The Poker Tournament Formula by Arnold Snyder...

[Radar_O'Reilly]

[ QUOTE ]
Somehow this discussion reminds me of an example from "Gambling Theory and other Topics". On page 12 Mason writes about rolling a dice 10000 times for $1 and then 1 time for $1 million. Statistians will tell you that there was only one roll, because the results are all clustered around that one big bet.

Fast tournaments are similar. From my limited experience I can tell that people are playing the biggest pots when their M is between 5-10. Statistically those 20 minutes when the stack is still in the green zone at the beginning of the tournament shouldn't matter.

[/ QUOTE ]]

First, your stack in the Friday night Orleans tournament is in the green zone for a full hour, not 20 minutes. That's what makes it a good fast tournament. One of the things The Poker Tournament Formula does is provide players with a formula for choosing tournaments where you can genuinely obtain an advantage. There is no point in playing crapshoot tournaments if you intend to make money. All you will do in crapshoot tournaments, over time, is lose the house fee.

Second, in addition to agreeing with BigA/K's response, I want to add that you are misunderstanding the significance of when bad players are getting in most of their action. Good fast tournament players, who have built big stacks early, will tend to be in the green zone for most of the time in the tournaments they play. The whole point of optimal tournament strategy is to use a strategy that will get you into the green zone and keep you there.

When you are routinely playing in the green zone, while the fish are waiting to get in their action at times when they have no edge, you are going to dominate.

So, I will actually agree with you that the fish, who are the majority of players in fast tournaments, get in the bulk of their action at 5-10M. That is precisely why they are fish. You are right, for fish any action in the green zone is statistically insignificant. Good players, by contrast, make most of their money in the green zone. The green zone is where they are getting in their statistically significant action.

[alegendaryplayer]

Inbetween Levels inbetween M theory (ILIMT)

When you find your self in the position of being in the small green zone almost in the yellow and when the level change you will find your self in the yellow zone. And there isn´t enough hands left of the current level that will in random you will be dealt one conservative hand. Then you must change your strategy. Because now you M system doesn´t work as well i think. How to overcome this? Simply do some creative bluffing/stealing when the timing is right. Pretty simple be aggressiv to stay in the green zone. Also it will help you reduce some of your supertight image. Works well, not to much of a risk. Then when you got the greenzone M of the next level and wait for that conservative hand and win a huge pot.
To sum it up, Use your skill when you got it. Instead of wait till your skill has been reduced. I think both Harrington and Snyder says this in a way. But if I remeber Harrington miss to explain when you should try to maintain your skill. And Snyder solves the problem by playing the aggressiv or superaggressiv style, but the conservative works well but when the random good hand maybe not come in this level then you are in the BM zone (between M). And if your M switches when the blins go up, you should play little different.

[Ortho]

[ QUOTE ]
There comes a point in all fast tournaments and many slow tournaments where due to the ratio of blinds to average stack size the tournament has become a crapshoot. If all the survivors reach this point with the same stack size then statistically they'll all have an equal chance of winning. If we say for our example that this happens when reaching the final table and it will have 10 people then everyone has a 10% chance of finishing in each of the top 10 positions. When a tournament reaches this point (still assuming equal stack sizes) then skill no longer influences the outcome, only short term luck in the cards you're dealt and whether they hold up or not. In the book there is a method to rate how fast a tournament is and lays out a strategy for each. Certain tournament speeds are essentially crapshoots from the beginning. But for those that are slower than these, but still fast there is a distinct advantage to reaching the "crapshoot" portion with a bigger than average stack. The best time to build that stack is when your opponents are playing the traditional conservative strategy.

[/ QUOTE ]

I am quite interested in this discussion and am so intrigued by the main question under discussion here that I don't have an opinion about it, but I know that this is wrong.

Of course there is a point where a tournament turns into a crapshoot, implying that there is no skill possibly involved because either the structure precludes it (i.e. the tournament is only one hand long and everyone has less than the ante or something) or that the skill factor is so small that everyone will be able to play correctly.

