The Table Selection Game!

Yeah, I robbed this idea from another forum, but imitation is the greatest form of flattery, so nyah! And I'd like some of the newer players to take a shot at this. Doesn't help much if like Zachvac comes in and gives all the answers away :P

Which table would you rather sit at?

And you can't say "none, because these are all at Ultimate Bet".

This is obviously 6max 10c-25c NLHE.

Assume that the following player types have the following stats:

Fish: 65/3/0.5 (plays too many hands, very passive)
Nit: 9/5/1.2 (plays very few hands, moderately aggressive)
Shark: 20/19/3.1 (very solid, aggressive player)

Situation #1:

Table Kingman or Table Little Rock?

The % is players per flop, and the $ value is the average pot size.



Situation #2:

Table A or Table B?

Table A



Table B



Situation #3:

Table A or Table B?

Table A


Table B



Situation #4:

Table A or Table B?

Table A


Table B



Might do a few more of these if people are interested, but I figured I'd start with the basics.

Table Kingman. Lots of fast money going on that table. It's ripe for the picking.

Table A. Fish will go in with anything and hit with the same. You have a chance at this table of controling the play and getting value for good hands.


Table B. I want the fish to my right to call his massive all in bet with A2os and having nothing on the board.


Table A. I want the shark not to be able to control my bets.

Which ones better, #1 or #2?

#1 or #2?

#1 or #2?

Feels like the optometrist lol

Situation #1: how about both! Ok, putting aside the question of multi-tabling and/or if you should sit in the first place at all, here's how I see it:

1.JPG (http://www.cardschat.com/attachment.php?attachmentid=12013&d=1217205030)
A/Kingman, higher vp$ip

2.JPG (http://www.cardschat.com/attachment.php?attachmentid=12014&d=1217205030)
A, more fish

3.JPG (http://www.cardschat.com/attachment.php?attachmentid=12015&d=1217205030)
B, position on the fish

4.JPG (http://www.cardschat.com/attachment.php?attachmentid=12016&d=1217205030)
B, position on the shark

I do foresee an argument against these choices based on the false notion of "schooling". Therefore, I preemptively offer:

Schooling by Ian Taylor aka piemaster

You are dealt AcKc in early position, and you raise your premium holding. Three players cold-call your raise, as do both the blinds.The flop is a nice looking Kh6s4s. You bet and all five opponents call.
The turn is 9c. You bet and three of your five opponents call.
The river is Qd. You bet and get raised. You make a crying call and are shown JdTs for the straight.

I think this story will resonate with most poker players, especially those who play (or have played) in the lower limits. Most winning poker players realize that they need to play against inferior players to win. However, sometimes it seems like your opponents are so bad that they actually become more difficult to beat. So many players are staying around with so many random hands, that one of them is bound to hit a hand better than your’s.

And so the theory of schooling was born. A school is a collective noun for a group of fish. Likewise, at the poker table, schooling is a word used to describe the behavior of a group of fish at the poker table…fish in this context referring to poor players. The theory is that bad poker players can collectively protect each other. Beyond a certain point, additional bad players might actually decrease your expectation, making the game harder to beat than one with only a few bad players. The ideas behind this are as follows:
1. While each of your opponents may have only a few outs, collectively they have a lot. For example, imagine you have top pair on the flop and you have one opponent with a gutshot, one with an underpair, one with an overcard and one with a backdoor flush draw. Between them they may have in the region of 11 outs and will overtake you (collectively) by the river around 50 percent of the time if they all call down, even though all their draws are individually weak. Add in a couple of players with legitimate draws and suddenly you are dodging an insane number of bullets.
2. The more players that are in a hand, the better the hand that is likely needed to win. The hands that we traditionally consider as “good” are those that make good one pair hands. When a better hand (such as two pair, a set, a straight, or a flush) is needed to win, the edge that “better” hands have over trash is smaller than when one pair is likely to be good. A pair of twos is just as likely to make a set as AA. 83s is just as likely to make a flush as AQs. Any two random cards can hit two pair.
3. Each player that stays in the hand gives every other player better pot odds to hit their draw. For example, a bad call with a gutshot on the flop might retrospectively become a good call once three more players call, adding three more bets to the pot. All the bad players are effectively validating each other’s play.

