Propping the $500 Minimum Buy-In 5-10 NL

I'm back from my honeymoon, and I started my new job propping the $500 NL game at the Bike. When I left three weeks ago, the game was seldom being played, so I had the impression that I wouldn't really have much to do. To the contrary, I've played almost 30 hours already in four days. The game is pretty good - most players are too loose preflop, as usual, but other than that they play mostly okay. Of course, there are also some very good players and one or two terrible ones.

I'm a little unused to playing deep-stack no-limit. My job for the past year and a half had me playing mostly limit games. When I did play no-limit, it was always at a small buy-in for short periods of time, meaning I rarely had time to build up a deep stack to play with. So, for this week at least, I've been buying in for less than $1000 every day. There are some built-in strategic advantages to having a short stack, and I think it's necessary to be much better than your opponents in order to overcome that. Plus, I think having a short stack significantly reduces volatility. (I recently read an article in a magazine suggesting that having a short stack actually increases volatility! The claim was unsubstantiated, and I don't see how it could be right.)

I've lost three out of the four days so far, but the losses were minimal. Overall, I'm up about $600, plus my table hit a jackpot on Thursday and I won a $950 table share. (Yes, even the $500+ buy-in game has a jackpot now, to my chagrin. This has been the case for at least six months now.) I think once I get over my jet lag and become more comfortable with the game, I will have a big enough advantage on most of my opponents that I can start buying in for $1000, maybe more. On the other hand, I sometimes have issues with concentration, and that is likely to get worse as I get more comfortable with a game. I also think I may get sloppy about giving off tells if I get too comfortable. I'll have to keep an eye on this.

I hope to write my analysis of Concept 13 tomorrow. I basically disagree with it, but the analysis is complicated.

Analyzing NLHE:TAP Concept 12

This will be my last post until at least September 28. I'm heading to Paris for my honeymoon.

Concept No. 12: Be wary of overcallers.

Yes! Good idea. Overcallers are often on a draw, but they are also often slowplaying a big hand. This is especially true if there are no draws on the board, such as the JJ4 rainbow flop in the example in the book.

That's all I have to say for this one. See you in a few weeks!

Analyzing NLHE:TAP Concept 11

I'm commenting on the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller. Let me apologize in advance: this one is a little more mathematical and a little less conclusive than most.

Concept No. 11: A big bet is the most relevant and accurate information at the table.

Once again, I think Sklansky and Miller's advice here is probably bad, but this one is particularly difficult to analyze because it's unclear what is meant by "relevant and accurate information." In any case, this concept's claim is far too broadly stated, and only holds in some circumstances.

If we take the claim in the most literal sense, this concept is not always true. Infinite counterexamples exist. Perhaps you know that your opponent always makes big bets; in such a case, the big bet provides essentially no information at all. Or, sometimes you may have the nuts, which is probably the most "relevant" factor if you're trying to figure out how to proceed with the hand. As far as "accurate" information goes, usually preflop play is most accurate, since you will have observed your opponent in many more preflop situations than postflop situations. Of course, all of this varies from player to player. It seems overly bold for S+M to make a claim that a big bet is (presumably, always) the most relevant and accurate.

If we're not to take this concept literally, let's consider whether it is at least good advice in a figurative sense. This concept seems suggest that players should respect the big bet more than they do, and thus fold to it more. Do players tend to underestimate the importance of a big bet when trying to determine their opponent's possible hand? Human nature actually suggests the exact opposite; there is a phenomenon called the "base rate fallacy" that seems like it could apply here. It has been established that people tend to discount base rates (which could correspond to your read of your opponent before the big bet), and focus only on the most immediate and salient information (such as the big bet) when estimating likelihoods. Are poker players similarly likely to focus to much on the most immediate information? I think sometimes yes, sometimes no. There are certainly a lot of players who are not sensitive enough to bet sizes, and for these players, taking this concept to heart is probably a good idea. I'm not sure that most players fall into this category, though.

In their explanation of this concept, Sklansky and Miller say "all information from the past takes a back seat to the fact that they've made a big bet." I think a fair way to interpret this is "the probability your opponent holds the nuts, or nearly the nuts, given that he just made a big bet, is greater than the likelihood that he did NOT hold the nuts before he made that big bet." Mathematically, we can write this as:

P(nuts|big bet) > p(nuts' before the big bet). That is: P(nuts|big bet) > p(nuts').
(Note that nuts' means "not the nuts.")

I'm fairly confident that this is not always true, although it is might be true if your opponent is a very good player. I think that Sklansky and Miller might have succumbed to the base rate fallacy and are underestimating the importance of their initial read of their opponent's preflop tendencies. Let's do some Bayesian analysis of the example they give in their explanation of this concept.

Suppose we are facing a big bet and we think our opponent is either bluffing or holding the nuts. Before he made the big bet, suppose we thought that the way he played the hand meant he had only a 0.05% chance of holding the nuts. This seems reasonable in S+M's example where your opponent is very tight, raised pre-flop, and the nuts is 74 (actually, .05% seems a bit too high, but let's give S+M the benefit of the doubt). Now let's say we think our opponent would make a big bet 80% of the time if he held 74. Otherwise, he would make the same big bet 2% of the time as a bluff. The base rate fallacy would be to think that your opponent would now be holding the nuts 80/82 times, or about 97.6% of the time. Of course, this is way too high because it ignores base rates. In this example, we can use Bayes' theorem to find the actual probability that you are up against the nuts. Bayes gives us the following equation:

P(nuts|big bet) = P(big bet|nuts)*P(nuts) / (P(big bet|nuts)*P(nuts)
+ P(big bet|nuts')*P(nuts'))

From our assumptions above, we have:

P(big bet|nuts) = .8
P(nuts) = .0005
P(big bet|nuts') = .02
P(nuts') = .9999

and so:

P(big bet|nuts)*P(nuts) = .0004
P(big bet|nuts')*P(nuts') = .019998

Then,

P(nuts|big bet) = .0004 / (.0004 + .019998) = .0004/.020398
= .0196

So, under these assumptions, our opponent holds the nuts less than 2% of the time when he makes a big bet! You may quibble with the rates I chose, but even if our calculations are off by a factor of 10, our opponent will still only be holding a winning hand 20% of the time, and bluffing 80%, making it correct to call any sized bet.

