A simple optimization problem

Here's a simple optimization problem that doesn't require anything other than high school algebra and maybe some basic calculus to solve.



The technique it illustrates is just one of basic substitution when you have a problem that can easily be reduced to a problem with a single variable.

What is optimization?

Here's a video of Leon Lasdon giving a talk with some examples of successful applications of operations research.



Lasdon is one of the old guys in operations research, and he says something at the start of his talk that struck me. "Everybody knows what optimization is", he says.

I used to think that was true also. But it's really not. In the poker world many people confuse the idea of optimal with that of equilibrium. In game theory you can find the equilibrium solution as an optimal solution of a min/max problem. So among poker math dweebs it's become common to term a solution of a game theory model as optimization and to describe exploitave.

In the poker world optimization has become exploitive and equilibrium has become optimization.

Outside the poker world optimization just means doing the best you can within whatever operating constraints you might have, just like Lasdon says in the video.

Sometimes I feel like Don Quixote tilting at windmills to try to use optimization to mean optimization when talking to poker dweebs.

What is operations research?

A 6 minute overview of uses of operations research.

Orthogonal

In recent arguments before the Supreme Court some lawyer used the word "orthogonal" in a way that I thought was a pretty natural meaning. (see Simple Justice, Washington Post, or Althouse.

MR. FRIEDMAN: I think that issue is entirely orthogonal to the issue here because the Commonwealth is acknowledging -
CHIEF JUSTICE ROBERTS: I’m sorry. Entirely what?
MR. FRIEDMAN: Orthogonal. Right angle. Unrelated. Irrelevant.
CHIEF JUSTICE ROBERTS: Oh.
JUSTICE SCALIA: What was that adjective? I liked that.
MR. FRIEDMAN: Orthogonal.
CHIEF JUSTICE ROBERTS: Orthogonal.
MR. FRIEDMAN: Right, right.
JUSTICE SCALIA: Orthogonal, ooh.

I was going to make a post about what dummies we have on the Supreme Court until I mentioned it to my girlfriend (whose degree is in psychology but she's still not a dummy) and she said, "Huh, what does that mean?".

So I guess the dummy is me, the one that just assumed that if it's a word I've commonly used it must be a word that everyone knows.

Card shuffling

How many dovetail shuffles suffice?

Anchors

Poker is partly a game of card distributions and partly a game of psychology. The card distribution aspects of the game can easily be straightforwardly modeled via rather simple mathematics (even if if might be computationally complex). The psychological aspects are often not so straightforward.

One of the psychological complications is the concept of anchoring.

Anchoring and adjustment is a psychological heuristic that influences the way people intuitively assess probabilities. According to this heuristic, people start with an implicitly suggested reference point (the "anchor") and make adjustments to it to reach their estimate. A person begins with a first approximation (anchor) and then makes adjustments to that number based on additional information.

Anchoring can manifest itself in many ways in poker, the most prevelant is the tendency to use pot size as an anchor in determining bet size in no limit poker. Bhy manipulating the pot size we can effect the tendency of our opponents to pick a bet size on future betting rounds. Anchoring our bets on pot size has become so common in poker that it seems natural.

It's a tendency that can be manipulated -- not just by manipulating the pot size, but by manipulating the physical size displayed by the number of chips. By using larger denomination chips we might make the pot seem smaller to the opponent. Using a green chip ($25) in a red chip ($5) game might do that. But using a black chip ($100) in a red chip ($5) game might have the opposite effect, the unusually large denomination might have the effect of making the pot seem huge.

One thing you can be sure of -- your bet denomination choices will effect your opponents future behavior, even if you can't be sure what that effect is.

A Computer Scientist in a Business School has some examples of anchoring.

Informs Blog

INFORMS is an academic society for Operations Research and Management Science. It was formed a few years ago by merging two groups (Operations Research Society of America and The Institute of Mangement Science) that were formed separately in the 1950's. They used to be separate organizations that had joint meetings -- twice a year. One called ORSA/TIMS and one called TIMS/ORSA. I used to go to almost every meeting but since nobody is paying my travel and registration expenses these days I don't go anymore.

I did go to the one in Pittsburgh a couple of years ago to give a short talk on Poker Bankrolls and was going to go to a Regional Meeting in College Station last year to give a similar talk, but I had a heart attack and went to the hospital instead.

The merged group doesn't have two meetings a year, just one. And this year it's in San Diego and it's going on right now. What's cool about this years meeting is that it's being blogged in a group blog.

The blog is worth checking one, it's giving a pretty good superficial introduction to what Operations Research is all about.

I went to an ORSA/TIMS (or was it TIMS/ORSA?) meeting in San Diego back in the 1970's and gave a talk on a flaw in the way a game theory model of poker that had been published in the flagship journal (Operations Research) treated hand values in draw poker. Back then there were entire all-day sessions devoted to gambling models. Primarily because blackjack research was in it's heyday and modern mathematical finance was just starting out and often using gambling models to study financial markets.
INFORMS doesn't cover gambling so well anymore. The topic has kind of played itself out among math dweebs. They do cover applications in sports, but not so much sports betting as in sports tactical decisions.