Given this moderately logical reasoning, it is not hard to see why a lot of players buy into the idea of schooling. You can also see why a lot of players might want to believe in it. Every low-limit player has played in one of those sessions where their opponents have played terribly, but they have been crushed as these opponents hit hand after hand. Rather than put it down to acceptable variance or admit that they didn’t adjust properly, they can just blame schooling. Players like to have someone to blame for their failures. The theory of schooling allows them to place the blame exactly where they want to – at the feet of their weak opponents.
“It’s impossible to beat a game like this, you idiots are just too terrible” - A. Nit

In this two-part article, we will be discussing concept of schooling. The opinion on it is split, with some players considering it accepted poker theory, while others consider it rubbish. Hopefully, by the end of this article we can answer the question of whether schooling really is a valid concept or not. We will do this first by discussing the theoretical concepts behind schooling and then, in next month’s article, exploring the topic empirically by attempting to model schooling situations.

Schooling and the Theory of Poker
A good place to start (as it so often is) is with Sklansky’s Theory of Poker. Boiled down to its bare essentials:
Whenever an opponent makes a mistake, you make money.
Whenever an opponent makes a correct play, you lose money.

So how does schooling fit into this theory? Well, it doesn’t really. Schooling would suggest that if too many players make mistakes then a good player would actually lose money as a result. This doesn’t sit well with the Theory of Poker at all. By definition, a mistake in poker is something that costs you money (in the long term), so where is that money going? Poker is a zero-sum game, so every mistake that costs one player money must benefit another (there may also be an increase in the rake, but this will be negligible).

Hence, at first glance it would seem that the Theory of Poker makes a mockery of schooling, but this is not quite the case. Remember the three arguments in favor of schooling that we identified above? The third of these is that when many players are calling with weak draws, these draws actually become less weak. This actually fits in quite nicely with the Theory of Poker, because Sklansky is careful to carve out an exception for multi-way pots. In a heads-up pot, when your opponent makes a mistake, you make money. In a multi-way pot, when an opponent makes a mistake then somebody makes money, but it might not necessarily be you.
For example, let’s say that you have the best hand on the flop and bet. Players A, B and C all make bad calls and the action comes to Player D. Player D also makes a bad call, but the dead money adds only to the equity of Players A, B and C and not to your’s. Player D might carve his small slice of the pie directly from your slice and this might more than compensate for the fact that the pie is now bigger. Thus, his bad call may in fact cost you money, in theory at least.

So in fact, schooling is not disproved by the Theory of Poker; both theories can sit side by side. Unfortunately, it doesn’t really prove it either. In certain circumstances, additional weak players in the pot can cost you money, but the question that really matters is “how often will this happen in practice?” Or to look at it another way, do a large number of bad players cost you money in general or just in certain individual hands? We will have to dig a little deeper if we really want to find out.

Unfortunately, it is not a question that is easy to answer. In next month’s article, we will be modeling some situations that may help to answer the question. However, this is never going to be entirely accurate because the hands that you simulate will obviously be cherry-picked. The other way to answer the question is to argue it from a common sense point of view. At the beginning of the article, we looked at the arguments in favor of schooling. So here is the other side of the argument, the arguments against the existence of schooling.

Variance
When you are in a game with a large number of loose players, two things happen: the pots get larger on average (especially if they are loose aggressive players), and your chances of winning each pot that you enter go down somewhat. Combined, these two variables cause your variance (the swings you experience) to increase by a considerable amount. Sometimes you will win a lot of money, while other times you will get crushed by strings of bad beats.

The problem is that players who frequent these types of games misunderstand this variance. When they have a great session, they will feel they deserved it. After all, they were playing better hands than their opponents, so they deserved to win the hands that they did. On the other hand, when they have a bad session, they will blame schooling. It seemed no matter how good their hand was going in, one of their many opponents would suck out on them. If they have a string of these sessions (which will happen from time to time) they might conclude that it is impossible to beat this type of game.

Of course, both the good sessions and the bad sessions were two sides of the same coin. In the good sessions, they underestimated how much of their success was down to luck (it never seems like luck when you are winning). On the other hand, during the bad sessions they seemed to be getting more bad luck than should be possible. They get beat up so bad that they forget about the good sessions that came before. Schooling is a convenient explanation that helps to make sense of the volatile results, so players like to cite it whether or not it is actually correct.

Very bad calls
Schooling is based upon the idea that players make bad calls that are validated by all the other bad calls that are being made. However, this only works if the calls were not that bad in the first place. For example, calling the flop or even the turn with a gutshot straight draw is rarely a huge mistake in loose games, because, generally speaking, the pot will be quite large and you will have four strong outs. If you get called by four opponents who each have four strong outs each, then it is indeed quite possible to get schooled.