If you don't like the rates I chose, I guess it's most likely because you think that even very tight players tend to hold 74 on the river more than .05% of the time in this situation (the situation: he raised preflop, and 74 is the nuts on the river). I admit, this is a tricky one to estimate, but we can do another Bayesian inference to examine my .05% claim. That is, we want to know if .05% is a reasonable approximation for how often a tight, pre-flop raiser holds 74 on the river in this situation. That is, we want to find P(74|saw river).

First of all, let's assume our "tight" player raises preflop with 74 only 1% of the time when dealt to him. Also, assuming we don't have a 7 or a 4 in our hand, our opponent will have been dealt 74 only 1.3% of the time. So, P(74) = .013*.01 = .00013.

Second of all, we need to approximate how often 74 will see the river in this situation. Remember, the situation is: 74 has already raised preflop and seen a flop that gives him a draw to the nuts. IN order to be conservative and to simplify the math, let's assume he will never fold before the river in this situation. So, P(saw river|74) = 1.

Third of all, we need to approximate how often a player would have seen the river in this situation given that he raised preflop holding anything. This is another tough one. I think this is likely over 50%, but let's be conservative and choose 26%, which will also help out with the arithmetic. So, assume P(saw river) = .26. Bayes theorem then gives us:

P(74|saw river) = P(saw river|74)*P(74) / P(saw river)
= 1*.00013/.26 = .0005 = .05%

Well, this is precisely the number I used above, and I was using conservative numbers in this example. Of course, you could still contend that my numbers or other assumptions are unreasonable, but I have at least convinced myself that in Sklansky and Miller's example, our opponent's big bet usually will not indicate that he has the nuts.

Analyzing NLHE:TAP Concept 10

I'm working through all 60 concepts at the end of Sklansky and Miller's No Limit Hold 'em: Theory and Practice.

Concept No. 10: Sometimes you should go for a check-raise bluff on the river when a bluff bet would be unprofitable.

Sklansky and Miller are technically correct that you should sometimes check-raise as a bluff, but the advice is still bad. It's confusing for them to state this advice without noting the unusual circumstances under which it holds. They say, "sometimes you should..." Well, yes, but rarely. Readers who take Concept 10 at face value are in danger of trying check-raise bluffs indiscriminately, which would probably be a big mistake. My problem with this advice is actually very similar to Concept No. 4: "Sometimes you should bluff to stop a bluff." In both cases, Sklansky and Miller are missing the main point, an idea that I've attributed to Mike Caro (though I can't find it anywhere - maybe I thought of it myself!): If your opponent bluffs either way too much or way too little, be more willing to check to him. Or, more generally: If you've identified any weakness in your opponent's play (such as bluffing too much), try to put him in situations that will allow you to exploit this (for example, by checking and letting him bluff).

In Concept 4, Sklansky and Miller refer to an opponent who folds way too often to a small bet. You should bluff often against this opponent. Here in Concept 10, they use an example where your opponent bets 5/9 of the pot and is bluffing "the majority of the time." This is too often. (When betting 5/9 of the pot, game theory suggests you should be bluffing only 5/14 = 35.7% of the time.) Against an opponent who bluffs too much, checking is commonly the best play. This is the real lesson of the example they give: If you know your opponent bluffs too much, exploit it!

I know Sklansky and Miller are not talking about game theory here, but I just want to acknowledge that theoretically, it is indeed sometimes profitable to check-raise bluff even if your opponent is playing perfectly. For an optimal strategy, these bluffs are needed to balance the times you check-raise with a strong hand. In this theoretical case, the hands that are best to check-raise bluff with are actually not the very worst hands in your range (which are the best hands to try regular bluff bets with). Instead, the best hands to check-raise bluff with are the very best of the hands that you would otherwise fold. For example, if 66 is the worst hand you would call with in a given situation, 55 is actually the best hand to try a check-raise bluff with. In practice, if you want to try a check-raise bluff, the decision should depend a lot more on your read of your opponent than on your own hand, but I always think it's worth considering what game theory has to say about a situation.

Analyzing NLHE:TAP Concepts 8-9

Discussing the concepts at the end of Sklansky and Miller's No Limit Hold 'em: Theory and Practice.

Concept No. 8: Other things being equal, when you're in one of the blinds your preflop raises should generally be a little larger than normal.

I often follow this advice in my own play, but I'm not convinced that it is generally correct. Maybe it is, but I'm not sure. This is rather difficult to analyze objectively, and I think it will be a subject of discussion among poker theorists and enthusiasts for a long time. Anyway, Sklansky and Malmuth list three reasons why they think this advice is correct. Let's look briefly at each.

1. S+M say:
You'll be out of position, and raising bigger increases the chances you'll win right away.
Me: Yes, but you could also argue that you'd rather play a small pot if you're out of position, and so you should either raise smaller or only with very strong hands like JJ+.

2. S+M say: Cuts down your opponents' implied odds.
Me: Well, yes, but it also costs you more. Is it worth it?

3. S+M say: In early position, it's more important that you narrow down your opponents' possible hands, which you can do by raising more.
Me: Good point. Again, I wonder: is it worth the extra investment?

Finding the right strategy for raising in the blinds is something I'm still working on. It probably deserves a lot more consideration than I'm giving it in this post, but I don't feel that I have anything insightful to say about it beyond what I'm writing here. My current strategy is this: In the blinds, I like to raise only with a small number of strong hands. The actual range will depend on who has limped into the pot so far, but sometimes I will check with a hand as strong as pocket tens (although I will usually raise this hand). Occasionally, I will bluff with weaker hands (sometimes even extremely weak hands such as 72o if I think my image is very tight and I will likely make everyone fold). Since I seldom bluff from the blinds, I don't usually feel the need to make my raises particularly large. If my opponents know me well, they should fold to a normal-sized raise of about 2 BB larger than the current pot size, which is about what I consider normal-sized from other positions, as well. However, I will often raise larger than this if my opponents don't know me or if they seem to play too loosely. Since this is often the case, I actually do raise larger than normal from the blinds pretty often.

A related question is how much to raise in early position versus late position. I've seen all three alternatives argued: larger raises in early position; larger raises in late position; keep raises about the same size. The argument that you should raise bigger from early position is the most popular: you don't want to get called and then have to play the pot out of position, which is the same as S+M's 1st point above. I've also seen it argued that you should raise the same amount from each position. One argument for this is that it will always give the blinds the same pot odds if nobody else joins the pot. I've rarely seen it argued that you should raise bigger from late position than from early position, but this is what Chen and Ankenman argue in The Mathematics of Poker. They say that since your raising range is much smaller from early position, it's not necessary to raise as much. Also, by raising small, you save money if one of your opponents reraises, which is much more likely if you are raising from early position with 7-9 players yet to act than if you raise from the button with just 2 players left after you. Personally, I've decided to take the middle road and raise about the same regardless of my position. For me, this philosophy extends to how I play from the blinds, where I raise about the same as from anywhere else.

