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- cef apostas
- Pé de atleta (tinea pedis):Acomete os pés, causando coceira, vermelhidão, desconforto, inchaço e bolhas.
- Coceira do fungo (tinea cruris):Acomete o inguinal, causando coceira, vermelhidão, desconforto e rugas vermelhas.
- Sarna (scabies):Pode acometer o corpo inteiro, causando erupções cutâneas, manchas avermelhadas, coceira ou prurido.
- Candida:Pode acometer a pele ou o sistema genital, causando vermelhidão, dor ou desconforto, e seiva branca ou amarela.
- Pitiríase:Pode acometer a pele, causando manchas ou escamas na pele.
- Nem todos os sites de apostas esportivas e casino online oferecem bônus Onabet.
- Nem sempre é preciso fazer um depósito antes de obter o bônus Onabet, pois alguns sites oferecem bônus Onabet sem depósito.
- Você deve cumprir as condições de wagering antes de poder retirar as ganhanças obtidas com o bônus Onabet.
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- No seu navegador de internet, acesse o site
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- Clique no botão "Entrar", localizado no canto superior direito da página.
- Na tela de login, clique onabet baixar no celular onabet baixar no celular "Criar conta".
- Preencha o formulário de registro com suas informações pessoais, incluindo nome completo, data de nascimento, gênero, endereço de e-mail e número de telefone.
- Crie uma senha segura e confirme-a.
- Marque a caixa "Eu concordo com os termos e condições".
- Clique onabet baixar no celular onabet baixar no celular "Registrar".
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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
Em junho de 2024, Marta chorou de desespero após a eliminação do Brasil nas mãos da França. Quase 🛡 cinco anos depois, ela chorou de alegria ao veronabet baixar no celularnação se classificar para a final olímpica de 2024. A 🛡 nova geração brasileira, liderada por jogadoras como Debinha, Andressinha e Adriana, superou a Espanha, campeã mundial, por 4 a 2, 🛡 garantindo a Marta uma última chance de conquistar uma medalha de ouro olímpica.
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.
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
Este torneio olímpico tem sido uma verdadeira corrida contra o tempo, com jogos a cada três dias e 🛡 quatro dos seis jogos de eliminação direta indo para o tempo extra. Brasil e Estados Unidos chegaram à final graças 🛡 àonabet baixar no celularvontade e à capacidade de se esforçarem mais do que os outros.
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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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:
Como a Onabet atua e quais são as consequências do seu uso
A Onabet atua suprimindo o crescimento ou eliminando o fungo que causa a infecção, fornecendo alívio dos sintomas desconfortáveis, como coceira, vermelhidão e dor. O uso regular da Onabe reduz os sintomas das infecções fúngicas nas áreas afetadas, evitando a propagação delas. Embora os medicamentos OnaBE sejam seguros para o uso, alguns indivíduos podem apresentar efeitos colaterais leves, comococeira no local do contato da pele com a substância.
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 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.
Pesquisas indicam que o 🍊 horário ideal para jogar no Onabet é durante os eventos esportivos de maior procura. Isso geralmente ocorre durante os finais 🍊 de semana, especialmente aos sábados e domingos, quando uma variedade de jogos e partidas estão disponíveis para aposta.
Além disso, as 🍊 principais ligas e competições esportivas, como a Premier League, a Liga dos Campeões da UEFA, a NBA, a NFL, e 🍊 outros, atraem um grande volume de jogadores e, por isso, podem oferecer melhores cotas e probabilidades. Portanto, é recomendável aproveitar 🍊 esses eventos para maximizar suas chances de ganhar.
No entanto, é essencial lembrar que as condições do mercado de apostas podem 🍊 variar e, portanto, é essencial manter-se atualizado sobre as últimas notícias e tendências esportivas. Fazer uma pesquisa adequada antes de 🍊 se envolver onabet baixar no celular onabet baixar no celular apostas pode ajudar a tomar decisões informadas e aumentar suas chances de sucesso.
Em resumo, o melhor 🍊 horário para jogar no Onabet é durante os fins de semana e durante as principais ligas e competições esportivas. Fique 🍊 atento às variações de mercado e mantenha-se informado sobre as últimas notícias esportivas para maximizar suas chances de obter sucesso 🍊 onabet baixar no celular onabet baixar no celular suas apostas.
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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.
Como se qualificar para o bônus no Onabet?
Para se qualificar para o bônus no Onabet, é necessário se inscrever onabet baixar no celular onabet baixar no celular um site que ofereça essa promoção. Isso geralmente envolve fornecer alguns detalhes pessoais básicos, como nome, endereço de e-mail e data de nascimento. Em alguns casos, é possível que seja necessário fornecer um código promocional durante o processo de inscrição.
Para não se perder no mundo dos bônus online
Pasos a seguir | Conseguir bônus Onabet |
---|---|
Passo 1: | Escolha um site de bônus Onabet que se ajuste às suas necessidades. |
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O que fazer depois de se qualificar para o bônus no Onabet?
Uma vez que você se qualificou para o bônus no Onabet, você está pronto para começar a aproveitar plenamente seus jogos de casino online ou apostas esportivas favoritas. Basta seguir as regras estabelecidas nas regras do bônus e ter uma boa sorte!
Respostas às perguntas mais frequentes:
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No mundo da beleza, surgem constantemente novos produtos que prometem trazer benefícios incríveis à nossa pele. Um desses cosméticos é 💰 o Onabet B Cream de um emoliente e tem ganhado popularidade no mercado brasileiro! Neste artigo a nós vamos explorar 💰 os usos desse crea do idioma Kannada ( falado na Índia).
O que é o Thenabet B Cream?
Onabet B Cream é 💰 um emoliente hidratante que contém uma combinação única de ingredientes naturais e sintéticos. Sua fórmula exclusiva foi projetada para proporcionar 💰 a hidropatação profunda à pele, ajudando A manter onabet baixar no celular formavidade com elasticidade!
Usos do Onabet B Cream no Kannada
No Kannada, o 💰 Onabet B Cream é conhecido como "ನಬ屋ಟ್ abandonouಿ naಕ destroçosರೀಮ↑". Ele foi usado de várias maneiras. incluindo:
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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.
Aqui, você encontrará uma breve orientação sobre como se registrar no site OnABET:
Após concluir o processo de registro, você receberá um e-mail de confirmação. Siga as instruções nesse e-mail para ativar onabet baixar no celular conta e aproveitar do mundo das apostas esportivas no OnABET.
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O Onabet é uma plataforma de apostas esportivas que oferece aos seus usuários uma ampla variedade de opções de apostas 😗 onabet baixar no celular diferentes esportes e eventos ao redor do mundo. Dentre as opções disponíveis, estão presentes os chamados "horários pagantes", que 😗 são horários específicos onabet baixar no celular que os usuários podem apostar onabet baixar no celular determinados eventos com cotas melhores do que as normais.
Mas como 😗 funcionam exatamente esses horários pagantes no Onabet? E como é possível aproveitá-los ao máximo? Neste artigo, responderemos a essas e 😗 outras perguntas sobre o assunto.
O que são horários pagantes no Onabet?
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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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