable amount of money left,” and it is entirely dependent on this tournament’s blind structure. For the rest of this article, I will refer to this more accurate structure-based measure as “True M.” True M for this real-world tournament would indicate to the player that his survival time was less than half that predicted by Harrington’s miscalculation of M. [/QUOTE]

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