Of course there is a point where this is the case, but it is much later than you think. Late in a tournament, often the biggest mistake that you can make is to fold too much when the blinds and antes are so valuable compared to your stack size. However, in every tournament I've ever played (thousands of stts, hundreds of multis), you can see people making this mistake all the time. In general, they are not aggressive enough when they push and not tight enough when they call. In order for the tournament to truly be a crapshoot, these players would have to be playing correctly in these situations, and the fact is simply that they are not.

I don't think that it matters that much to the real discussion that's going on here, because if you can show, as mentioned several times above, that it is correct to take -ev situations in order to stay in the green zone or to maintain a certain stack size (everyone agrees that its +EV to take +EV situations, at least everyone who's arguing for a fast style here, so we can leave that aside), then you don't need all this hand-waving about crapshoots and luckboxes and how no one has a skill advantage. I have played in lots of insanely fast tournaments, and these things would be a crapshoot if everyone played well, but they don't.

[Ortho]

[ QUOTE ]
There is no point in playing crapshoot tournaments if you intend to make money. All you will do in crapshoot tournaments, over time, is lose the house fee.

[/ QUOTE ]

I agree with all your other points in this thread, but, as with the other poster, this is incorrect. Of course a player's edge is significantly smaller in a 'crapshoot' tournament, but, unless you are playing bingo instead of poker, it still exists. And, even if my edge is very small, I can make money in tournaments applying it. Plus, a faster structure enables me to play more tournaments/day, so online (or live, if you are profitable in side games) it is not such a big concern whether my ROI/tournament is maximised. Can an edge be so small as to make it impossible to overcome the entry fee? Of course, theoretically, but certainly very few online tournaments have a structure that fast. Perhaps you are commenting more on live play, and perhaps there are much faster structures in live (there is a live rebuy here in London that starts you with 500 chips and blinds at 25/25 and I do not think that this is too fast for me to have a huge edge, because the players are so bad), and perhaps those are more common than I realise, but your assertion is not true online.

As I said, I agree with or am at least intruiged by most of the points that you're making here. I am beginning to think that if the "tournament speed" assertion is wrong, it is because the player's late-game and bubble edge is being assumed away (i.e. it is possible that Mason is here paying not enough attention to the forest and too much to each individual tree, but if you are wrong, it will be, imo, because you are looking too much at only the forest).

And, you don't have to have a dig at Mason to make your point. I don't care for many of David or Mason's posts, but it is not too much to be polite when we're talking, if only to make sure that this interesting conversation is to continue.

[Mason Malmuth]

[ QUOTE ]
This, in my opinion, is irresponsible of you, Mason. And acting hurt about a perceived insult may pull in the troops to defend you, but does not resolve the problem.


[/ QUOTE ]

Speaking of pulling in the troops, where did you come from. You never posted here before until this book began to be discussed and it's the only topic you have ever posted on.

Now let me explain it to you one more time. Tournament speed has nothing to do with how you should play a hand. What is important is the cost per round and how your chip stack relates to that. This is what Dan Harrington and Bill Robertie call M in Harrington on Hold 'em: Volume II.

Furthermore, it just so happens that in the type of tournaments that Snyder is addressing, your M will usually, but not always be low. Thus the very aggressive plays that he recommends are usually right. But they're not right because because the stakes go up every 20 minutes as compared to every 40 or 60 minutes. They are right because you will, using Harrington terminolgy, most of the time be out of the Green Zone. However, on those occasions where you are playing one of these tournaments and you just happen to be in the Green Zone, you should not play as Snyder advises (unless it is a situation where you can take advantage of an opponent's tight play).

Now let me add one more thing which I have already stated several times in this thread. The Poker Tournament Formula will help most people play with a higher expectation than they currently do in the small buy-in tournaments. So again trooper, thanks for the insults.

