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Literário Lbeck
Abeck – Rainha da Liga Hanseática - tem um charme e uma vulnerabilidade desvanecimento ausente dos gostos Berlim, Munique ❤️ ou Hamburgo... E a maior parte Alemanha. Eu amei minha viagem lá vagando pelas ruas paralepípedas ; escalar cada torre ❤️ gótica igreja tijolo gótico onabet 2 cream geral sozinho! Thomas Mann escreveu o insuportavelmente triste romance Buddenbrookes ali (Buddner) então fugiu do ❤️ nazismo nos EUA no 1939 O autor Gúnter-vida agora viveu plenamente Grassem casadae depois:
Martin Charlesworth
Maravilha gótica de Marburg, Hesse.
A cidade ❤️ universitária de Marburg.
: Deutschland/Alamy
Marburg, a pequena e antiga cidade universitária de uma hora ao norte do trem Frankfurt é um ❤️ destino contode fadas porque já foi o lar dos Irmãos Grimm. Cada pista leva para cima até à colina da ❤️ vila onde se erguem as pedras acima Oberstadt onabet 2 cream madeira que está enquadrada por marburgos; este castelo recebeu Martinho Lutero ❤️ no ano 1529 (a Elissabelkirche), das principais igrejas gótica greco-alemã: A Igreja Gótica Alemã era importante local medieval!
Gocklhahn
) bater suas ❤️ asas mecânicas para marcar a hora.
Anna Anana
Torre de visão brilhante, Stuttgart.
Panorama de Stuttgart.
: Westend61 GmbH/Alamy
Para a:
fernsehturm
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Weinstuben
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Tim Proctor
Perfil perfil
Dicas dos leitores: envie uma dica para ter a chance de ganhar ❤️ um voucher 200 por pausa no Coolstays.
Viagem de um dia a partir da Munique
Mosteiro Andechs.
: Shotshop GmbH/Alamy
A cerca de 25 ❤️ milhas a sudoeste da cidade é
Mosteiro Andechs mosteiro
– naonabet 2 creammais idílica e autêntica Baviera. Sentado no topo Ammersee (Lago ❤️ Ammem), este mosteiro Benedicitine igreja de peregrinação é popular por suas cervejarias, restaurantes ou jardins cervejeiros timo dia: pegue o ❤️ metrô Munique para Herrsching onabet 2 cream seguida caminhe 40 minutos suavemente subindo através da floresta encantadora Na chegada recompenda- se com ❤️ os altos do grande vinho que você tem à frente a bela St Martin'S Igreja - onde está indo!
Sonutschka
Cultura e ❤️ arte onabet 2 cream Nuremberga
Museu Nacional Alemão.
: B O'Kane/Alamy
Se você puder, passe um tempo na bela cidade de Nuremberga com seus museus ❤️ incríveis: o Germanische Nationalmuseum é equivalente ao Museu Britânico e a maior coleção da história cultural alemã. O Neues Museum ❤️ tem uma impressionante colecção do renomado artista visual Gerhard Richter onabet 2 cream pinturas; Zukunftsmuseu (o museu) oferece excelente ciência para ficar ❤️ no hotel Karl August – duplo dos 159 quartos apenas -- seu design moderno deslumbrante!
Até
Passeio de bicicleta pelo Báltico ❤️ via Rostock.
Praia onabet 2 cream Khlungsborn.
: Reprodução/Alamy Fantasy
Eu tive um tempo brilhante na Alemanha no verão passado, andando de bicicleta pela estrada ❤️ do penhasco da praia. Coloquei meu próprio carro-de duas rodas onabet 2 cream Birmingham e saí para Wismar norte alemão; depois ❤️ segui a rota bem sinalizada ao redor das encantadora vila à beira mar K'hlungborn (a cidade velha com o seu ❤️ nome é uma ilha). Pared for an lir beach time at Warnem -nde and have some sardinha to my wild ❤️ báltical Berry’ gry glaceed by the sist balking cafees Rostock isse
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País da Reforma ao sul de Berlim
Mercado de Wittenberg.
