Tuesday, May 10, 2011

Poker probability in non-poker life

While I was in Florida with Cardgrrl in March, somehow we got talking about refractive eye surgery (LASIK and other such procedures). I said that I would love to be free of glasses, but the life consequences of any significant visual loss are too terrible for me to be willing to risk it, even though the chance of such an outcome is small.

She agreed, and noted that playing poker has given her a greater respect for small-percentage results. Playing poker a lot, you see 1% scenarios happen often enough to make a lasting impression that they are real. On paper, that 1% looks like a trivial, negligible fraction, but playing thousands of hands of poker, of course you're going to see a fair number of them come out.

I agree with her that playing poker has changed my perspective on rare events. It's not that I think things happen more often that the math would predict, it's just that I've come to incorporate, in a front-of-the-awareness manner, the reality that small percentages multiplied by a large number of opportunities means that the rare things not just might but actually do occur with regularity.

Translated back to the surgical situation, if I had to have a tumor removed to save my life, of course I'd accept the small risk that the surgery itself would have some freakishly rare adverse outcome. But I'm not willing to accept that risk when the only advantage is losing the little bit of nuisance that glasses represent.

Today I found another example in which my occasional study of poker probability has influenced the way I think about something. I heard on the news that the Fourth Circuit Court of Appeals hearing one of the big Obamacare constitutionality lawsuits had "randomly" selected a panel composed of two Obama appointees and one Clinton appointee. (See here, e.g.) I'm not normally inclined to conspiracy theories, but that immediately struck me (and, undoubtedly, many others) as a stacked deck. So I looked into it.

I found that the court currently has 13 members, of which five are Republican appointees and eight are Democratic appointees. (See the tally here.) I've run enough poker scenarios to have become reasonably familiar with the math on permutations and combinations, and quickly determined that there are 286 different ways of selecting groups of three judges from a pool of 13. There are only ten ways of drawing panels of three Republican appointees, 56 ways of drawing panels of three Democratic appointees, and 220 ways of drawing a mix.

If, therefore, you ask the question, "What is the probability that a random assignment would result in a three-judge panel of all Democratic appointees?", the answer is 56/286, or about 20%. It's not the most likely outcome, but it's hardly in the range of rarity that makes sensible people don tinfoil hats. It's in the same ballpark as your opponent hitting his flush draw on the river after all the money is in on the turn--i.e., run-of-the-mill unlucky, not extraordinarily unlucky.

I understand probability a lot better now than I did after taking a graduate course in statistics, and it's entirely because of poker. The optimist in me would like to think that teaching everybody poker would have a beneficial effect on the populace's generally abysmal understanding of probability and statistics. But the realist in me remembers all of the stupid ideas about randomness that even experienced poker players develop ("I never win with aces," "I figured he couldn't have diamonds two hands in a row," "Jacks are coming up a lot today," "A new deck of cards will end my bad streak," etc.), and it crushes any sprouts of hope.


taximike44 said...

Good call on nixing the eye surgery, though i'm not sure why you flew to florida, or more to the point, traveled to florida, seeing as how a plane crash or bad interstate highway crash will probably cause you to lose more than your eyesight. I figure it was an oversight on your part, but in the future you should be a little more careful.

Anonymous said...

Hi mr grump

If u haven't tried them I would really recommend contact lenses, I can't live without them, pop em in when get up and leave them in until bed.

I've not had them that long and was bit worried would have to use glasses for long periods on the tables in Vegas but happy to say no problem at all!

DuggleBogey said...

I disagree with you about the lasik.

You might think your glasses as a "slight annoyance" but the pleasure of not needing them is something you can appreciate EVERY WAKING MOMENT OF EVERY DAY.

Lasik was the best thing I ever bought for myself, by far.

Yes, there is risk, but there is risk crossing the street or driving your car. There's nothing you can do to keep the car in the other lane from turning into you, but that doesn't keep you from driving, does it? It doesn't even stop you from driving when you don't really need to.

But what do I know? I ride motorcycles. They're not as safe as cars, but life is an adventure. If you live it like your afraid of all outliers, then you're barely living.

Rakewell said...

Duggle: Serious question here, not trying to be snarky. If you had turned out to be the 1 in 1000 (or whatever the number is) that had a terrible outcome--scarring, irreparable visual loss--do you think your thoughts dealing with it every day would be (A) "Wow, that was a stupid decision I made--what was I thinking?" or (B) "The chance to live without glasses was totally worth the risk of enduring what I have to put up with now"?

When I get all my money in as a huge favorite but lose to a one-outer, I'm obviously unhappy about it, but I still know that I made the right decision in terms of risk/benefit analysis. I'm not at all sure that if I hit the LASIK one-outer I would retrospectively judge myself to have made a good decision.

Michael said...

Interesting post. I've wore glasses or contacts all my life. My eye doctor has told me that I'm the type of person he'd recommend Lasik too. My hold up so far I guess has been from % as well, while I don't over concern myself with the catastrophic effects, I've become so accustomed to contacts that I worry about the hardening of the lenses making it impossible to wear them if needed.

My solution has been to wait, I've essentially weighed the reward against the risk and determined that the longer I wait, then the less years that I'd have to deal with the issue if there is a problem.

Certainly not the most logical conclusion.

Carl said...

While I agree with your line of thinking (and the general points you made here), there are several other things that enter in to the likelihood of you having an issue with Lasik, specifically.

The number that you get for "Likelihood of bad outcome" isn't really the probability of your procedure going wrong. It's the total number of bad outcomes over the life of the procedure, divided by the number of procedures. If the rate were constant, those would be the same, but it goes down over time, as technology improves, practitioners improve, etc.

It also includes results from all practitioners. And with Lasik, specifically, the requirements for performing the procedure are shockingly low. Cosmetic surgeons can do it. I would assume that their rate of complications is higher than the rate of someone who does corneal transplants as well as Lasik.

This is definitely a case of "lying" with statistics. An average gets presented as if there is a uniform distribution of outcomes, when that's far from true. That said, regardless of how non-uniform the distribution is, the probability of a really bad result is never actually zero in any case. But, in this case specifically, you can take steps to reduce it.

It could be that I'm just justifying my decision to undergo Lasik (confirmation bias? of course!). My outcome was not ideal (about 20/25), but I still think it's worthwhile. I really only need glasses now to prevent eyestrain after a longer stretch reading, etc. I can do a lot of things without, which I couldn't before.

You might enjoy Fooled By Randomness, if you haven't read it. There's quite a bit on topics similar to this one.

Rakewell said...

I have read it.

Sebastian X said...

Get one eye done. If it goes well, get the other done.

Jeff Simpson said...

I like the one-eye-at-a-time suggestion, if only because you can then legitimately sport a monocle.
Very Col. Klink, and maybe intimidating at the table.

Anonymous said...

Wow, Grump. I'm surprised. I think in this case, "poker" thinking has led you astray.

I would certainly agree that in playing poker, those rare scenarios do happen often -- but only because you see so many trials. To equate that to increased risk in your personal life is quite a stretch. To state the obvious, an event with a 1% likelihood will occur about once in 100 trials. But if you run 100,000 trials, you'll see 1,000 "rare" events. But it's of course no more likely to occur -- just more likely to be seen. I know you state that you don't think they happen any more frequently than the math would indicate, but I would say that your heightened awareness translates into an overstatement of the risk, specifically in this case.

And to relate it to Lasik -- you'll only be doing one trial (arguably two, but most stats I've seen seem to be per surgery, not per eye). So I think you're overstating the risk. Also, stats I've read show that significant loss of vision is much more rare than 1%, with no cases of blindness ever being reported.