There is a nice post on the Math and Poker blog on the importance of identifying key variables and the flexibility that is available for many decisions in a process. The example begins with a standard critical-path type scheduling example, making the point that jobs not on the critical path have some flexibility. This point is extremely well known, of course, but it is interesting to think about what to do with this flexibilty. In poker, the author of the blog (I can’t see who it is), notes that there are a lot of situations where the difference between the best and next best decision is not a lot, but can be used to set up the opponents in particular ways (EV in the following is Expected Value):
The way that most people think about EV in poker is like treating each of these tasks independently. If I bet this hand what happens? Things like folding when the pot is small even if calling is +EV for this hand are ignored even though doing so might set up other players, or that player, to make a big bluff on some other hand.
If you really want to optimize your stratagy and maximize your win, they you just have to look at the game in a global sense. A strategic Expected Value of a collection of actions is what you need to consider, not a tactical Expected Value of one action.
So what does this have to do with airline scheduling? A lot of work is being done right now to combat the fragility of airline schedules. David Ryan of the University of Auckland gave a talk last week at the EURO conference on his work with New Zealand Air (my plans are to visit David for most of next year, so I was particularly interested in his work). In this work, David had a measure of fragility of a schedule (generally due to crews changing planes with a short layover: one late plane could quickly affect many others). David showed that there were near-optimal solutions (based on the main objective of minimizing cost) that had much better properties with regards to fragility. Things got even better if the schedule could be modified slightly.
The problem with both the poker example and crew scheduling is that the objective is much “fuzzier” than the underlying main objective. And that makes it much harder to “optimize”.
The idea of robustness is certainly very interesting and has rightfully received growing attention during the last number of years. As computers have become faster and algorithms better we are as operations researchers in many situations able to produce plans that are simply “too good” – they are too sensitive to changes in the initial assumptions, and there will be a lot of changes as we start executing the plans in “real life”. Together with disruption management it will be the theme of the 2009-edition of the EURO “Management Science Strategic Innovation Prize”. More information will be available on the EURO webpage http://www.euro-online.org.
I’m the author of the mathandpoker.com blog.
Your takeoff on my post about poker is interesting and that’s part of what I was talking about.
The other part is that in gambling people tend to think in terms of a static, myopic model. That’s because the idea of EV in determining card game tactics started with Thorpe and blackjack. Thorpe made a splash by pointing out that in blackjack things aren’t static — every card that gets played changes the distribution of the cards left in the stub.
Blackjack players have realized that the players can exploit that sometimes not just with bet size, but by eating up cards to change the distribution on purpose. In team play you might sometimes have a team member making a minimum bet and taking -EV hits to eat up cards so that the “big player” can later make +EV large bets.
In the poker world though the literature seems to ignore the ability to change the distribution of your opponents future behaviors. Given an opponent strategy you can formulate an optimal strategy of your own to exploit his strategy (assuming he makes errors). But when people talk about EV of a particular action they just take the opponents behavior as a given — but you can change his future behavior. His response to your act is a function of his hand and his perception of you. If it’s a small +EV to exploit his perception of you it’s almost a universal recommendation to take that profit.
What I’m saying is that you should often forgo that profit if it’s small because doing so will cause him to recalibrate his assessment of you, inducing him to make bigger mistakes later.
I’m not talking about a fuzzy objective, the objective of maximizing EV is the same, what I’m talking about is introducing a dynamic in the model that isn’t in what generally passes for optimallity in poker.
I think I’m starting to talk in circles again.
I think I am referring to “you should often forgo that profit if it’s small because doing so will cause him to recalibrate his assessment of you, inducing him to make bigger mistakes later” when I talk about fuzzy objectives. Since there is no underlying model of the opponent’s perceptions and assessments, these decisions are, by their very nature, less well defined than the underlying maximizing EV objective. But, as you note, they are critical to the effective solution of this problem.