MM

[Mason Malmuth]

Hi Ortho:

[ QUOTE ]
As I said, I agree with or am at least intruiged by most of the points that you're making here. I am beginning to think that if the "tournament speed" assertion is wrong, it is because the player's late-game and bubble edge is being assumed away (i.e. it is possible that Mason is here paying not enough attention to the forest and too much to each individual tree, but if you are wrong, it will be, imo, because you are looking too much at only the forest).


[/ QUOTE ]

Assuming you're a good tournament player there is no question that your edge is smaller in a fast tournament than in a slow one. But that's because you will play a proportionately smaller number of hands in the Green Zone, and it's in the Green Zone that you are a complete poker player.

Put another way, when you're in the Red Zone, your play and that of a live one won't be very different, which is unlike the case of when you are in the Green Zone. (The exception to this would be a player who still insists on playing very tightly when low on chips.) However, and here it is again, you should make your playing decisions based on your chip position and that of your opponents. If it turns out that your M is low, you'll play one way, and if your M is high, you'll play another. It also turns out that in the fast tournaments your M will frequently be low and thus the correct decisions become consistent with Arnold's advice.

By the way, when you read the Harrington books many of the examples are from fast tournaments. But it doesn't matter. The decisions are based on M.

Best wishes,
Mason

[Mason Malmuth]

Hi Everyone:

The following are a few quotes from our new friend that appeared on Arnold Snyder's site at www.blackjackforumonline along with my comments. By the way, I have known Arnold for a very long time and consider him to be one of the good guys in the world of gambling literature. I do however, don't agree with his premise that tournament speed determines your strategy.

[ QUOTE ]
I have to point out that Mason is responding to points in the book without actually having read the book.


[/ QUOTE ]

I've read the first 216 pages and by just thumbing through the remaining pages it appears to address completely different topics than what we have addressed in this thread.

[ QUOTE ]
It is the first and only book in the poker tournament literature to address how tournament speed affects optimal tournament strategy.


[/ QUOTE ]

That's not true. I can think of three others.

[ QUOTE ]
It is the first and only book to show that the strategies provided by Harrington, Cloutier, and the rest of the literature are incorrect for fast tournaments, and suboptimal for slow tournaments made fast in later stages by field size.


[/ QUOTE ]

First off, the Cloutier books are not the most highly thought of. Second, this is all addressed in Harrington II: The Endgame.

[ QUOTE ]
It provides a radically different playing strategy than Harrington, Cloutier, and the rest of the literature for any point in a fast tournament where a player has a competitive chip stack. It also shows how to alter this strategy as tournament structure is altered.


[/ QUOTE ]

I agree with your statement about Cloutier. But even Arnold himself told me that the advice was very similar to what was in Harrington II.

[ QUOTE ]
It is the first and only book in the poker tournament literature to provide the mathematical foundation for the value of a big chip stack.


[/ QUOTE ]

Again, back to Harrington II.

[ QUOTE ]
It is the only serious mathematically based discussion in the literature of optimal rebuy strategy.


[/ QUOTE ]

That's not true. Most of this was originally written up almost 20 years ago.

[ QUOTE ]
It is the first and only book in the poker tournament literature to discuss the mathematical basis for bankroll requirements for tournaments, and show how these requirements are altered by field size.


[/ QUOTE ]

That's not true either.

Finally, I do agree that tournament speed does affect the luck factor in tournaments. The faster the tournament, the more important luck and the less important skill. I also agree that there might be some tournaments out there which are so fast that they're not really worth playing assuming you're a skillful player. Where I disagree is that this means you alter your strategy away from your M and the M of your opponents.

Best wishes,
Mason

[Radar_O'Reilly]

I am a professional gambler and a well-known poster and moderator on Arnold Snyder's web sites www.blackjackforumonline.com and www.pokertournamentformula.com.

Again, Mason simply restates his belief that tournament structure does not affect optimal strategy, without refuting the case made in The Poker Tournament Formula. Instead of refuting the case made in the book, he attempts to dismiss the book's case with an attack on my newness at this site.