I think this topic deserves a much more objective, EV-based analysis, but this seems like a big project. I'm not up to the challenge just yet. I hope to return to this question at some point after I'm done going through the rest of these concepts, but that will not be for quite a while.

Concept No. 9: Bets are usually more important than pots.

I'm tacking this one on the end here because I don't have much to say about it. The concept's claim is not literally true because even in no-limit holdem, bets are usually smaller than the pot, but S+M's point is well-taken: in contrast to limit poker, winning or saving extra bets is extremely important in no-limit poker.

No-limit players should be much more willing to give up a pot in order to save a bet. In limit poker, on the other hand, the pots tend to be big compared to the bets, and so calling is much more commonly the right decision.

For limit players, it can be difficult to adjust to this difference. I had the opposite problem when I started playing more limit holdem last year: I was folding way too often for a limit game. My experience with no-limit poker had gotten me used to the idea that saving bets was important, and giving up pots was okay. In limit, the exact opposite is true!

Analyzing NLHE:TAP Concept 7

It's my weekend again, so it's time to get back to analyzing Sklansky and Miller's No Limit Hold 'em: Theory and Practice concepts. I'll try to do one or two during the week, as well.

Concept No. 7: Don't telegraph that you have one pair unless you can profitably call big bets.

Sklansky and Miller say, "One pair can be a very tricky hand to play in deep stack no limit." I agree with this statement, but I do not agree with Concept 7 as stated. It suggests that except under certain circumstances, you need to play your pairs abnormally in order to throw off your opponents. This is terrible advice. You want your "normal" game to maximize EV. Thus, any advice to deviate from this is, by definition, going to lose some expected value. Losing EV=bad.

Certainly, we do not generally want our opponents to know what we are holding. So, the advice that we not telegraph that we have one pair seems sound. The problem with this advice is the implication that by playing a hand in our normal way, we "telegraph" our hand to our opponent. If this were the case, our entire poker strategy would need a complete overhaul. If we are playing a well-rounded game, we will never be telegraphing our hands (or if we do, it's not in a way that our opponents can exploit). Even if our strategy is not so well-rounded, it takes an extremely perceptive opponent to discern our hand precisely.

Let's consider for a moment S+M's suggestion that it's okay to let your opponents know what you have under certain circumstances. Specifically, they say, "If you welcome a big bet with one pair because you expect that bet to be a bluff, then it's ok to telegraph your hand by playing in a way that makes it obvious what you hold."

I don't really know what to make of this. If it's okay to "telegraph" my hand, should I just reveal my hand to my opponent in such a case? Surely not, although by the logic included in this concept it would seem that S+M would expect that this would accomplish the desired goal of inducing a bluff. This is plausible, but it still doesn't seem like the best way to play the hand.

Obviously, S+M are not advising that we telegraph our hands by simply revealing them to our opponent. What they mean by "telegraphing" is playing the hand in a normal, straightforward manner. However, as I said before, your normal strategy should not be telegraphing your hand, anyway.

I think Sklansky and Miller's advice is designed to protect the reader from developing a strategy that is too predictable. It's true that a NL player needs to disguise his paired hands, but it should not be done by playing them abnormally. Instead, just make sure that you play some drawing hands in the same way, as well as some stronger hands. I think conventional Sklansky-wisdom is overly concerned with playing hands in a way that avoids difficult decisions. It's good to avoid difficult decisions, but not if it means playing abnormally and thus losing EV.

Promotion!

Yesterday, I was offered a new position and a $10/hr pay raise. My new responsibilities would be to help the $500+ buyin NL holdem game. That's about it. The floormen would no longer be able to move me from one game to another, and I would have some more flexibility about whether to stay in a game or get up for a player who is waiting. If no $500 NL game is running, I can play whatever game I want, but I would be required to help start new $500 NL games. My hours would be pushed back two hours from 9am-5pm to 11-7, which I think is somewhat better because the traffic should be lighter.

I told my supervisor I would have to think about it. Before I was hired by the Bike, I used to routinely play the $500 NL game at Hollywood Park, so working the $500 NL at the Bike might seem like an ideal situation for me. However, I've come to prefer the limit game over the past year. My results are better, and I feel more comfortable in limit. Also, the $500 NL players have extra intense egos, and I like to try to avoid getting too involved with such people. Since there are pretty much the same people at the $500 NL game every day, it will be difficult for me to escape their bullshit.

After thinking it over last night, though, I decided to take the job. I don't think it will take long for me to become comfortable with it. Hopefully only a day, and no more than a few weeks, I'd guess. As for dealing with the out-sized personalities in that game, I'm hoping it won't be too much of a problem. I already have to deal with plenty of BS in the holdem and hi-lo stud games I play every day, but somehow it seems that the variety of different people it comes from makes it more tolerable. Having to deal with the same people every day is going to be at least a little grating. I decided I could put up with it for the extra $10/hr.

Since I'm taking time off from Sept 11-27 for my honeymoon to Paris, my supervisor decided I should wait until October 1 to start in my new position. Anyway, this means I'll be playing way more no-limit pretty soon, so it's quite appropriate that I've been analyzing No Limit Hold 'em: Theory and Practice this past week. I hope to continue that tomorrow night.

Analyzing NLHE:TAP Concept 6

From No Limit Hold 'em: Theory and Practice by Sklansky and Miller.

Concept No. 6: It can be right to call with decent hands that have little chance of improving even if you plan to fold if there is a bet on the next round.

I like this one. It's not groundbreaking, and it should be pretty obvious, but it's common for experienced players to give the opposite advice: don't call a bet on the turn if you can't face another bet on the river.

Well, often enough, that river bet never materializes after you call on the turn. As S+M say, "there are plenty of reasons to bet the flop, but check the turn if called (or to bet the turn, but check the river if called). You'll do it, and so will your opponents." I agree.

Again, this seems pretty straightforward, but I'll go through the basic idea. Many players who bluff on the turn and get called will expect you to follow the conventional wisdom and call any river bet as well. Naturally, these players will often give up the bluff and just check on the river, since they figure any further bluffs will be called. This means that if they do bet again on the river, they will have a stronger range of hands. This necessitates a stronger calling range on your part. That is, you'll have to fold some of the decent hands that you called with on the turn.

