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    Marta inspira a nova geração do futebol feminino brasileiro

    Marta, capitã do Brasil e pioneira onabet baixar no celular todos os sentidos, incentiva as 🛡 jogadoras mais jovens a dar mais de si mesmas, a se treinar mais e a se cuidar mais. Ela destaca 🛡 a importância de estarem prontas para jogar 90 minutos mais 30, pois o futebol feminino precisa delas para sobreviver. Essa 🛡 mensagem ganhou força após a eliminação precoce do Brasil na Copa do Mundo de 2024 e, agora, com a chegada 🛡 da final olímpica de 2024, a nova geração brasileira tem a oportunidade de mostrar seu valor.

    Lágrimas de alegria substituem as 🛡 lágrimas de desespero

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    Um momento amargo para Marta

    No entanto, as coisas 🛡 quase ficaram diferentes para Marta. Durante o jogo de abertura contra a Espanha, ela recebeu um cartão vermelho direto por 🛡 uma entrada dura contra Olga Carmona. Ao perceber que essa poderia seronabet baixar no celularúltima partida internacional, a desilusão foi visível 🛡 onabet baixar no celular seu rosto.

    Desespero de Marta após ser expulsa contra a Espanha.

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    grafia: Juan Manuel Serrano Arce/Getty
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    Um time para confiar

    Marta agora 🛡 pode contar com um time sólido para apoiá-la. Apesar de inúmeras lesões e problemas, as jogadoras brasileiras se classificaram para 🛡 a final olímpica de 2024, garantindo o retorno deonabet baixar no celularcapitã para uma última chance de conquistar a medalha de 🛡 ouro.

    Um desafio exaustivo

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    Dois finais perfeitos

    A final olímpica de 2024 🛡 pode ser o cenário perfeito para duas histórias maravilhosas. A despedida dourada de uma das maiores jogadoras do futebol feminino 🛡 ou o início de uma jornada bem-sucedida para uma nova gerência no futebol internacional.

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    Onabet SD Solution é um medicamento usado parapara gerenciar a pele fúngica; infecções;. É projetado para tratar condições como pé de atleta, coceira, micose e pele seca e escamosa. Esta solução fornece alívio da dor, vermelhidão e coceira na área afetada e promove mais rápido. Cura.
    Se você tem pé de atleta, lave bem as meias ou meias e troque os sapatos diariamente, se possível. Os efeitos colaterais mais comuns do uso da Loção Onabet incluem reações no local de aplicação, como queima, irritação, coceira e vermelhidão. Evite o contato direto com o seu Olhos.
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    Introdução à Onabet

    A Onabet é uma marca reconhecida mundialmente na produção e distribuição de medicamentos antifúngicos eficazes. Oferecemos produtos que aliviam os sintomas desconfortáveis e prejudiciais causados por infecções fúngicas na pele, como pé de atleta, coceira do fungo, intertrigo e sarna, entre outros. Embora ninguém saiba exatamente quem é o dono da Onabe, sabemos que nossos produtos estão sempre a disposição para ajudar a combater essas infecções.

    Aplicações e localizações do tratamento da Onabet

    A Onabet é eficaz no tratamento de várias infecções fúngicas na pele, incluindo:

    • Pé de atleta (tinea pedis):Acomete os pés, causando coceira, vermelhidão, desconforto, inchaço e bolhas.
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    Como a Onabet atua e quais são as consequências do seu uso

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    Conclusão

    Quem é dono da Onabet? Embora não se saiba exatamente quem é o dono da Nonabet, sabemos que nossos produtos são eficazes no tratamento de várias infecções fúngicas na pele. Além disso, os medicamentos da Oabet têm um historial comprovado de segurança e eficácia. Recomendamos o uso da O nabet para quem quer aliviar rapidamente e eficazmente os sintomas das infecções fungicas.

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    O creme candid-B contém uma combinação de dois medicamentos - beclometasona e clotrimazol. Clotrin Paysanduole é um medicamento antifúngico quepara o crescimento de fungos, interrompendo suas células. membranasBetametasona é um medicamento esteróide que reduz a inflamação, coceira associada com fungos. infecções;
    O efeito colateral mais comum deste medicamento inclui:coceira, secura. vermelhidão e sensação de queimação na aplicação. E-mail:. Estes são geralmente auto-limitantes, Efeitos colaterais graves São raros! Você deve consultar o médico se você tiver qualquer reação alérgica (erupção de coceira a inchaço ou falta d ar, etc.).) )

    O Onabet, também conhecido como Betano, é uma plataforma popular de apostas esportivas que opera onabet baixar no celular onabet baixar no celular vários países, incluindo 🍊 o Brasil. Muitos jogadores curiosos perguntam qual é o melhor horário para fazer suas apostas no site.