However, if you have five or six players calling the flop every hand, then you can pretty much guarantee that they are calling with hands with far less than four outs. They are probably calling with weak overcards, backdoor straight and flush draws, under-pairs and all kinds of other garbage. Or maybe they are hands that look reasonable, but are actually dominated. These very bad calls are not hands that are going to school you. You want these hands to call no matter how many other players are in the pot because their pot equity is so small. Their presence might cost you the pot one time in 20, but the dead money they contribute to the pot more than makes up for this.

Big hands and big draws
The great thing about having lots of loose opponents is that they won’t only be around when you have a vulnerable top pair, but they will also be around when you have a hand where you want a lot of opponents. This is the case when you either have a strong draw that benefits from multi-way action or when you have a hand so good that you want as many callers as possible, because most are likely drawing dead or very slim.

The great thing about these situations is that your extra opponents are giving you a huge increase in expectation – not the tiny fractions of big bets that schooling might shave off your pot equity, but the multiple big bets that clueless, loose players are willing to pay chasing a pair when you already have a set. When you win a 25 big bet pot with a flopped set or a flopped nut-flush draw that gets there, you start to see what a boon these loose callers actually are.

Poor adjustment
A lot of intermediate players suffer in low-limit games, not so much because of schooling but because they don’t make the adjustments necessary to beat these games. From their point of view, they are playing all the right hands and making the right plays, but are getting beaten by trash time and time again. Once again, schooling gets the blame.

However, what is actually happening is that they don’t realize that you can’t just take your game that might work quite nicely in a reasonably tight, mid-limit game, play it in a loose game and expect it to work. Amongst other things, you need to take into account that:

- Pots are larger
- Implied odds are greater
- Weak outs must be discounted more
- Bigger hands are often needed to win
- Bluffing is ineffective
- Strong drawing hands are more valuable
- Top pair is very vulnerable

If you have AK and see a flop of K98 against six opponents, then you are going to lose a lot of the time. You can expect to lose. Even if your opponents hold completely random hands, your pot equity is under 40%. That’s not schooling, that’s just poker. Take some solace in the fact that the times your top pair does hold up, or you improve, the pot will be very large.

Summary
In this article, we have learned that schooling is a valid concept in theory. In practice it is not something that is likely to be an issue, even in very loose games. If you play very loose, low-limit games and feel you are being “schooled” then it is far more likely that you are playing sub-optimally or are just going through a downswing at that time. One thing you can be sure of is that playing limit hold’em in extremely loose games is highly profitable. Next month, we will continue our discussion of schooling, modeling several poker situations to see if we can determine its effect on your results.
Until then, good luck at the tables.

Schooling: Part II by Ian Taylor aka piemaster


This is the second of a two-part article on schooling. The first part can be found here.

Schooling is a controversial poker concept describing the behavior of groups of weak players, typically in low-limit games. The theory suggests that a large number of loose players in a limit hold’em game help each other out by pooling outs and giving each other better pot odds. In fact, some say that games with too many players are actually harder to beat than games with only a few loose players.

In last month’s article, we discussed the concept of schooling from a theoretical standpoint. We illustrated how it is possible that a large number of players calling with weak draws can serve to hinder a player with a vulnerable made hand. But then we proceeded to question whether this genuinely made the games harder to beat in practice. After all, when you have a big hand or a big draw, all these loose callers should give your hand more value than what they strip from it when you have a weaker hand.

But all the arguments on both sides were theoretical. In this article, we will try and add some cold, hard numbers to the debate. Using Poker Stove and the odds calculator on ITH, and starting with a basic model, we will attempt to empirically prove what effect schooling will have on your expectation and results in various poker situations.

A Simple Model
Let’s say you are playing in the strangest poker game ever. Each of your opponents fall into one of two categories:
1. Rocks: They don’t actually want to play poker, they are just passing the time. As a result, they fold every hand pre-flop so they can lose their money as slow as possible.
2. Maniacs: They want to gamble as much money as possible every hand. No matter what cards they hold, they will raise all the way to the river.

Obviously this is a completely unrealistic scenario, but it can be used to explore the concept of schooling quite effectively because it eliminates a lot of the variables that make poker complicated. You are unable to protect your hand, bluff, or value bet at all, because every street will be capped regardless of what you do (unless all nine opponents are rocks, in which case you can steal the blinds on every hand). You will also be completely unable to put anybody on a hand, because each opponent behaves the same regardless of what hand he holds.

Let’s say you are playing in this game and you are dealt aces in middle position (in fact, position is irrelevant in this game). Obviously you are going to play this hand, but how many opponents would you like to play with you? In other words, how many rocks and how many maniacs would you like in the game?