Sometimes I find myself in a game where I get called a lot pre-flop, but then my opponents tend to give up easily on the flop. I think they often have decent hands on the flop, but they don't want to face another bet on the turn, so they figure they should fold right away. By folding too early, though, they make it far too easy for me to win these small pots.

Analyzing NLHE:TAP Concept 5

One by one, I'm analyzing the concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 5: When you first sit down, evaluate your game and decide whether your profit should come more from big pots or small pots.

I don't have a whole lot to say about this one. It's certainly a good idea to consider your situation when you sit down at the table, so I guess the only question here is whether deciding between big pots and small pots is really a top priority. Frankly, I don't know how to analyze this concept. I'll try comparing it to what I do when I first sit at a table.

If you were to ask me what the first thing you should do when you sit down in a NL holdem game is, I would tell you to first note your opponents' stack sizes. Then, listen to any table banter. This might give you an idea of who is winning and losing, who is aggressive, and who is passive. You'll need to take these impressions with a grain of salt, but they can give you hints as to how your opponents might behave or how they think about the game. Then you should watch the action closely, noting who plays lots of hands and who plays few. Ask yourself "is this table generally loose/aggressive, or are they more tight/passive? Do they tend to call too much preflop and fold too much on the flop? Generally, how can I exploit my opponents at this table?" This is a lot to think about, so maybe there is some value in simplifying things a little and just asking myself whether I should be trying to win big pots or small pots, as suggested by this concept.

Evaluating this concept further doesn't really fit my brand of analysis. The best approach probably depends on your personality. In any case, I like this concept because it encourages the reader to focus on his opponents, to assess his situation, and to think about how to exploit it.

Analyzing NLHE:TAP Concept 4

The third installment of my analysis of the Concepts in Sklansky and Miller's No Limit Hold 'em: Theory and Practice.

Concept No. 4: Sometimes you should bluff to stop a bluff.

This is a really interesting idea, but after giving it a lot of consideration, I'm confident that it is generally wrong.

There are, of course, plenty of situations where your hand has some showdown value but you'll fold if your opponent bets. Obviously, your opponent will gain a lot if he bluffs in these situations. What this concept says is that sometimes it's worth bluffing with these mediocre holdings yourself in order to avoid being put in a difficult situation. This is almost true in some extreme examples, but it's kind of a stupid way to think about it because the reason you bet isn't really that you want to stop a bluff. I remember a similar piece of advice, I think it is from Mike Caro, that is much more insightful: If your opponent bluffs either way too much or way too little, be more willing to check to him. This gives you a chance to exploit his extreme bluffing frequency. Call if he bluffs too much, fold if he never bluffs. Let me explain how Caro's advice is similar and superior to S+M's.

Against most opponents, it's not a bad idea to assume they play about as well after you bet as they do after you check. If you've noticed that a certain player does not fit this description, you can try to exploit it. As Caro points out, if they play terribly after you check (by not bluffing a reasonable amount), you should tend to check very often. This is especially true if your opponent plays reasonably well after you bet. On the the hand, if your opponent plays terribly after you bet (eg by folding way too much), you should tend to bet very often. This is especially true if your opponent plays reasonably well after you check.

In the example Sklansky and Miller use to illustrate their point, they describe an opponent who folds to a bet of 30% of the pot 50% of the time. This is way too much. (In this example, he should call/raise with over 75% of his hands.) Bluffing such an opponent is extremely lucrative, and should be done as often as possible. To make this point even stronger in the book's example, your opponent bluffs reasonably often if you check.

The thing is, Sklansky and Miller do not acknowledge that this opponent is folding way too much, which is the real lesson of their example. Instead, they frame the example around the fact that you are holding a hand that is difficult to play against a bluff. Thus, the reader is given the impression that players with mediocre hands should usually consider bluffing. This is only true against opponents who play terribly when facing a bet! Even in these cases, you are not really betting to avoid a bluff, as Sklansky and Miller put it; rather, you are betting to exploit a weakness in your opponent's play (ie, he folds way too much). Against most opponents, betting mediocre holdings is a big mistake! Note also that against the opponent in this example, you should be bluffing not only with mediocre holdings, but also with all weaker hands. The weaker the hand, the more profitable it is to bluff. This is a basic lesson from game theory. Assuming Sklansky and Miller know this, they obscure this point so badly that they make it seem like it is actually better to bluff with mediocre hands than with weaker ones.

Although I think this Concept's claim is sort of correct, it's very misleading and seems based on bad reasoning. I think that if readers were to take this concept's advice to heart, it would make them play worse! Instead, take Mike Caro's advice and try to exploit your opponents' weaknesses by putting them into situations where they don't play as well.

So far Sklansky and Miller are a surprisingly bad 1 for 4 in their Concept advice. Of course, you may think they are correct and I am the one who is a surprisingly bad 1 for 4 in my analysis! Anyway, I'm quite surprised to see how little I agree with them after only four concepts. When I started this project, I knew there were a few points I disagreed with, but I thought I was mostly going to be integrating their advice into my poker consciousness. I had no intention to be quite so contrarian. I am hoping things are less contentious from here on out, but I guess disagreement probably makes for more interesting blogging!

Back to Work

I went back to work at the Bike this week. Yesterday was the first day of the main event of the Legends tournament, and there were quite a lot of people milling about. Men "The Master" and David Pham were the only TV stars I'm sure were there. I think I saw Amir Vehedi, too. Not the most impressive list. The Bike's new tournament room is quite nice, though. I took a peak yesterday after the tournament started. There weren't as many players as I expected, but then again, there are at least two start days. In the corner were a bunch of people on laptops set up in official-looking rows. I guess this was the "press box."

There is more action than usual at the Bike, but not like last August, when we had tons of games going round the clock. This week, we haven't had any big games going when I got to the casino at 9 am. Even on a normal day in June there were overnight 20-40 limit holdem games going at least twice a week. On the other hand, the place was pretty packed by about 2 pm.

I have the next two days off, so I'm hoping to be able to get through Concept 6 of my NLHE:TAP analysis by Tuesday.

Analyzing NLHE:TAP Concept 3

This is the second installment of my analysis of Sklansky and Miller's No Limit Holdem: Theory and Practice.

Concept No. 3: Most of your actions should include an inherent randomness against perceptive opponents.