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    O que é Onabet?

    Onabet é um site de bônus de apostas esportivas e casino online que oferece uma variedade de bônus aprimorados e promoções. Com um processo de inscrição simples e uma plataforma fácil de usar, Onabet é ideal para jogadores de todos os níveis.

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    Como se registrar no site de apostas esportivas OnABET

    Os jogos de apostas estão se tornando cada vez mais populares no Brasil, e um dos sites que está se destacando nesse mercado é o OnABET. Para começar a aproveitar das suas diversas opções de apostas, é necessário se cadastrar e criar uma conta.

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    “True M” versus Harrington’s M and Why Tournament Structure Matters

    by Arnold

    Snyder

    (From Blackjack Forum Vol. XXVI #1, Spring 2007)

    © Blackjack 🌈 Forum Online

    2007

    Critical Flaws in the Theory and Use of “M” in Poker Tournaments

    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 Harrington on Hold’em II (HOH II). My book, The 🌈 Poker Tournament

    Formula (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.

    The Basics of

    Harrington’s M Strategy

    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.”

    What Is “M”?

    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 survival indicator.

    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: Chip Value in Poker Tournaments.)

    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,

    with a reasonable amount of money left.” (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, with a reasonable amount of

    money 🌈 left.”

    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 The Poker

    Tournament Formula 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 by ignoring

    the tournament structure.

    Why Tournament Structure Matters in Devising Optimal

    🌈 Strategy

    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?

    M = 3000 / 150 = 20

    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 🌈 entirely dependent

    on the tournament’s blind structure.

    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 three rounds 🌈 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 9 rounds.

    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.

    True M in Fast Poker

    Tournaments

    To really drill home 🌈 the flaw in M—as Harrington defines it—let’s look at a

    fast tournament structure. Let’s assume the exact same 3000 in 🌈 chips, and the exact

    same 50-100 blind level, but with the 20-minute blind levels we find in many small

    buy-in 🌈 tourneys. With this blind structure, the blinds will be one level higher each

    time we go through them. How many 🌈 rounds of play will our 3000 in chips survive,

    assuming we play no pots? (Again, I’ll use the Caesars WSOP 🌈 levels, as above, changing

    only the blind length.)

    150 + 300 + 550 + 1100 (4 rounds) = 1950

    The next round 🌈 the

    blinds are 300-600 with a 75 ante, so the cost of a ten-handed round is 1650, and we

    only 🌈 have 1050 remaining. That means that with this faster tournament structure, our

    True M at the start of that 50-100 🌈 blind level is actually about 4.6, a very far cry

    from the 20 that Harrington would estimate, and quite far 🌈 from the 9 rounds we would

    survive in the 60-minute structure described above.

    And, in a small buy-in tournament

    with 15-minute 🌈 blind levels—and these fast tournaments are very common in poker rooms

    today—this same 3000 chip position starting at this same 🌈 blind level would indicate a

    True M of only 3.9.

    True M in Slow Poker Tournaments

    But what if you were playing 🌈 in

    theR$10K main event of the WSOP, where the blind levels last 100 minutes? In this

    tournament, if you were 🌈 at the 50-100 blind level with 3000 in chips, your True M would

    be 11.4. (As a matter of fact, 🌈 it has only been in recent years that the blind levels

    of the main event of the WSOP have been 🌈 reduced from their traditional 2-hour length.

    With 2-hour blind levels, as Harrington would have played throughout most of the years

    🌈 he has played the main event, his True M starting with this chip position would be

    12.6.)

    Unfortunately, that’s still nowhere 🌈 near the 20 rounds Harrington’s M gives

    you.

    True M Adjusts for Tournament Structure

    Note that in each of these tournaments, 20

    🌈 M means something very different as a survival indicator. True M shows that the

    survival equivalent of 3000 in chips 🌈 at the same blind level can range from 3.9 rounds

    (39 hands) to 12.6 (126 hands), depending solely on the 🌈 length of the

    blinds.

    Furthermore, even within the same blind level of the same tournament, True M

    can have different values, 🌈 depending on how deep you are into that blind level. For

    example, what if you have 3000 in chips but 🌈 instead of being at the very start of that

    50-100 blind level (assuming 60-minute levels), you are somewhere in the 🌈 middle of it,

    so that although the blinds are currently 50-100, the blinds will go up to the 100-200

    level 🌈 before you go through them three more times? Does this change your True M?

