Carl Sagan

I read Sagan's books Cosmos and Pale Blue Dot last year, and can wholeheartedly recommend them for anyone interested in science in general and history of science in particular. Just a few days ago, I re-read his fictional work, "Contact" (later a major motion picture starring Jodie Foster and Matthew McConaughey). It's a good book. It's also a good movie, with a surprisingly true-to-the-book script. As always, movies take away a lot of the learning experience of a book because it doesn't make good drama to have a voice-over explaining all the science, a problem CSI has solved by invoking corny conversations between their characters ("what the DNA-analysis does is...", explained to a person who's supposedly an expert on the topic).

I'm sliding off-topic here. Anyway. My somewhat recent elevation of Sagan as a scientific hero of mine (a promotion earned not necessarily for his academic achievments but for his contageous enthusiasm and efforts to make others interested in the subject) made me think the video below was a little bit more cool than I think most of you will find it.



--

My last post, on river bet-sizing, sparked some misunderstandings when discussed on CardsChat. I'm not saying that a small bet-size is optimal for a river bet. I'm saying that a smaller bet-size is what you should be shooting for. Smaller isn't necessarily small, if that makes sense. Now, bet-sizing for value was actually just a build-up to the post I was going to make next: Bet-sizing for bluffs. I'll put that up later this week, but cunning readers may guess where I'm going with it.

--

Okay, one more video to link: Sam Harris spoke at TED in February. I saw that his name was on the speakers' schedule and have been waiting for them to publish it ever since. Now they have, and I wasn't disappointed.

On river bet sizing with the nuts

Here is the graph outcome of my simulations that I mentioned in the last post I was going to make. I'm using a very simplified model in these simulations and I'll explain some of the problems with it at the end of the post, but for the time being we'll just go with it. In order to understand the graph and what it says, I should explain what the program does and what I'm trying to show:

When we have the nuts on the river, extracting value is the only thing that should be on our mind. How do we make the most money? Often, the answer is "bet big." In fact, that's usually what books suggest, and while the correct decision always hinges on board texture, our opponent's range and varying degrees of level thinking, what I want to get across is this: If your opponent is likely to have a medium strength hand and you think he'll on average call a bet-size of X with that hand, then you should bet less than X.

Let's give it a number so we don't have to have that frightening variable name 'X' looming over us: Let's say that our opponent will on average call a bet of $100 and then compare what our outcome is if we bet $90 compared to $100. What we mean when we say "on average" in this case is important. It means that the bet our opponent is willing to call lies somewhere around $100. If we bet over whatever his breaking point is, he's just going to muck his hand because he's not willing to pay that much to see a showdown, and if we go below it, we're guaranteed a call. So far, so good, yes?

So what we mean when we say that he'll on average call $100, that means that his maximum amount for calling lies somewhere in the range of perhaps $80 to $120. Or differently put, he'll always call $79, but never $121. In between those amounts, we're not sure exactly what he'll do. But then our bet size should be much closer to $80 than to $120. And it's relatively easy to explain even without a graph, because if he'll call on average $100, that means - with this usage of average - that our expected value for betting $100 is $50. Half the time, he'll fold and half the time he'll call, and so we'll make $50 on average. Right?

But our expected value for betting $79 is $79, because he'll always call. So we're doing much better betting smaller.


The horizontal axis is the bet size. The vertical axis is the average profit.

a and b denote the min and max of our opponent's calling-amount range. x is the average amount he'll call. The straight line that rises up to the left of a is the amount of money we'd make if we bet less than his minimum, and then our profit will go up linearly until we reach a. Making the maximum bet, b, is clearly the inferior option.

The easiest way to understand the conclusion is perhaps to consider a hypothetical opponent where we happen to know exactly where his breaking point lies. Let's say that Bob has his breaking point at $80. That means that if we bet $81, we make absolutely nothing but if we bet $79, we win $79. That's what this graph reflects.