"Avoid making virtually any play 100 percent of the time against good players." A few years ago, I was a big believer in this one, but now I just don't buy it. The idea, of course, is that you want to be unpredictable and thus difficult to read. If you never play 62, you are vulnerable if the flop is 662 or 345. Also, if you always raise with AA, your opponent can be sure his QQ are best with a AQ7 flop after you limp in. So, according to this idea, you need to limp at least rarely with AA.

I disagree. As an extremely example, I'm quite confident you should never raise 62o against good opponents when you are five off the button in limit holdem. This holds true for just about any hand worse than about 97o, and sometimes even for hands as good as ATo if your opponents are very tough.

So, why don't you need to worry about flops like 662 or 345 if you never raise with 62o? Three reasons:

1. Even the most perceptive opponents won't be able to figure out exactly what you are raising with anyway. Even if you do raise with 62o sometimes, your opponents are still pretty safe assuming you don't have this hand when 662 flops.

2. There are other, stronger hands that you can play that will make your opponents think twice on flops like this. Instead of playing 62o, play 67s, A6s, and/or 66. These hands do well enough on 662 and 345 flops, and they connect with plenty of other flops as well.

3. Even if you never play 67s, A6s, 66 and always fold when the flop is 662 or 345, this is probably okay! You will still win plenty of other times because the overwhelming majority of flops a card higher than a 6. Even if your opponents know you will always fold when the flop is all under 7, they can't really capitalize on this because those flops rarely show up! This is a very interesting point that I can't remember seeing anywhere else: it's okay for your raising range to include NO hands that connect with certain flops, even if your opponents knew exactly what your range is (which they don't).
**EDIT** 4. This relates to point 2 below. There may be situations where you actually will raise 62o. Who knows, maybe you actually think you opponents are so bad that you think you have +EV in this situation. The point is that your situation encompasses more than just your cards and your position at the table. So, even if your opponents know you never play 62o in the situation they perceive you to be in, you still might have 62o, because you will have perceived the situation at least somewhat differently. Note that this does not mean you should randomize your play like Concept 3 suggests. If you were to play 62o, it would be because the situation seemed to be profitable (+EV).

Another thing Sklansky and Miller say in this concept is "You might sacrifice a little bit of profit in this hand, but by doing so you make all your future hands more profitable." According to game theory, as I understand it, this is just plain bad advice. While it can sometimes be optimal to mix up your game by occasionally playing some hands, these hands need to be profitable in and of themselves... or, at least, not unprofitable.

I also don't really think you need to worry much about randomizing your actions when you have a good hand like AA. If you think raising AA preflop is the best play in a given situation, then it's probably worth doing every time. If you raise with plenty of other hands in similar situations, it's impossible to tell you have AA. You may be worried that you then give up too much information when you limp, since you are essentially announcing "I don't have AA because I always raise AA in this situation!" I have two things to say to this:

1. As in point 3 above, this is probably okay! Just as there are not many flops with three cards under 7, there aren't that many situations where your opponents can exploit you here. For example, even if they know you will always fold to an all-in raise, your opponent cannot exploit this by raising you out, because there are usually several other players for your opponent to worry about.

2. Even if your opponents somehow knew exactly how you play AA in a given situation (and again, they don't), they can never know exactly how you have perceived the situation at hand. For example, I might have noticed a tell that the player to my left is planning to raise, so I might limp in with AA. The player to my right might not have noticed this, and thus he will perceive the situation differently. If he perceives the situation as one in which I would never limp with AA, he would be liable to make a big mistake if everyone folds to him and he tries to bluff me out of the pot. Even more simply, maybe I am in a situation where I always raise with AA, but I misread the situation and call instead. This sort of thing happens all the time.

Some of my conviction on these points comes from studying some game theoretic examples from The Mathematics of Poker by Chen and Ankenman. There actually are situations in poker where you need mix up you play in a given situation (in game theory this is called a "mixed strategy"), but this always happens at the margins of your decisions. For example, if you've somehow determined that you should always raise with K8o on the button but always fold with K6o on the button, there is probably some rate between 0% and 100% at which it is optimal to raise with K7o. Clearly, whether you choose 20% or 80% is not going to make much difference in your results, and you'll be fine at either 0% or 100% as well. Notice, however, that with all other hands, including K8o and K6o, you should not be randomizing your play whatsoever according to game theory. K8 is a raise, K6 is a fold, period. Admittedly, mixed strategies can also be optimal at the extremes, like with AA, but, as I said above, I think you can safely play a fixed strategy, since nobody else really knows what you are thinking, anyway!

This took longer than expected, so I'll save "Concept 4: Sometimes you should bluff to stop a bluff" for next time. Preview: I am not convinced!

Analyzing NLHE:TAP Concepts 1-2

This is the first in what I'm hoping will be a series of discussions of the "Concepts" section of No Limit Holdem by Sklansky and Miller. There are 60 concepts total. Today I'll look at the first two.

Concept No. 1: When in doubt, bet more.

Right off the bat, I have to say I'm not a big fan of this one. My main problem is that it's not really clear what this means, although the discussion in the book gives some clues.

Taken literally, this concept suggests that it is always best to just push all-in: since there is doubt inherent in every poker situation (even with the nuts, it's not clear how much is best to bet), we should always be betting more than any given amount X, unless X is all-in. I know this is not what they are trying to say, so I guess we should not be taking this concept so literally.

Taken more figuratively, I can see two reasonable interpretations. One is that players are generally inclined to bet less than they should, especially when they are in a lot of doubt as to how much to bet. I think this is good advice, actually. Beginners, especially, tend to bet far too little (compared to what would maximize EV), and one reason for this is probably that they doubt themselves. However, in my experience, lots of intermediate players tend to bet too much when they are in doubt, trying to end the hand immediately. In any case, I don't think this is the interpretation that Sklansky and Miller were thinking of, either.

Judging by the discussion in the text, I think the authors are saying that the EV lost when betting too little is worse than the EV lost when betting too much. "Try to err on the big side," they say. "In general, you're better off betting a bit too much than you are betting a bit too little." These comments suggest that there is a bet size that maximizes EV, and I whole-heartedly agree with this. I also agree that it can be difficult to determine this bet size (usually, it's impossible). However, I do not agree that a player should stray from the bet size that he thinks will yield the greatest EV. They say: "try to err on the big side." I say: "try not err." If trying to decide between betting $X or $X+1, the authors suggest you bet $X+1. I suggest you choose whichever seems better!