If all nine opponents are rocks, it is straightforward to see that you will win 0.75 big bets if we assume a standard blind structure. If n players are maniacs then your expectation will be (((n+1) x 12) x Y) – 12 big bets. This looks like a complicated equation, but it is fairly simple. (n+1) x 12 represents the money in the pot at the end of the hand. If every street is capped, then each player including you will put 12 big bets in the pot (two pre-flop, two on the flop, four on the turn, four on the river). Y is a variable representing your pot equity against n random hands. The 12 at the end is obviously your own investment that you need to subtract from the pot to calculate your expected net profit. Note, that if you have exactly one maniac opponent, then you can prevent every street being capped. However, we will assume that you will be happy to cap each street in this case. It takes a pretty horrific board for aces not to be favored over one random hand.
Here is a table showing your expectation against various numbers of maniacs:

maniacs.JPG (http://www.cardschat.com/attachment.php?attachmentid=12017&d=1217205755)

A number of interesting things can be seen here. Despite the fact that aces are unlikely to make a big hand (trips or better), you can see that you are better off with many opponents as opposed to few. Each random hand decreases your pot equity, but increases your overall expectation due to the increased size of the pot.
However, you can observe evidence of schooling! When we add the ninth maniac opponent, your overall expectation goes down. A player capping every street with a random hand is actually decreasing your overall expectation, even though individually you figure to be a big favorite against him. It would be interesting to see what the effect of adding a 10th and 11th opponent would be, but unfortunately I don’t have the software to simulate this.

In order to try to observe this schooling effect better, I decided to try the same experiment with a different hand. Aces are always a fun hand to simulate, but intuition dictates that schooling will be more prevalent with a hand that has less monster potential. The following are the results when this experiment is repeated using AJo as the hero’s hand. This hand was chosen as a quintessential top pair hand that is traditionally thought to struggle in multi-way pots.

multi way pots.JPG (http://www.cardschat.com/attachment.php?attachmentid=12018&d=1217205832)

With this weaker hand, the effects of schooling are even more pronounced. Upwards of six opponents, you would welcome the additional maniacs, but beyond that point they are decreasing your expectation. However, while schooling is clearly a factor here, there are two things worth noting:
1. One difference you have holding AJo rather than aces is that you can afford to fold. If you don’t flop a pair or a draw with AJo against nine opponents, then your pot equity will drop to around six percent or below and you can safely fold. This makes situations with a large number of opponents more profitable than they initially appear.
2. Although schooling does decrease your expectation with more than six opponents, it does so only by a small amount. You are far better off having nine opponents rather than two, for example, which would certainly surprise the most devoted disciples of schooling.

Of course, this very simple model has its limitations. No matter how bad you think your opponents are, you would be hard pressed to find even one player who plays like the maniacs described above, let alone a whole table full of them. Typically, you will be up against opponents who make many mistakes, but will play in a way that at least makes sense. Whether this will have a positive or negative effect on schooling is difficult to prove empirically. Obviously, you would much rather be up against opponents with completely random hands than ones with legitimate (albeit weak) draws. On the other hand, you won’t play many hands where you have six or more opponents who all have a legitimate draw on the turn, because there are only so many draws available on any given board.

A More Realistic Model
To explore the effects of schooling further, we will need to use a more realistic model, one where both you and your opponents make decisions as they might in a real game (this doesn’t necessarily mean correct decisions, of course). Unfortunately, by doing this we are going to lose a lot of the objectivity of the previous model, as whatever hand we choose is going to be somewhat contrived. However, it should give us a good indication of how schooling affects your expectation in real life hands.

In this hand, you hold KhQh. On the turn, the board is: KsJs7d2c
There are seven big bets in the pot. Your opponents happen to hold the following hands (you won’t know this of course).
MP: 8c9h
Button: 3h3d
SB: Ac6d
BB: Kd4d
This has the potential to be a classic schooling situation. All of your opponents have weak draws, but they are all chasing different outs and are, collectively, quite likely to beat you. Although you have the best hand with only one card to come, your pot equity is only around 68 percent. If all four opponents call on the turn, then you are going to lose almost one-third of the time, even though none of your opponents have more than four outs.