    It

    most certainly does. That True M 🌈 of 9 in this tournament, as demonstrated above, only

    pertains to your chip position at the 50-100 blind level if 🌈 you will be going through

    those 50-100 blinds three times before the next level. If you’ve already gone through

    those 🌈 blinds at that level one or more times, then your True M will not be 9, but will

    range from 🌈 6.4 to 8.1, depending on how deep into the 50-100 blind level you are.

    Most

    important, if you are under the 🌈 mistaken impression that at any point in the 50-100

    blind level in any of the tournaments described above, 3000 in 🌈 chips is sufficient to

    go through 20 rounds of play (200 hands), you are way off the mark. What Harrington

    🌈 says “M tells you,” is not at all what M tells you. If you actually stopped and

    calculated True M, 🌈 as defined above, then True M would tell you what Harrington’s M

    purports to tell you.

    And if it really is 🌈 important for you to know how many times you

    can go through the blinds before you are blinded off, then 🌈 why not at least figure out

    the number accurately? M, as described in Harrington’s book, is simply woefully

    inadequate at 🌈 performing this function.

    If Harrington had actually realized that his M

    was not an accurate survival indicator, and he had stopped 🌈 and calculated True M for a

    variety of tournaments, would he still be advising you to employ the same starting 🌈 hand

    standards and playing strategies at a True M of 3.9 (with 39 hands before blind-off)

    that you would be 🌈 employing at a True M of 12.6 (with 126 hands before blind-off)?

    If

    he believes that a player with 20 M 🌈 has 20 rounds of play to wait for a good hand

    before he is blinded off (and again, 20 rounds 🌈 at a ten-player table would be 200

    hands), then his assessment of your likelihood of getting “…a better hand in 🌈 a better

    situation, with a reasonable amount of money left,” would be quite different than if he

    realized that his 🌈 True M was 9 (90 hands remaining till blind-off), or in a faster

    blind structure, as low as 3.9 (only 🌈 39 hands remaining until blind-off).

    Those

    radically different blind-off times would drastically alter the frequencies of

    occurrence of the premium starting 🌈 hands, and aren’t the likelihood of getting those

    hands what his M theory and strategy are based on?

    A Blackjack Analogy

    For 🌈 blackjack

    players—and I know a lot of my readers come from the world of blackjack card

    counting—Harrington’s M might best 🌈 be compared to the “running count.” If I am using a

    traditional balanced card counting system at a casino blackjack 🌈 table, and I make my

    playing and betting decisions according to my running count, I will often be playing

    incorrectly, 🌈 because the structure of the game—the number of decks in play and the

    number of cards that have already been 🌈 dealt since the last shuffle—must be taken into

    account in order for me to adjust my running count to a 🌈 “true” count.

    A +6 running

    count in a single-deck game means something entirely different from a +6 running count

    in a 🌈 six-deck shoe game. And even within the same game, a +6 running count at the

    beginning of the deck or 🌈 shoe means something different from a +6 running count toward

    the end of the deck or shoe.

    Professional blackjack players adjust 🌈 their running count

    to the true count to estimate their advantage accurately and make their strategy

    decisions accordingly. The unadjusted 🌈 running count cannot do this with any accuracy.

    Harrington’s M could be considered a kind of Running M, which must 🌈 be adjusted to a

    True M in order for it to have any validity as a survival gauge.

    When Harrington’s

    Running 🌈 M Is Occasionally Correct

    Harrington’s Running M can “accidentally” become

    correct without a True M adjustment when a player is very 🌈 short-stacked in a tournament

    with lengthy blind levels. For example, if a player has an M of 4 or 5 🌈 in a tournament

    with 2-hour blind levels, then in the early rounds of that blind level, since he could

    expect 🌈 to go through the same blind costs 4 or 5 times, Harrington’s unadjusted M would

    be the same as True 🌈 M.

    This might also occur when the game is short-handed, since

    players will be going through the blinds more frequently. (This 🌈 same thing happens in

    blackjack games where the running count equals the true count at specific points in the

    deal. 🌈 For example, if a blackjack player is using a count-per-deck adjustment in a

    six-deck game, then when the dealer is 🌈 down to the last deck in play, the running count

    will equal the true count.)