There actually are situations where there rules might not allow you to bet the amount you think is optimal. For example, you might want to bet $17.50 in a game where you are required to bet in increments of $5. So what is better? Betting $15 or $20? Honestly, I don't know, but this concept suggests you should bet $20. Let's come up a sample situation. I doubt this will be very fruitful, but sometimes this can help to get a better idea of what's going on.

Suppose I'm bluffing into a $30 pot, and would like to bet $17.50 because I think I would win the pot 50% of the time with this bet (EV = $30*.5 - $17.50*.5 = $6.25). However, the rules require $5 increments, so I'll bet either $15 or $20.

Suppose betting $20 will win the pot 52% of the time. Then EV = $30*.52 - $20*.48 = $6.

Suppose betting $15 will win the pot 48% of the time. Then EV = $30*.48 - $15*.52 = $6.60.

Oops! my example broke because betting less than my supposed "optimal" amount was actually better than "optimal." Of course, these numbers are entirely dependent on my approximations of folding rates, but it doesn't look too good for the "bet more" philosophy!

Now let's try those same numbers again, except now I have a hand that I think beats my opponent 90% of the time.

My supposed "optimal" amount is still $17.50.

50%: my opponent folds and I win the $30 pot.

40%: my opponent calls and I win $47.50.

10%: I lose $17.50.

EV = $30*.5 + $47.50*.4 - $17.50*.1 = $32.25.

Betting $20: EV= $30*.52 + $50*.38 - $20*.1 = $34.60.

Betting $15: EV = $30*.48 + $45*.42 - $15*.1 = $31.80.

Once again, my example broke, but this time betting more had a higher EV than my supposed "optimal" bet size of $17.50. I have to admit that if these numbers were correct, I would do better betting $20 than $15 in general, but I think the real issue here is that I should have made my opponent more responsive to changes in bet sizes so that my examples actually made sense (maybe I should have used 55% and 45% instead of 52% and 48%). In any case, I think it's still an open question whether it's better to "err on the big side," but I still say it's better not to err at all if you don't need to!

Concept No. 2: Don't give action to tight and trapping players. Know who not to play big pots against.

I think we can all agree with this very straightforward advice. Tight players tend to have better cards, so you must be careful! I'm not sure why this was worthy of it's own "concept" on the list, but I suppose it is a common mistake people make.

Hitting the Books

As I mentioned last time, I'm taking some time off from work, and I wanted to use some of my free time to analyze poker. As planned, I did absolutely nothing poker-related for my first week off, but now I've started to hit the books. I reread a few sections of The Mathematics of Poker (probably my favorite poker book despite typos and other flaws), and I'm almost done with Gus Hansen's book, Every Hand Revealed. The only thing really earth-shattering about Hansen's book is his humility, which is very uncharacteristic of poker players. He unabashedly admits that he often doesn't know what the best play is, but describes his thinking of the pros and cons of each option. It's a good book, as it gives the reader a taste for how to play a super-aggressive style and what it's like to play in one of these big televised poker tournaments, but I don't feel that I've taken much away from it strategically except that I may be playing too tight in the blinds and with suited connectors.

In addition to The Mathematics of Poker and Every Hand Revealed, I'm also revisiting No Limit Hold 'Em: Theory and Practice by David Sklansky and Ed Miller. I never got around to writing a review for this book, but I thought it was mostly quite good. There are already lots of reviews online. (The book is three years old now, but one extensive review was just published yesterday.) However, I remember thinking that there was a lot of questionable advice, and, as always with "2+2" publications, astonishingly feeble editing. Anyway, the last part of the book, called "Concepts and Weapons," is simply a list of 60 NLHE concepts, and I've always thought this would be fertile ground for some poker discussion. I think it might be interesting to go through them all and give my impression of them. No promises, but I think I'll start that tomorrow. I go back to work at the Bike the next day, but hopefully I'll eventually work my way through the whole list.

The other thing I thought I might do before I go back to work was play in the $1070 tournament in the Bike's Legends of Poker. However, my plans for being staked by other players fell through, and I opted not to pay for it myself.

Summer Vacation and Being Staked

Starting last Saturday (Aug 1), I'm taking two and a half weeks off and going back to work on August 20. This should give me time to run errands, make appointments, do some reading, plan a honeymoon, think about my future, and maybe start an online course. (Did you know MIT puts all their courses online?) I'm also going to Cleveland for a few days (after Hawaii airfare almost doubled). All the props at the Bike were encouraged to take time off this month because the big Legends tournament attracts plenty of action to the Bike. Of course, the action would probably have been profitable for me if I stayed and played, but they offered unlimited time off in August without penalty- but without pay, either.

For the first week or so I'm not doing anything poker-related (other than this blog post). I think it may be beneficial for me to take a step back from poker for at least a few days. I've been having more difficulty concentrating at the table, and it's interfering with the quality of my play. Also, I've been doing almost no analysis of my game when I'm not at the casino. Analyzing poker theory, strategy, and tactics not only keeps my game sharp, it also is what keeps the game fun for me. When I don't study, I don't have as much fun playing, I don't concentrate as well, and I have almost no chance of getting any better. If I'm not getting better and I'm not having a lot of fun, what's the point of playing poker? Well, there's the money, of course, but I don't make enough for that alone to justify it. I haven't completely lost interest yet, but if I can't get myself to refocus on studying the game, I think I'd be making a mistake if I kept on playing just for the money and job benefits.

In the second week of my break, after my poker hiatus, I want to re-immerse myself in poker analysis. Discovering new theories and strategies has always been the driving force that has made poker fun for me and made me want to get back to the tables. I'm hoping this will reignite my excitement in playing poker. I think there's a good chance that it will. The real challenge will be to maintain this interest for more than a few months.

At the end of July, I had several people offer to put me into various tournaments during Legends. I haven't played any tournaments in quite a long time. There are lots of reasons. Essentially, I just think I can make more money in cash games, and for the past year I've been paid a salary by the Bike when I play in cash games. Tournaments have lots of hidden fees that make them tough to beat: they often take 20% up front, plus sometimes another 2% for "bonus chips", plus often 3% goes back to tournament staff and dealers, and then they will certainly ask for a tip at the end, expected to be another 2-5%. I don't like having to prepare myself to play for 14 hours when I might be done after 1 hour. I also don't like the culture of tournaments. For one thing, there is a lot of pressure to chop the winnings at the final table, and I find the negotiations for the chop to be an unwelcome distraction from the game. I could just refuse to chop, as I've done in the past, but this actually incentivizes the other players to try to knock me out as soon as possible. In a cash game it is profitable to have people gunning for me, but in tournaments it is very unprofitable. Another problem with tournaments is that people routinely work together. For example, players might sell 50% of their winnings to other players in the tournaments for 50% of the entry fee. The problem here is that these players have incentive to let each other stick around, which is unfair to all players who are not involved in such deals because it makes it more difficult to outlast those who have made deals. Of course, people push chips to each other and soft play in cash games a lot, too. I just don't think the effect is nearly as deleterious as in tournaments.