---

But, like I said, the model I used for the simulations was heavily simplified, and so let me be clear on how:

1. I used a uniform distribution for their calling amount. In other words, their breaking point was as likely to be $85 as $115, when the reality probably is different; perhaps a normal distribution around the average? This would affect the shape of the graph, but not the conclusion.
2. I did away completely with psychology, obviously. It's not entirely out of the question for some situations that larger bets are more likely to get looked up than smaller bets because they think a bigger bet looks suspicious.
3. I also didn't factor in the possibility of getting raised. While simplification #2 builds a case for a bigger bet than what my model suggests, the possibility of a smaller bet inducing a raise (bluff or otherwise) should counteract that at least to some extent.
4. Most importantly, this model targets a specific hand that our opponent has. In reality, our opponent is going to have a range of hands, some stronger and some weaker, and it's not at all as clear cut exactly how we should bet when his distribution of hands includes some strong hands. For instance, 90% of the time he may have middle pair top kicker and the graph above applies, but 10% of the time he has an overpair and will in fact call a much bigger bet. Now the distribution is definitely different and this will have quite an impact. In fact, we might end up with a graph with several local maximums.
5. I'm also assuming we have the nuts (or rather, that we'll always win when he calls). This is not a big problem with the model, though, because firstly there are plenty of river decisions where we can feel confident that the risk of our opponent having a better hand is negligible, and secondly it doesn't actually affect the conclusion: if some of his calling range beats us, that (mostly) speaks in favor of betting smaller.
   

Despite these shortcomings of a very simple model, I think the conclusion is an important one and is often valid: A bigger bet isn't necessarily more profitable. If our opponent's likelyhood of calling it goes down, we're mostly better off just betting smaller.

Whoops

So, uh, yeah. If anyone happened to catch a post I wrote earlier today with a weird picture of Bennie in it; just ignore it. I had a friend over who wanted some help with Blogger.com and I was going to show her basically how to add a picture and some other stuff; long story short I accidentally posted the sandbox experiment and that was that.

Anyway. Poker related:

Sometime this weekend, I'm going to do some coding (I'm on paternity leave and need to stay at least a little bit sharp) and make a program that runs some simulations on what I think is a fairly important concept in no-limit poker. The idea is to use the output of the simulations to create some Excel graphs to illustrate the concept. So keep an eye out for that.

I'm normally hesitant to post teasers like this because every so often it ends up not getting done and then I feel like a schmuck for saying I'll do something and end up not doing it, but I wanted to post something other than "if you happened to see my last post, pretend you didn't see it." So there. And maybe now the code will actually get written instead of the idea just staying in my head in the category of "neat, but I'll get to it when I have some time."

Books Arrived

Yay! Excitement! Happiness!



I'm currently reading Uncle Tom's Cabin and while I'm enjoying the book, I still look longingly at the pile that arrived today and feel like the kid who needs to finish his vegetables before he can have chocolate cake. Oh well, the veggies are good for me, I suppose. In the meantime, I get to walk around the pile and think about which one I'll dive into first.

Better than christmas morning, this is.

Now Playing at iPoker

I hinted in the last post that I was doing alright so far this year, and that has brought on a convenient problem to have: I'm seriously overrolled for 1/2 and feel like I should really move back up to the midstakes. Why is this a problem at all? Because I get most of my poker played between 10 to 11a.m. and 2:30 to 3:30pm, European time - and those are not prime hours for picking good tables at Party Poker. In fact, in the morning hours I'd be lucky if I could even get a seat at six tables in the hour I have to play.

So I decided to give iPoker a whirl. So far, I'm so very not impressed. I've played iPoker before, but I didn't realize how many issues there were with their software that bugs the hell out of me. I have to make three clicks in order to get on a waitlist? What the... Non-resizeable tables? You've gotta be kidding me! Taylor hinted that I should install MiniMaxMod, so I did - and promptly spent three hours trying to get it to work in a way that made sense at all, and failed. So I gave up, at least until someone can help me figure out how to get it to work. I'm also not getting my BetPot script to work (despite it supposedly having iPoker support) so now I'm doing it old-school. Not happy about it. Not sure if I'll stick around for more than just this one month that I decided to spend giving it a try. We'll see.

I'm amused by the fact that apparently iPoker has set a "quota" of how many winning players a specific skin is allowed to have. I thought this was a joke at first, but it appears it isn't. I have no idea how they figure this is good business, but if I'm informed that I'm limited to playing 10NL, off to greener pastures I go. Anyone have any suggestions for greener pastures? Requirements include a decent number of tables running 24/7 at the midstakes and it being a European site for taxation purposes.

I just wish Stars or FTP would move their servers to Gibraltar. Would make my life a lot easier.