: Animaflora/Getty 
Imagens
Em 1517, Martinho ❤️ Lutero pregou suas 95 teses na porta da Schlossekirche em
Wittenbergae
, mudando para sempre o mundo ocidental dando início à Reforma. ❤️ Explorar este canto do leste da Alemanha revelará belas cidades e vibrantes cidade raramente visitadas por turistas ocidentais Wittenberg (60 ❤️ milhas a sudoeste de Berlim), onabet 2 cream si é uma maravilha medieval no rio Elba! Fora dos trilhos batidos está Eisleben ❤️ - Uma vila enxaimel onde você pode visitar local natal Luther'S O Wartburg É um imponente castelo que se eleva ❤️ sobre Eisenach A terminaronabet 2 creamviagem na casa principal
Halle
A máscara de morte do Lutero pode ser vista na Igreja Mercado, ❤️ onde ele também deu alguns sermões. Aqui outro grande alemão compositor George Frederick Handel foi batizado e tocou órgão ❤️ da igreja quando estudava Wilhelm Friedemann Bach (filho mais velho) Johann Sebastian era organista aqui 1764-1765.[1]
Nick.com
Ethos punk e delícia turca, ❤️ Kreuzberg onabet 2 cream Berlim.
Street art onabet 2 cream Kreuzberg.
: David Angel/Alamy
A grande comunidade turca de Berlim deixou uma marca indelével na cultura culinária ❤️ e artística da cidade como um todo, é no bairro Kreuzberg onde esta fusão única está melhor experimentada. Comece com ❤️ a refeição do restaurante Mardin que serve os melhores kebabs fora Turquia juntamente
ayran
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Bruno
Colônia além da catedral
Parque Palais im no ❤️ jardim botânico, Colónia.
: Joern Sackermann/Alamy
Eu realmente gostei de Colônia enquanto visitava minha filha. É uma cidade tão relaxada, com grande ❤️ população estudantil e longe da incrível catedral gótica – a atração mais popular do futuro alemão - há história para ❤️ ser descoberta onabet 2 cream todos os tipos dos lugares que são melhor explorados por bicicleta nas ciclovia roades (estrada) através vários ❤️ parques O museu urbano Klnisches Stadtmuseum é o lugar onde você se mudou recentemente na Minoritenstrasse como um belo local ❤️ no mundo!
Mark Anstee
Dica vencedora: bandas de oompah e lager onabet 2 cream Knigssee, Baviera.
Lago Knigssee, Baviera.
: Marco Bottigelli/Getty 
Imagens
No verão passado, ❤️ meu parceiro e eu acampamos no lago de Salzburgo (acostar) na Alemanha com o 49 Deutschland-Ticket oferecendo transporte público ilimitado ❤️ onabet 2 cream todo país por um mês. Um destaque foi explorar Kínigsee para uma estação ferroviária conectada ao parque nacional Berchtesgadener ❤️ da Baviera; este pequeno resort oferece fantásticas rotas pedestres ou ciclismo que variam nos níveis das dificuldades do dia: você ❤️ subiu à pé pelo ônibus Jennenbahn! A temporada completa é feita pela cervejaria
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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). ♠
site de apostas é legal
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OnABet: Por que não oferece bônus e por que isso é importante no Brasil
No mundo dos cassinos online, os bônus são uma ferramenta comum usada por muitas plataformas para atrair e recompensar seus jogadores. No entanto, existem algumas plataformas, como a OnABet, que optam por não oferecer bônus aos seus jogadores. Neste artigo, vamos discutir por que isso acontece e por que é importante no contexto brasileiro.
Antes de entrarmos no vivo do assunto, é importante entender o que é exatamente um bônus de cassino online. Em geral, um bônus de cassino online é uma oferta promocional oferecida por um cassino online para incentivar os jogadores a se inscreverem, depositar e jogar onabet 2 cream seu site. Esses bônus podem assumir a forma de dinheiro gratuito, giros grátis ou outras recompensas.
Por que a OnABet não oferece bônus
Existem várias razões pelas quais a OnABet pode ter decidido não oferecer bônus aos seus jogadores. Algumas das razões mais comuns incluem:
Por que é importante no contexto brasileiro
Embora a OnABet possa ter suas razões para não oferecer bônus, é importante considerar o contexto brasileiro. No Brasil, o jogo online é uma atividade popular e onabet 2 cream expansão, o que significa que há uma grande demanda por plataformas de cassino online que ofereçam bônus atraentes.