Anyway, I have had several people offer to stake me for the Legends of Poker tournaments. I have almost never made any deals in poker. The exceptions include a few intances involving close friends when I first started playing casino poker and one chop I agreed to at a final table in a tournament. My general philosophy regarding such things is that even if I were willing to trust other players, such deals often have insidious effects on the integrity of the game. However, as long as the person staking me has no other "horses" in the tournament and does not enter himself, I don't see how there could be any conflict of interest. I suppose I have to take my backer's word that he is not backing anyone else, but as long as I don't know of anyone else, there shouldn't be any problem (unless that person is aiding me unfairly without my knowledge, but this idea is pretty far-fetched). The deal, by the way, would be that my backer would pay my entire entry fee and we would split any winnings 50/50. According to one of my prospective backers, I can even ask the tournament director to cut me two checks, each with the taxes taken out, to make it a little more official. I've had one person offer to back me for as many of the tournaments as I am willing to play. Frankly, though, only the bigger ones are worth my time, even playing for free. Most of the tournaments are only $300, which is too small. I'm considering playing in the $1070 NL holdem tournament on Aug 17. As a rough guess, I'd say my EV for this tournament is around $1400. This means that buying myself into the tournament, I'd expect to net about $330, but by getting backed for it, it's worth about $700 to me. Also, my volatility is obviously much lower if I pay no entry fee and only get half the winnings.

Frankly, I think my backers are overly optimistic about my chances: my EV would have to be at least $2140 after taxes for them to make a profit on me. Then again, I may be shortchanging myself; I have very little idea of what the level of competition will be. Another reason it seems like a bad idea to stake someone to a tournament is that it would be so easy for the "horse" to screw you over. For instance, if I took five people up on their offer for one tournament, I could take the $5350 and then intentionally dump off my chips before reaching the money, ensuring that I wouldn't have to pay anyone off! Of course, this would require quite a bit of subterfuge on my part, which has never been my strong suit.

"Exterminator" Mike Defends his Honor

On Saturday, there was a strange occurence at the 20-40 limit holdem game. As you might expect, players are not allowed to turn over the cards of another player under any circumstances, even if the hand is over and they are just curious about what the player had. This would be considered a form of cheating, and, ideally, the offending player would be thrown out of the casino indefinitely. In actuality, this happens every few weeks, and is usually taken as a joke and not such a big deal. The floorperson will, at worst, give the offending player a stern talking to. This seems way too lenient to me, but I can live with it. A much worse offense, of course, would be to turn over another player's hand while the hand is still being played out. A player who did this intentionally should probably never be allowed back into the casino. Until last week, I would have told you I would be unwilling to play with such a player ever again. However, this exact situation occurred on Saturday, it was done pointedly to screw over the other player, and, remarkably, I was quite willing to keep playing in the game with the offending player. Oddly enough, he revealed the hand of the player next to him on the river in order to defend his poker honor.

The player in question is a latino guy named Mike (AKA "Exterminator" Mike because he runs an exterminator business), who I have since learned was in the Marines. He's generally been pretty straight, only rarely getting in arguments, and always keeping his cool. He also happens to be one of the few other players who (like me) doesn't chop.

Here's what happened. An unfamiliar player saying he usually plays at Commerce was in seat 4. I was on the button in seat 7, a talkative Asian man was in seat 8, and Mike was in seat 9, next to the dealer. I wasn't paying very close attention to the hand until the end, but this is how I remember it. Seats 1-3 folded before the flop, seat 4 raised, and only seats 8 and 9 (the blinds) called.

The flop was something like 973 with two spades. The turn was the 7 of spades, and the river was the 6 of spades. So, there were 4 spades on the board. I'm not sure how big the pot was, but probably around $240.

On the river, seat 8 bet out, saying something along the lines of "I have the flush, save your money!" Of course, it's not acceptable to talk like this when there are still more than two players in the hand, but it happens a lot. Anyway, Mike asked, "what's that?" and seat 8 repeated, "save your money, throw it away!" At this point, seat 4 became upset, complaining about the chatter. "Are you guys working together? I'm still in the hand here!" Mike tried to explain to seat 4 that he didn't know the guy in seat 8, but the player in seat 4 pointed out that he had no way of knowing if Mike was telling the truth.

At the time, I didn't really understand what Mike was doing or why, but he suddenly threw his own hand in the muck and simultaneously flipped over seat 8's hand. It was J9, no spades. "There, see! He doesn't have a flush!" Seat 4 called, showing 44 with the 4 of spades for a small flush. A quite impressive scene ensued, wherein seat 8 became considerably animated and angry and called the floorman over. Mike immediately said, "it's my fault. I was out of line." The ruling was that seat 4 would be awarded the pot, and in my opinion this was a pretty easy decision. No "disciplinary" action was taken whatsoever except to tell everyone at the table that there would be no more talking during hands and no more turning over people's cards.

I thought about the situation after the hand and I can't think of any other way Mike could have convinced seat 4 that there was nothing fishy going on. Personally, I wouldn't have screwed over seat 8 like that in order to prove that I wasn't cheating, but that really was an incredibly effective way to prove it. Still, I can't understand why he wasn't at least forced to take a 20 minute "time-out."

Mike was back again today. He said "hi," and I joked "they let you back in here after what you did last week?" He laughed and said "Yeah, any other casino and I would have been 86ed for at least a month."

In other news, I wanted to mention that for the first time in my life I was dealt one of the two candidates for the best possible opening hand in Omaha Hi: AAKK double suited. The other candindate is AAJT double suited. I was playing $80NL Omaha (a new game at the Bike that I think has some hope of catching on... they have also spread it at $100NL), and I won about $50 in the hand by limp-raising and then betting on the flop with a set of kings (both players folded).

Jackpots, My Win Rate, and Volatility

Shortly after winning over $20k in a jackpot and another $1500 table share, I won yet another table share of over $1000.