But my newness at the 2+2 site has nothing whatsoever to do with the legitimacy of the claims in The Poker Tournament Formula, or my insistence that Mason must show how these claims are to be refuted if he is to be considered to have made his case that structure doesn't affect optimal strategy. In order to show that tournament structure doesn't affect optimal playing strategy, he has to show one of the following:

1. He has to show that in a fast tournament you will be as likely to remain in the Green Zone--a fully functional poker player, with a fully functional poker player's skill options and edge--with conservative play as with fast play. Let's look very closely at the likelihood of that. In the Mirage Tuesday night tournament, a fast tournament where the blinds go up every 30 minutes, you have 30 minutes in the green zone assuming you don't play a hand, and assuming you go through the blinds only one time. In the WSOP main event as of the time Harrington published the first volume of his book, an event in which blind levels lasted 2 hours, you had 6 hours in the green zone, assuming you never played a hand and paid the blinds every 20 minutes. In order for Mason to be correct that tournament structure doesn't matter, he has to show that a player will get as many of Harrington's green zone starting hands in the 30 minutes available at Mirage as you would get in the 6 hours available at the WSOP main event.

Again, as I said in my post titled "I think Mason is relying on too narrow a definition of M", on p. 132 of Harrington on Hold'em II, Harrington defines the underlying logic of M this way: "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."

In the Mirage tournament in this example, you need to make a 50% increase in your chips in 30 minutes, or 15 hands, in order to stay in the green zone (or maintain an M greater than 20). That is, because the blinds at level 2 equal $150, you need to have increased your stack in only 15 hands by over $1000, up from $2000 to $3000, to stay in the green zone in the Mirage tournament.

A player in the WSOP main event with 2-hour blind levels, by contrast, must increase his stack by only 10% to stay in the green zone into the 7th hour of play. With blinds/antes at Level 4 of $550, this player must increase his $10,000 to an amount over $11,000, over a period of 6 hours (or approximately 180 hands) in order to maintain an M greater than 20.

Clearly, you do not have the same likelihood of increasing your chip stack sufficiently with Harrington's conservative green zone strategy in the 15 hands available at the Mirage as you do with the same strategy in the 180 hands available in the WSOP event. You do not have the same likelihood of meeting Harrington's own criterion of getting "a better hand in a better situation, with a reasonable amount of money left." (Honestly, Harrington recommends on p. 57-58 of HOH II that the conservative player should bluff approximately once every hour and a half, or every 50-60 hands, and he is including stealing the blinds. That is a recipe for death in a fast tournament.)

In the Mirage tournament, Harrington's "Formula M" becomes a false measure of the underlying logic of M because the M is declining so rapidly.

If staying in the Green Zone is important (and again, Harrington himself states, on p. 129 of HOH II: “In the Green Zone you’re a fully-functional poker player, and it's worth taking some risks to stay there" (and the italics are Harrington's) then the conservative green zone strategy clearly won't often fit the bill in the fast Mirage tournament.

Instead, you need to switch to a fast strategy, which means that your strategy options have been altered by the tournament structure.

And, by the way, some of the players in this thread seem to believe that a fast strategy is a negative EV strategy. There is no basis for this belief. Harrington in no way makes any claim that his conservative strategy is the only viable poker tournament strategy. Mason himself states, in an earlier post in this thread, that the fast strategies in Arnold Snyder's book are used by some of the best players in the world. Any player who believes a fast strategy is a negative EV strategy has too narrow a view of what gives a player an edge in a poker tournament. A conservative strategy relies primarily on one set of poker skills that can give a player an edge. A fast strategy relies on a different, but at least equally valuable, set of poker skills that can give a player an edge.

I have already posted several times that there are two other points Mason could try to refute to counter the claims of The Poker Tournament Formula. Here are points 2 and 3:

2. Mason could refute the claims of The Poker Tournament Formula by showing that Arnold's math is wrong in Chapter 10 of the book, where Arnold shows the mathematical basis of the edge a big chip stack has over a small chip stack in a tournament. If both Harrington and Snyder are wrong about the value of a big stack (or staying in the Green Zone), then there would be no need to change your strategy in fast tournaments to stay in the Green Zone.

