This article was interesting, but not surprising. For example, take the following from the article:

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So, while there can be a significant disadvantage to treating betting rounds independently, and for real poker games there is almost certainly a significant disadvantage to doing so, for some types of games it's possible that such an abstraction may not be as horrendous as it first appears.

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I submit that such an abstraction may not be "horrendous" at all. There are very good players that choose to play street-by-street every day. I also sumbit that for players who make street-by-street decisions, but are also good multistreet players, given a large enough sample size of played hands, one could actually measure just how "horrendous" street-by-street playing really is.

Who are these successful steet-by-street players? Multitablers, or course.

Obviously, someone playing 24 tables* can not usually implement multi-street strategies. There are several reasons for this. A multitabler misses a lot of the action, so he really doesn't know whether other players are reacting to his strategy, or to other players in the hand. And even if he is capable of looking at the table for 3 seconds on every street, and then completely comprehending all the strategy and action, that doesn't mean he'll be able to keep it in his head and sort it out from the 23 other tables that he is playiing. (This might be an interesting thing to ask Sklansky about on the Pokercast).

In fact, I submit that it is safer to, as Dan Harrington would say, "keep it simple", then to try to remember the details of multistreet strategies on every table. For most players, it would be too easy to get confused and actually make a worse decision than if they were making decisions on a street-by-street basis.

So, given a large enough sample size, we could record the results of players at 24 tables up to a statistically valid sample size. Then we could have those same players single-table, we could record the results, and we could see how large the difference is.

But there is a problem. Multitabling is profitable in and of itself, regardless of the win rate of the player. Just as it is sometimes profitable for a baseball player to deliberately make an out (for example, a sacrifice bunt that allows the runner on third base to score), it can also be profitable for a multitabler to accept a lower win rate in exchange for more rakeback, frequent player points, reload bonuses, etc.

I just started playing poker full-time this year, starting at the micros and grinding my way up. Even if I have what I would consider a very good year playing on PokerStars, another player could actually lose money playing poker, but make several times my income because he multitables and plays high enough that he gets reload bonuses, cash bonuses from the FPP store, milestone bonuses, and SuperNova Elite status. Joe can earn a six figure (over $100,000 US) income even if he is a slight loser at the tables.

So, multistreet playing is more profitable (in the sense of actual cash dollars won, or tournament cashes). A simple experiment with good multistreet players could measure this difference. But in the end, it may not matter. I want to make a profit at the tables, thereby building a bankroll to play higher. Joe next door wants to play a bunch of tables at a high enough level to become a Supernova Elite, and actual poker-playing profits are nearly irrelevant.

While Joe's approach will lead to mostly single-street playing, his decison is not "horrendous" at all. Like the batter who deliberately makes an out so that his team scores a run, Joe's decison to deliberatly sacrifice profit and use a single-street strategy strategy, in order to make Suprenova Elite, is not horrendous. It's plus EV.



*In fact, some players many more tables than this. In the Official Double or Nothing Strategy Thread, one player stated that he plays 50 tables, playing on both Full Tilt and PokerStars.

This is the classic trade-off...
Between "optimal play" and "volume"...
In all Zero Sum Games played by a human.

You can make a LOT more money...
** Sub-optimally ** playing 12-16 tables at 3.0 BB/hour...
Than ** optimally ** playing 4 tables at 6.0 BB/hour.

Rakeback magnifies this phenomenon.

I deal with this as a trader every day...
It's obvious that I make a LOT more money...
Executing 1,500 "5 second" sub-optimal decisions/day...
Than with 200 "60 second" optimal decisions/day.

If Grandmasters played chess for money...
They would play a sub-optimal variation of speed chess.

Genius level abstraction and simplification plays a big role...
Elite players/traders use multiple short cuts...
That ** approximate ** optimal decision making...
But allow rapid action and maximize volume.

I doubt this kind of abstraction can be taught...
It's very much a function of 1,000s of hours experience...
And is largely automatic... on a sub-conscious level.

It's not necessarily 3bb vs 6bb, it can be more like 3bb vs 12bb, or even a lot higher like 20+bb. You need to factor that in the realistic amount of tables you need to play to make up for bbs lost and how many to actually make it +EV.

Also you need to factor in burnout rate, how long can you stay focused at 24 tables vs say 6 tables.

It can be more a question of playing style, the 24 tables are prob more ADD and drink too much coffee vs a more laid back focused style.

As the author of the article, I completely agree with the statement made in this post. Online massive multi-tablers are a good example of successful players who largely play street-by-street strategies.

It wasn't clear from my article, but when I suggested that street-by-street play might appear to be horrendous strategy at first blush, I was comparing it to an optimum multi-street strategy. Obviously, one can still be a successful poker player playing a horrendous strategy as long as one's opponents play worse, and as the original research suggests, but doesn't prove, it's not clear that a street-by-street strategy couldn't come close to an optimal strategy anyway.

Nothing I said in the article should imply that I think that people shouldn't be multi-tabling. The analysis folks in this thread are doing represent exactly the right trade-offs when deciding how many tables to play. I'm just glad someone found the article worth reading.

I really liked the article and I'm looking forward to the next part.

I have a decent math/game theory background and made it through "The Mathematics of Poker" (at least the parts I'm interested in) but most of the academic articles on poker still go over my head. They always seem to leave out some critical details that would help recreate what they did, and there is a lot of jargon as well. Can you suggest books/reading material that might help bridge the gap?

Thanks. I expect to have another article like this for the August issue. If there are specific publications or areas of research that someone thinks would be good to cover, let me know. I'm curious as to what the readership thinks would be most worthwhile to them.

The difference between a text book such as "MoP" and a journal article is that the journal article assumes a great deal of background on the part of the reader. If you're trying to understand an article in a research field that's new to you, typically you'd go through the list of citations, track most of those articles down, see what they cite, track those down, and work your way back until you understand the basis for the research in question. It's a lot of work for anyone, including seasoned academics. The "Abstraction Models" article is about as gentle as these things get.

I'm not sure any general background material would help, it depends on the specific avenue of inquiry. It's tough to do this work without access to a good university research library.

Great article. Abstracting an article about abstraction - I like it!