I make daily records of my results in an Excel spreadsheet. I have it set up to calculate my hourly win rate and hourly standard deviation. After I won the jackpots, I simply included them each in a row of my database, listing each as having taken one hour. Of course, each jackpot actually only required one hand, so the assignment of one-hour time period was completely arbitrary.

Needless to say, the jackpots have a had an effect on my win rate and standard deviation. My SD especially has gone haywire: it went from about $350/hr over the course of my entire career to about $600/hr. My SD for this year comes to $1218/hr after being only $338/hr last year. In other words, recording the jackpots in this way is screwing with my volatility metric. What can be done about this?

I could just leave it like it is. After all, it's true that the jackpots increase the volatility of my income. However, the arbitrary choice of 1 hour per jackpot has far too much influence on the SD for me to be comfortable. For example, if I change the entries to say that each jackpot took only 1/10th of an hour, my SD increases from $600 to $1564/hr, and my 2009 SD skyrockets to $3721/hr.

I think a better solution is to try to separate out my poker-playing results from the jackpot results. I'm reluctant to do this because, in reality, the two are entangled quite insidiously. For example, I am much more likely to call with QQ when there are three aces on the board if I know there's a good chance I'll win a $20kjackpot. Similarly, my opponents certainly play differently - a few will play anytime they have an Ace before the flop because these hands have the best chance at making a jackpot. Many players would not be willing to play the game in the first place if not for the jackpot, and most players won't play with fewer than 4 opponents (the minimum needed for the jackpot to go into effect). Also, my win rate in jackpot games has always been dampened by $2-$8/hr because $1 is taken out of each pot for the jackpot.

Still, what I'm going to try to do is separate out the jackpot results from the poker results. I'll ignore all the above complications except for the most straightforward: I'll subtract out my jackpot winnings and add back in the $4/hr that I approximate I pay into the jackpot drop.

One other thing: the Bicycle Casino is being sued by some poker players over the jackpot drop. The owner is quoted a few times in the LA Times article.

30-60 Holdem, Other Games Returning to the Bike?

I played 30-60 limit holdem at the Bike this past week, and the game was also spread at least two other times since then. This is the first time in months that the Bike has had anything between 20-40 and 200-400. It's a welcome sight to me, because although I do not have to play in games bigger than 20-40 limit, I usually have the option to do so. If I were playing on my own (rather than propping for the Bike), I think I would be playing 40-80 limit mostly. The competition is actually often worse at 30-60 and 40-80 than at 20-40, because the worst players from the 20-40 game are actually the most likely to move up in stakes. In particular, these are often the extremely wealthy people who come to blow off steam but have no patience for trying to play well. I think they just like the comraderie of the game and the excitement of gambling.

Meanwhile, some other new games have been spread at the Bike the past couple of weeks. The most successful is a $100-$300 buyin NL game that has replaced the $100 fixed buyin NL game. It still uses 2-3 blinds, but now players can buyin up to $300. Obviously, this game overlaps with the $200 NL game, which has indeed suffered. Usually, in the afternoon there have been about four $100-$300 and one $200 NL game, although there have been as many as ten $100-$300 NL games at once.

Another thing I'm keeping my eye on is an effort to convert the 20-40 stud hi-lo game into a mixed game combining that and Omaha hi-lo. Hollywood Park has been spreading this exact mix game for years now, and supposedly they often have two games a day (as they did last time I was there). So far I haven't seen this mixed game get started, but other mixed games have occassionally been spread at the 15-30 limit level. For example, I played a badugi-razz mix for two hours two weeks ago, a badugi-razz-holdem-2/7 triple draw the next day, and a badugi-razz-stud hi/lo-2/7 triple draw this week (I won $580 total). I tend to do well in these mixed games. I like to think that it's because I have a good understand of genreal gambling/poker theory, but for the amount I've played, the results depend mostly on luck.

Jackpot(s)!

I've mentioned my disdain for the jackpot promotions in poker rooms quite a few times in this blog. As I was complaining to my brother this weekend, nobody will be willing to listen to my complaints anymore, as I won a jackpot for over $20k on Friday (the 10th) around 3pm. Then, on Tuesday, the jackpot was hit again at my table, and I won an additional $1477 for the table share. I've calculated that I've contributed between $5k-$10k to the jackpot drop since I started, so I'm now up a considerable amount. I still think the jackpot is stupid. Anyway, here's how it happened:

I was in the big blind, playing 6 handed. The first player limped, the second player (Joel, a host for the $500 NL game), raised, and everyone folded to me. I reraised with QQ, the limper folded, and Joel called. The flop was A86, and I bet (not my standard play, but I think it was okay against Joel, who I think is more likely to call me with a pocket pair than to try to bluff my with one). Joel called. The turn was another A. I checked, Joel bet, and I called (I had the jackpot possibility in mind at this point, but I likely would have called anyway). The river was a third A. I sat straight  up a bit in surprise. Again, I checked, Joel bet, and I called. 

"I hope you have it," said Joel, but I wasn't sure if he meant he hoped I had the A (he could have been holding KK, QQ, JJ, or TT, and hoping that I had the A, but he probably would have expected I would keep raising in that case). He showed AJ. The bad beat jackpot require that both cards in both players' hands play. The losing hand must be aces full of tens or better, and the winning hand must be four of a kind or better. I've come close to winning before, but was thwarted by my opponent's small kicker not playing. 

The jackpot was up over $46k (it starts at $40 and goes up by a few hundred a day until it is hit). I got 45% (20,911), Joel got 20%, the other four player in the hand got 5% each, and the players at the other 20-40 table shared the last 15%. 

We had to wait two hours to get paid (the excuse was that another jackpot was hit in the casino just after ours, and we had to wait for all the paper work to be done). After finally getting my money (paid in chips), I opened a player's bank account so that I would not have to carry it all home with me. So now I have money at the casino that I can withdraw whenever I want, which is nice because I don't have to carry much cash to the casino with me anymore.

New Schedule,Again

This past week I've been working on a new schedule. It's not all that different: I now go in at 9am instead of 7am. I'm not thrilled about the change, since it means I have to drive through traffic before 9 and then again at 5pm when I go home. The traffic isn't so bad, though (about 15 minutes extra in both directions), and it's nice being able to get up later than 6am. Also, I was ready for a change of pace after listening to NPR's Marketplace at 3pm every day for the past several months.

It seems like the 2-11 game has died out. I don't think the Bike ever spread it above 4-8.

I'm getting married this Saturday, so I'm taking most of the week off from work.