OR

3. Mason could refute the claims of The Poker Tournament Formula by showing that you are not limited in your skill options when you sink below the green zone. This appears to be the case that Mason is trying to make. He keeps stating that you play green while green, and switch to orange and red when you get down to orange and red, as if sinking to orange and red did not limit your ability to use a full range of skill options, and thus limit your edge. He seems to believe that the automatic change in strategy inherent in following strict Formula M in itself is the equivalent of the ability to use a full range of poker skills. But Mason is not only in disagreement with Snyder in this view, he is also flying in the face of his own author. Again, Harrington, starting on p. 129 of HOH II, clearly states that the Green Zone is where you are a fully-functional player, that it is worth taking some risk to stay there, and begins discussing the skill options that are stripped from you as you sink into the yellow, orange, and red zones.

Although Mason has repeated in numerous posts in this thread his belief that tournament structure does not affect optimal strategy, he has not refuted any of the above points, and thus has not refuted Arnold Snyder's claim that tournament structure affects optimal poker tournament strategy.

Mason further claims that the available edge from fast tournament play is limited by the fact that, with conservative strategy, your time in the Green Zone will be very short. Again, his claim of a limited edge is true only for players using a suboptimal conservative strategy, or who are playing in tournaments so fast that the structure essentially disables the edge of any skilled player by forcing him to play the same as every other desperate player. (Arnold Snyder provides a method of quantifying the speed and skill level of a tournament so that these too-fast tournaments can be avoided.) But many fast tournaments offer a very high edge for optimal strategy. Players using fast strategies optimized for the structures of fast tournaments will find that they have plenty of time in the Green Zone, and as a result have a truly strong professional gambling edge. Arnold states that he has maintained an edge over 200% throughout his fast tournament play.

The players whose edge will be sharply reduced are the players who insist on sticking to a suboptimal strategy for the tournament structure. If you are sticking to Harrington's conservative Green Zone strategy in fast tournaments, you will not be in the Green Zone long enough or often enough to get much of an edge at all.

[Men the Master]

Just a guess but I think Radar is to Arnold Snyder what Robertie is to Dan Harrington. Snyder, who has written a very good bookIMO, mentions Radar in the early part of the player classifications chapter and gives him credit for some of the player types discussed there.

[Radar_O'Reilly]

I will now address Mason's response to my posts on the poker forum at www.blackjackforumonline.com

In my post at www.blackjackforumonline.com, I stated that Mason was disputing the book without having read the book. Mason replies:

[ QUOTE ]
I've read the first 216 pages and by just thumbing through the remaining pages it appears to address completely different topics than what we have addressed in this thread.

[/ QUOTE ]

My response: In his first posts about the book, where he called the book a confused version of Harrington's M, Mason stated clearly that he had read less than half of the book. Then in a later post, after many assertions that the book was wrong, he stated that he had finally gotten to p. 172. The book is 350 pages, not counting the glossary, index, etc.

In my post at BJF I said: It is the first and only book in the poker tournament literature to address how tournament speed affects optimal tournament strategy.


Mason answers:
[ QUOTE ]
That's not true. I can think of three others.

[/ QUOTE ]

My reply: I read the 1985 McEvoy book you cited as the first book to address the effects of structure on optimal strategy. McEvoy wrote less than a paragraph on this issue. All he writes is a vague statement that fast tournaments require faster play, especially when they're rebuy tournaments. He in no way provides the detailed strategy or analysis that is provided in Snyder's book.

In my post at BJF I said: It is the first and only book to show that the strategies provided by Harrington, Cloutier, and the rest of the literature are incorrect for fast tournaments, and suboptimal for slow tournaments made fast in later stages by field size.

Mason answers: [ QUOTE ]
First off, the Cloutier books are not the most highly thought of. Second, this is all addressed in Harrington II: The Endgame.