    In rare situations like these, where 🌈 Running M equals True

    M, Harrington’s “red zone” strategies may be correct—not because Harrington was correct

    in his application of 🌈 M, but because of the tournament structure and the player’s poor

    chip position at that point.

    In tournaments with 60-minute blind 🌈 levels, this type of

    “Running M = True M” situation could only occur at a full table when a player’s 🌈 M is 3

    or less. And in fast tournaments with 15 or 20-minute blind levels, Harrington’s M

    could only equal 🌈 True M when a player’s M = 1 or less.

    Harrington’s yellow and orange

    zone strategies, however, will always be pretty 🌈 worthless, even in the slowest

    tournaments, because there are no tournaments with blind levels that last long enough

    to require 🌈 no True M adjustments.

    Why Harrington’s Strategies Can’t Be Said to Adjust

    Automatically for True M

    Some Harrington supporters may wish to 🌈 make a case that Dan

    Harrington made some kind of automatic adjustment for approximate True M in devising

    his yellow 🌈 and orange zone strategies. But in HOH II, he clearly states that M tells

    you how many rounds of the 🌈 table you will survive—period.

    In order to select which

    hands a player should play in these zones, based on the likelihood 🌈 of better hands

    occurring while the player still has a reasonable chip stack, it was necessary for

    Harrington to specify 🌈 some number of rounds in order to develop a table of the

    frequencies of occurrence of the starting hands. His 🌈 book tells us that he assumes an M

    of 20 simply means 20 rounds remaining—which we know is wrong for 🌈 all real-world

    tournaments.

    But for those who wish to make a case that Harrington made some kind of a

    True M 🌈 adjustment that he elected not to inform us about, my answer is that it’s

    impossible that whatever adjustment he used 🌈 would be even close to accurate for all

    tournaments and blind structures. If, for example, he assumed 20 M meant 🌈 a True M of

    12, and he developed his starting-hand frequency charts with this assumption, then his

    strategies would be 🌈 fairly accurate for the slowest blind structures we find in major

    events. But they would still be very wrong for 🌈 the faster blind structures we find in

    events with smaller buy-ins and in most online tournaments.

    In HOH II, he does 🌈 provide

    quite a few sample hands from online tournaments, with no mention whatsoever of the

    blind structures of these events, 🌈 but 15-minute blind levels are less common online

    than 5-, 8-, and 12-minute blind levels. Thus, we are forced to 🌈 believe that what Mason

    Malmuth claims is true: that Harrington considers his strategies correct for

    tournaments of all speeds. So 🌈 it is doubtful that he made any True M adjustments, even

    for slower tournament structures. Simply put, Harrington is oblivious 🌈 to the true

    mathematics of M.

    Simplifying True M for Real-Life Tournament Strategy

    If all poker

    tournaments had the same blind structure, 🌈 then we could just memorize chart data that

    would indicate True M with any chip stack at any point in 🌈 any blind level.

    Unfortunately, there are almost as many blind structures as there are

    tournaments.

    There are ways, however, that Harrington’s 🌈 Running M could be adjusted to

    an approximate True M without literally figuring out the exact cost of each blind 🌈 level

    at every point in the tournament. With 90-minute blind levels, after dividing your chip

    stack by the cost of 🌈 a round, simply divide your Running M by two, and you’ll have a

    reasonable approximation of your True M.

    With 60-minute 🌈 blind levels, take about 40% of

    the Running M. With 30-minute blind levels, divide the Running M by three. And 🌈 with 15-

    or 20-minute blind levels, divide the Running M by five. These will be far from perfect

    adjustments, but 🌈 they will be much closer to reality than Harrington’s unadjusted

    Running M numbers.

    Do Tournament Players Need to Know Their “True 🌈 M”?

    Am I suggesting

    that poker tournament players should start estimating their True M, instead of the

    Running M that Harrington 🌈 proposes? No, because I disagree with Harrington’s emphasis

    on survival and basing so much of your play on your cards. 🌈 I just want to make it clear

    that M, as defined and described by Harrington in HOH II, is wrong, 🌈 a bad measure of

    what it purports and aims to measure. It is based on an error in logic, in 🌈 which a

    crucial factor in the formula—tournament structure—is ignored (the same error that

    David Sklansky and Mason Malmuth have made 🌈 continually in their writings and analyses

    of tournaments.)

    Although it would be possible for a player to correct Harrington’s

    mistake by 🌈 estimating his True M at any point in a tournament, I don’t advise it.