Além disso, o Brasil é um mercado altamente competitivo, o que significa que as plataformas de cassino online precisam oferecer bônus competitivos para atrair e manter jogadores. A falta de bônus na OnABet pode ser um ponto negativo para alguns jogadores, especialmente aqueles que estão procurando por ofertas promocionais atraentes.
Além disso, é importante considerar que o Brasil tem uma taxa de jogo compulsivo relativamente alta onabet 2 cream comparação com outros países. Isso significa que as plataformas de cassino online no Brasil precisam ser especialmente cautelosas ao oferecer bônus, pois podem incentivar alguns jogadores a jogar de forma compulsiva.
Conclusão
A falta de bônus na OnABet pode ser um ponto negativo para alguns jogadores, especialmente aqueles que estão procurando por ofertas promocionais atraentes. No entanto, é importante considerar as razões pelas quais a OnABet pode ter decidido não oferecer bônus, bem como o contexto brasileiro onabet 2 cream que a plataforma opera.
Em geral, é recomendável que as plataformas de cassino online no Brasil ofereçam bôn
site de apostas é permitido no brasil
onabet 2 cream
No mundo moderno de hoje, estamos constantemente procurando por soluções rápidas e eficazes para nossos problemas diários. Isso é especialmente verdade quando se trata de nossa rotina de beleza. Com tantas opções disponíveis, pode ser difícil saber qual produto é realmente eficaz e vale a pena o investimento.
Um dos produtos que tem ganhado popularidade nos últimos tempos é a Onabet Cream. Essa creme especial é dita ter uma variedade de benefícios para a pele, desde a hidratação profunda até a redução de rugas e sinais de envelhecimento. Mas o que realmente faz a Onabet Cream se destinar e por que você deveria considerar adicioná-la à onabet 2 cream rotina de beleza?
onabet 2 cream
A Onabet Cream é uma creme hidratante avançada que é rica onabet 2 cream onabet 2 cream ingredientes naturais e clinicamente testados. Foi especialmente formulada para ajudar a combater os sinais do envelhecimento e manter a pele saudável e hidratada. Alguns dos principais ingredientes ativos da Onabet Cream incluem:
Como usar a Onabet Cream
A Onabet Cream é fácil de usar e deve ser aplicada diariamente na pele limpa e seca. Basta tomar uma pequena quantidade de creme e massajar suavemente onabet 2 cream onabet 2 cream todo o rosto e pescoço, concentrando-se onabet 2 cream onabet 2 cream áreas específicas de preocupação, como rugas e linhas finas. É recomendável usar a Onabet Cream duas vezes por dia, uma vez de manhã e uma vez à noite, para obter os melhores resultados.
Benefícios da Onabet Cream
A Onabet Cream oferece uma variedade de benefícios para a pele, incluindo:
Por que a Onabet Cream é diferente?
A Onabet Cream se destaca das outras cremes hidratantes graças à onabet 2 cream fórmula avançada e ingredientes naturais cuidadosamente selecionados. Além disso, a Onabet Cream é clinicamente testada e comprovada para ser segura e eficaz. Além disso, a Onabet Cream é uma opção cruelty-free, o que significa que nenhum animal foi ferido ou maltratado durante o processo de fabricação.
Onde comprar a Onabet Cream no Brasil
A Onabet Cream está disponível para compra online no Brasil. Quando você comprar a Onabet Cream, você pode ter certeza de que está obtendo um produto de alta qualidade a um preço justo. Além disso, a Onabet Cream vem com uma garantia de satisfação de 30 dias, então você pode experimentá-la sem risco. O preço da Onabet Cream no Brasil é de R$ 199,00 por unidade.
Conclusão
Em resumo, a Onabet Cream é uma excelente opção para aqueles que desejam manter a pele hidratada, saudável e jovem. Com onabet 2 cream fórmula avançada e ingredientes naturais, a Onabet Cream oferece uma variedade de benefícios para a pele, incluindo hidratação profunda, redução de rugas e linhas finas, proteção contra radicais livres e melhora geral da textura e tom da pele. Se você está procurando uma creme hidratante eficaz e de alta qualidade, a Onabet Cream é definitivamente vale a pena considerar.