[/ QUOTE ]

My comment: Snyder's book shows how structure alters not only optimal strategy at the end of a tournament, but, in a fast tournament, primarily at the beginning of a tournament. Also, Harrington's writing on the Endgame does not address how field size can speed up the end of a tournament and alter optimal strategy. Harrington talks about making moves at middle-sized stacks on the bubble. Snyder shows that the bubble can become the effective end of the tournament due to tournament structure. Harrington mentions that tournaments can become a headlong race at the end, but he doesn't identify the factors that make some slow tournaments a headlong race while others are not, nor does he address how to alter strategy to have an edge at the end when a tournament is going to become a headlong race due to its field size and structure.

In my post at BJF I said: It (The Poker Tournament Formula} provides a radically different playing strategy than Harrington, Cloutier, and the rest of the literature for any point in a fast tournament where a player has a competitive chip stack. It also shows how to alter this strategy as tournament structure is altered.


Mason's response: [ QUOTE ]
I agree with your statement about Cloutier. But even Arnold himself told me that the advice was very similar to what was in Harrington II.

[/ QUOTE ]

My response: It is similar ONLY in acknowledging that speed of play necessarily goes up as your stack gets short relative to the costs of a round. It is extremely similar to Harrington in the strategy for how to play once you've gotten short. But that is where the similarity ends. Arnold Snyder's basic strategy of fast play is unique. This type of fast strategy has never been written about in this detail before. He has presented an entire basic strategy of fast play that is, in fact, at odds with Harrington's conservative green zone strategy, as has been pointed out by many of the players posting in this thread, and as has also been pointed out by numerous players at blackjackforumonline.com.

From my post at BJF: It is the first and only book in the poker tournament literature to provide the mathematical foundation for the value of a big chip stack.


Mason replies: [ QUOTE ]
Again, back to Harrington II.

[/ QUOTE ]

My reply: No other author, including Harrington in HOHII, has shown the mathematical basis of the edge a big stack gains in a tournament over a small stack. Please provide the pages where Harrington provides comparable mathematical analysis.

I wrote in my post at BJF: It is the only serious mathematically based discussion in the literature of optimal rebuy strategy.


Mason says: [ QUOTE ]
That's not true. Most of this was originally written up almost 20 years ago.

[/ QUOTE ]

My reply: Again, if this is so, please provide your source. And, if this is true, please state why Sklansky, in Tournament Poker for Advanced Players, sends us for rebuy strategy to the inadequate treatment of the topic in Poker Tournament Strategies, by Suzuki (published by you in 1998). Sklansky is, in fact, incorrect in the very limited rebuy strategy he provides in Tournament Poker for Advanced Players. He says: "I think a decent rule of thumb would be to add on if you have less than the average amount of chips at that point, but not otherwise." The only exception he makes is for discounted chips. But he is incorrect, because he fails to recognize the advantage inherent in a bigger stack. Arnold Snyder shows the advantage in great detail. Sklansky and Suzuki also fail to recognize the value of extra chips in a situation where M is going to be declining so rapidly.

I said in my post at BJF: It is the first and only book in the poker tournament literature to discuss the mathematical basis for bankroll requirements for tournaments, and show how these requirements are altered by field size.

Mason says: [ QUOTE ]
That's not true either.

[/ QUOTE ]


My response: This is another of Mason's assertions with no proof. Are you saying that others have provided a mathematical basis for tournament bankroll requirements, with adjustments for field size? If so, please cite your source.


Mason says: [ QUOTE ]
Finally, I do agree that tournament speed does affect the luck factor in tournaments. The faster the tournament, the more important luck and the less important skill. I also agree that there might be some tournaments out there which are so fast that they're not really worth playing assuming you're a skillful player. Where I disagree is that this means you alter your strategy away from your M and the M of your opponents.

[/ QUOTE ]

My response: I have already refuted this statement in a post I made just prior to this one. The luck factor in fast tournaments is radically decreased by using strategy optimized for fast tournament structure. If you insist on using suboptimal conservative strategy in a fast tournament, however, you will have little to no edge.