First of all, let’s consider the possibility that all of your opponents play correctly (of course, they have probably already made errors in the hand, but we will wipe that slate clean). MP actually has a reasonable draw. His gutshot straight draw gives him four outs, but this doesn’t give him pot odds to draw (although with implied odds it would be close). The button and SB should also fold. They have two and three outs, respectively, which have to be discounted in such a large field (heavily in the case of SB). BB only has three outs, because you have him dominated. Obviously he won’t necessarily know this, so it is difficult to say whether he should fold his top pair from a good poker standpoint. However, mathematically he should obviously fold. Hence, if this flop was played out with all players playing correctly, then you would bet and everybody would fold. You would win the seven big bets in the pot.

The question is: How much better would you do if one or more opponents called you down? Let’s assume that if you have the best hand on the river, your opponents will call, and if you get outdrawn the winner will raise and you will pay him off. Obviously, neither of these scenarios is totally realistic. However, the former is favorable to you and the latter is favorable to your opponents, so hopefully they will go some way to canceling each other out.

So to simplify, if you win the pot you will win seven big bets (the existing pot) plus two times the number of callers (one bet for each on both the turn and the river). If you lose the pot you will lose three bets (one on the turn and two on the river). The following table shows your expectation with different numbers of callers. I have tried to make it realistic in regards to which players will call your bet (BB most likely, then MP, then SB then Button).

button.JPG (http://www.cardschat.com/attachment.php?attachmentid=12019&d=1217205905)

As you can see, your expectation rises with each of these bad calls that your opponent makes. Although each caller is giving the others better pot odds, it doesn’t compensate for the additional money that is going into the pot when you are a heavy favorite. In fact, it doesn’t even come close. Even the fourth caller gives you an extra 0.31 big bets in expectation, which in limit hold’em is a big chunk of pie.

As illustrated earlier, it is quite possible that when you get up to seven, eight, or nine callers, schooling might start to hurt you. However, even in the loosest games it is very rare to get seven players calling a bet on the turn. And if you did, it is likely that some of them would be drawing dead and you really don’t mind players that are drawing dead coming along for the ride. For example, if you add a sixth and seventh player in the hand above with KT and A5, respectively, they don’t remove anything at all from your pot equity. Even on scary boards, there are usually only a finite number of feasible draws.

Hopefully this article has illustrated two things about schooling:
1. It is a theoretical possibility that, in a big pot with a lot of opponents, additional players making bad calls might harm your expectation.
2. In reality it is very unlikely to happen and if it does it will be an oddity of that particular hand that will not make the game significantly less profitable overall.

As we stated last month, schooling is one of those phenomenons that players seem to want to believe in, because it helps them to explain why they sometimes experience horrific beats in what appear to be very good games. But schooling, as these players see it, is a myth. You want as many bad players as possible at your table. Even though occasionally they might school together to reduce your expectation, this will be far outweighed by the times that their bad calls add huge amounts to the value of your flopped draws and flopped monsters.
Schooling is an interesting idea. Interesting, but just not that relevant.

Nice! I was hoping to spawn a bit of discussion on schooling.

But first, I'd to address situation #4. I generally try to put strong players across the table from me. If they're 2 to my right, their button will be when I'm in the big blind, and their cutoff will be my small blind. I'd rather not be forced to put money in the pot when the toughest player at the table is the most active. Across the table, it should be pretty easy to avoid each other altogether.

Back to schooling, yeah, I think schooling is more of a limit concept at full ring. Might not apply as much at no limit. And yeah, it does take adjustment to consistently beat a loose game for the max, and I'm not sure players adjust well.

Honestly, I'm not sure which table I'd prefer to sit down at. My playing style definitely does better with 1 fish and a bunch of nits, so I generally look for those tables. But when I sit down with 5 fish, play solid ABC poker, and avoid going on tilt from the variance that comes with it, I usually profit pretty nicely.

I play stud all the time, and most low limit stud is playing with 7 fish at a time. Its hard to ever see the long run profit with so much variance in that game. Sometimes I almost prefer getting into situations that I know are going to be marginally (but consistently) profitable, rather than taking a bunch of longshots that have a high expectation.

If you had a 1 in a million shot at winning a billion dollars, that wager still has a high positive expectation, but the longrun would be pretty darn long to ever see profit.

I considered that. However, it's a cash game, so I'm not that worried about defending my blinds. Making a random re-raise of his steal occasionally, combined with having position on him in the other hands should be enough to compensate.

1. Kingman, bigger pots, higher vp$ip

2. I think im the only one to say B, with 3 nits at the table, it is easier to isolate the fish rather than gamble in 6 way pots like you would on table 1. The 3 nits allow certain blind steal opportunities

3. B Position on the fish

4. Given the choice, neither since you shouldnt be sitting with a shark 6 handed, but if i had to pick one, i agree with AG and pick B to have position on the shark