    Admittedly, it’s a pain in the 🌈 ass trying to calculate True M exactly, not something

    most players could do quickly and easily at the tables. But 🌈 that’s not the reason I

    think True M should be ignored.

    The reason is related to the overarching difference

    between Harrington’s 🌈 strategies and mine, which I mentioned at the beginning of this

    article. That is: It’s a grave error for tournament 🌈 players to focus on how long they

    can survive if they just sit and wait for premium cards. That’s not 🌈 what tournaments

    are about. It’s a matter of perspective. When you look at your stack size, you

    shouldn’t be thinking, 🌈 “How long can I survive?” but, “How much of a threat do I pose

    to my opponents?”

    The whole concept of 🌈 M is geared to the player who is tight and

    conservative, waiting for premium hands (or premium enough at that 🌈 point). Harrington’s

    strategy is overly focused on cards as the primary pot entering factor, as opposed to

    entering pots based 🌈 predominately (or purely) on position, chip stack, and

    opponent(s).

    In The Poker Tournament Formula, I suggest that players assess their chip

    🌈 position by considering their chip stacks as a simple multiple of the current big

    blind. If you have 3000 in 🌈 chips, and the big blind is 100, then you have 30 big

    blinds. This number, 30, tells you nothing about 🌈 how many rounds you can survive if you

    don’t enter any pots. But frankly, that doesn’t matter. What matters in 🌈 a tournament is

    that you have sufficient chips to employ your full range of skills, and—just as

    important—that you have 🌈 sufficient chips to threaten your opponents with a raise, and

    an all-in raise if that is what you need for 🌈 the threat to be successful to win you the

    pot.

    Your ability to to be a threat is directly related to 🌈 the health of your chip

    stack in relation to the current betting level, which is most strongly influenced by

    the 🌈 size of the blinds. In my PTF strategy, tournaments are not so much about survival

    as they are about stealing 🌈 pots. If you’re going to depend on surviving until you get

    premium cards to get you to the final table, 🌈 you’re going to see very few final tables.

    You must outplay your opponents with the cards you are dealt, not 🌈 wait and hope for

    cards that are superior to theirs.

    I’m not suggesting that you ignore the size of the

    preflop 🌈 pot and focus all of your attention on the size of the big blind. You should

    always total the chips 🌈 in the pot preflop, but not because you want to know how long

    you can survive if you sit there 🌈 waiting for your miracle cards. You simply need to

    know the size of the preflop pot so you can make 🌈 your betting and playing decisions,

    both pre- and post-flop, based on all of the factors in the current hand.

    What other

    🌈 players, if any have entered the pot? Is this a pot you can steal if you don’t have a

    viable 🌈 hand? Is this pot worth the risk of an attempted steal? If you have a drawing

    hand, do you have 🌈 the odds to call, or are you giving an opponent the odds to call? Are

    any of your opponent(s) pot-committed? 🌈 Do you have sufficient chips to play a

    speculative hand for this pot? There are dozens of reasons why you 🌈 need to know the

    size of a pot you are considering getting involved in, but M is not a factor 🌈 in any of

    these decisions.

    So, again, although you will always be totaling the chips in the pot

    in order to 🌈 make betting and playing decisions, sitting there and estimating your

    blind-off time by dividing your chip stack by the total 🌈 chips in the preflop pot is an

    exercise in futility. It has absolutely nothing to do with your actual chances 🌈 of

    survival. You shouldn’t even be thinking in terms of survival, but of

    domination.

    Harrington on Hold’em II versus The Poker 🌈 Tournament Formula: A Sample

    Situation

    Let’s say the blinds are 100-200, and you have 4000 in chips. Harrington

    would have you 🌈 thinking that your M is 13 (yellow zone), and he advises: “…you have to

    switch to smallball moves: get in, 🌈 win the pot, but get out when you encounter

    resistance.” (HOH II, p. 136)

    In The Poker Tournament Formula basic strategy 🌈 for fast

    tournaments (PTF p. 158), I categorize this chip stack equal to 20 big blinds as “very

    short,” and 🌈 my advice is: “…you must face the fact that you are not all that far from

    the exit door. But 🌈 you still have enough chips to scare any player who does not have a

    really big chip stack and/or a 🌈 really strong hand. Two things are important when you

    are this short on chips. One is that unless you have 🌈 an all-in raising hand as defined

    below, do not enter any pot unless you are the first in. And second, 🌈 any bet when you

    are this short will always be all-in.”

    The fact is, you don’t have enough chips for

    “smallball” 🌈 when you’re this short on chips in a fast tournament, and one of the most

    profitable moves you can make 🌈 is picking on Harrington-type players who think it’s time

    for smallball.

    Harrington sees this yellow zone player as still having 13 🌈 rounds of

    play (130 hands, which is a big overestimation resulting from his failure to adjust to

    True M) to 🌈 look for a pretty decent hand to get involved with. My thinking in a fast

    tournament, by contrast, would be: 🌈 “The blinds are now 100-200. By the time they get

    around to me fifteen minutes from now, they will be 🌈 200-400. If I don’t make a move

    before the blinds get around to me, and I have to go through 🌈 those blinds, my 4000 will

    become 3400, and the chip position I’m in right now, which is having a stack 🌈 equal to

    20 times the big blind, will be reduced to a stack of only 8.5 times the big blind.

    🌈 Right now, my chip stack is scary. Ten to fifteen minutes from now (in 7-8 hands), any

    legitimate hand will 🌈 call me down.”

    So, my advice to players this short on chips in a

    fast tournament is to raise all-in with 🌈 any two cards from any late position seat in an

    unopened pot. My raising hands from earlier positions include all 🌈 pairs higher than 66,

    and pretty much any two high cards. And my advice with these hands is to raise 🌈 or

    reraise all-in, including calling any all-ins. You need a double-up so badly here that

    you simply must take big 🌈 risks. As per The Poker Tournament Formula (p. 159): “When

    you’re this short on chips you must take risks, because 🌈 the risk of tournament death is

    greater if you don’t play than if you do.”

    There is also a side effect 🌈 of using a loose

    aggressive strategy when you have enough chips to hurt your opponents, and that is that

    you 🌈 build an image of a player who is not to be messed with, and that is always the

    preferred image 🌈 to have in any no-limit hold’em tournament. But while Harrington sees

    this player surviving for another 13 rounds of play, 🌈 the reality is that he will

    survive fewer than 4 more rounds in a fast tournament, and within two rounds 🌈 he will be

    so short-stacked that he will be unable to scare anybody out of a pot, and even a

    🌈 double-up will not get him anywhere near a competitive chip stack.

    The Good News for

    Poker Tournament Players

    The good news for 🌈 poker tournament players is that

    Harrington’s books have become so popular, and his M theory so widely accepted as valid

    🌈 by many players and “experts” alike, that today’s NLH tournaments are overrun with his

    disciples playing the same tight, conservative 🌈 style through the early green zone blind

    levels, then predictably entering pots with more marginal hands as their M

    diminishes—which 🌈 their early tight play almost always guarantees. And, though many of

    the top players know that looser, more aggressive play 🌈 is what’s getting them to the

    final tables, I doubt that Harrington’s misguided advice will be abandoned by the

    masses 🌈 any time soon.

    In a recent issue of Card Player magazine (March 28, 2007),

    columnist Steve Zolotow reviewed The Poker Tournament 🌈 Formula, stating: “Snyder

    originates a complicated formula for determining the speed of a tournament, which he

    calls the patience factor. 🌈 Dan Harrington’s discussion of M and my columns on CPR cover

    this same material, but much more accurately. Your strategy 🌈 should be based not upon

    the speed of the tournament as a whole, but on your current chip position in 🌈 relation

    to current blinds. If your M (the number of rounds you can survive without playing a

    hand) is 20, 🌈 you should base your strategy primarily on that fact. Whether the blinds

    will double and reduce your M to 10 🌈 in 15 minutes or four hours should not have much

    influence on your strategic decisions.”

    Zolotow’s “CPR” articles were simply a 🌈 couple

    of columns he wrote last year in which he did nothing but explain Harrington’s M

    theory, as if it 🌈 were 100% correct. He added nothing to the theory of M, and is clearly

    as ignorant of the math as 🌈 Harrington is.

    So money-making opportunities in poker

    tournaments continue to abound.

    In any case, I want to thank SlackerInc for posting a

    🌈 question on our poker discussion forum, in which he pointed out many of the key

    differences between Harrington’s short-stack strategies 🌈 and those in The Poker

    Tournament Formula. He wanted to know why our pot-entering strategies were so far

    apart.

    The answer 🌈 is that the strategies in my book are specifically identified as

    strategies for fast tournaments of a specific speed, so 🌈 my assumptions, based on a

    player’s current chip stack, would usually be that the player is about five times more

    🌈 desperate than Harrington would see him (his Running M of 20 being roughly equivalent

    to my True M of about 🌈 4). ♠

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