Wednesday, January 21, 2015

On Games And Knowing Yourself

I’m in a philosophical mood this morning, owing in part to a short exchange of thoughts I just had with Joseph P. Martino, a retired Air Force Colonel who’s done valuable work in several areas of strategic analysis. In reply to my thoughts here, Joe posted the following:

Granted, it does not make sense to try to estimate the probability that God exists. There's no way it can be done.

My dissertation adviser used to argue against using "expected value" to evaluate bets. He used the example, suppose you are offered 999,999 chances in a million of making a million, and one chance in a million of being shot (zero payoff). Clearly the expected value is almost a million, but the possible catastrophe makes it a bad bet. In any situation where there is a possible catastrophe, maximizing expected value is a poor strategy.

However, in Game Theory there are other strategies besides expected value. Minimax loss is one (minimize the maximum possible loss). Another is minimax regrets, where "regrets" are what you could have won had you had perfect foresight. There are others, but these serve as examples.

Pascal's Wager is clearly a minimax loss strategy, and need not have anything to do with the probability that God exists. It simply asks, "what is the worst that can happen" for each possible strategy, and chooses the strategy with the minimum possible loss. I don't think his recommended strategy is at all unreasonable.

All perfectly true...but it got me thinking about the under-layer of game-playing, which objective analysis never addresses for a simple reason I shan’t insult your intelligence by stating explicitly. That under-layer is worth a few hundred words all by itself.


As you probably know, I’m a chess aficionado. One of the things that dismays most contemporary lovers of the game is the attitude displayed among grandmasters toward the possibility of loss. Needless to say, they’d rather not. However, their typical aversion to even the possibility of loss is such that very few of them will take even a small risk – i.e., will adopt a plan of campaign that endangers their ability to force a draw – even if such a risk offers an excellent chance of winning. In consequence, the average top-level tournament is heavy with draws. Current practices set their frequency at about 55%.

An exhaustive objective analysis of the game of chess is currently beyond the powers of computation. Granted that there are programs which can outplay any human player; nevertheless, the state of the art in such programs continues to advance, which implies that there are further frontiers to be crossed. Among human beings, the game is hardly “played out,” despite the predominance of drawn games.

Those draws aren’t because draws are in some objective sense the “right” outcome. They’re the products of a prevalent aversion to losing that dwarfs other priorities.

Several players of the past few decades have become greatly beloved because they didn’t fear to lose. The brightest stars in the chess firmament include at least three such: Mikhail Tal, Bent Larsen, and Garry Kasparov. Their approaches to the game, while not perfectly consistent with one another, all exhibited a degree of risk-taking that many commentators have called romantic or enterprising, while a few have termed them piratical. In short, they were willing to take risks, sometimes large ones, because their highest priority wasn’t to avoid losing.

In a game between humans, whose analytical powers are limited and whose emotions often play at least as great a role as their intellects, the willingness to take risks will have its own rewards. This is especially the case when a Tal, a Larsen, or a Kasparov faces a player whose fear of loss eclipses all else about him.

It’s about priorities and emotions quite as much as about foresight about possibilities and accuracy of analysis.


“ If the probability of success is not almost one, then it is damn near zero.” – David Ellis, quoted by Paul Dickson in The Official Rules.

Probabilities matter. The severity of possible outcomes matters as well. No argument. But priorities and emotional proclivities matter even more. Let’s look at Joe’s example once more:

My dissertation adviser used to argue against using "expected value" to evaluate bets. He used the example, suppose you are offered 999,999 chances in a million of making a million, and one chance in a million of being shot (zero payoff). Clearly the expected value is almost a million, but the possible catastrophe makes it a bad bet. In any situation where there is a possible catastrophe, maximizing expected value is a poor strategy.

The final sentence above should get you thinking:

  • What outcomes would constitute a catastrophe that absolutely demands to be averted?
  • Is there no alternate outcome that might counterbalance such a catastrophe?
  • Do the probabilities not matter at all, regardless of their values?

I contend that the answers are other than Joe’s dissertation advisor claimed. If we limit ourselves to spatiotemporal outcomes, there is no catastrophe so bad that some potential payoff can’t be balanced against it. More, the probabilities do matter, as they who dwell in New York City demonstrate every time they cross a city street: A pedestrian in the Big Apple is hit by a car every 20 minutes. That hasn’t put a halt to street crossings on foot. Your probability of being in a fatal auto accident this year is on the order of magnitude of 0.000001 – the probability of being shot in Joe’s example – yet millions of Americans drive to work every morning, despite the rather lower probability of being given a million dollars when they get there.

The deciding factor is your personal “zero threshold:” how small a probability must be, in your estimation, for you to discount it as negligible for your personal decision-making purposes.

Of course, that you’ve classified some probability as negligible doesn’t mean that the associated outcome can’t happen. It only means that you regard that degree of risk as acceptable, given the other possible outcomes and their probabilities. You’ve made a priority decision. You make such decisions every day. Moreover, should you “roll snake eyes” some day and reap a terrible outcome that you regarded as an acceptable risk, it will have very little impact on the priority decisions of other persons.

Some of us “learn,” if alterations of our priorities and our personal risk-aversiveness can be called that, from others’ experiences...and some of us resolutely go our own ways despite the cautions and fears of those around us. And thus shall it ever be, until Man is no more.


As my retirement approaches, I’ve given ever more thought to financial planning. I’ve been something of a risk-taker up to now, placing my bets on aggressive growth stocks – high upside and high downside – when I invest. But at all times those risks were buttressed from underneath by my earning power, which has been sizable throughout my working life. More, up to fairly recently I was a glowing specimen of bodily health and personal energy. I was confident that whatever might happen to me, I could swiftly recover from it.

My earning years are about to end, and my health is no longer what it was. Given those developments, does it surprise you to learn that I’ve become more cautious about money than I once was? Don’t all answer at once, now.

The probabilities and the possible outcomes have changed somewhat. At this point a disease or an injury my younger self would have shrugged off might kill or permanently cripple me. I can’t rely upon a stream of above-average income to make up for losses in the equities market. Another person’s well-being is bound to mine. And of course, the political backdrop for all my decisions has darkened considerably since I first became self-reliant.

I’ve adjusted my priorities in recognition of those facts...but they remain my priorities. I know of several persons in roughly the same situation who remain gleeful risk-takers, often to the dismay of those who love and depend on them. And I know of others, again placed approximately the same, who’ve grown more risk-averse than I could ever dream of being.

This is what we are: individual human beings with individual motivations, capabilities, desires, and fears. Individual “zero thresholds.” Individual levels of confidence in our abilities to pick ourselves up, dust ourselves off, and continue onward. Those things might change over time, but they will always remain individual...idiosyncratic...as much a matter of emotion as of reason, if not far more so.

Anyone for a friendly game of Acey-Deucey?

7 comments:

Dystopic said...

Yesterday, heading back to work from lunch at a Tex-Mex chain, a friend of mine expressed incredulity at the notion that people still fly little single-engined Cessnas around. The things have a terrible safety record. Two of them crashed around here in the last few months.

I responded that the Wright Brothers took their leap into powered flight on a haphazardly constructed, untested airframe constructed from used bicycle parts.

Risk, today, has become a dirty word, a thing to be avoided at all cost. Nearly 50% of people in America are on some form of government assistance, because they cannot dream of standing on their own. They cannot imagine life without a safety net. It's too risky. They might not make it on their own. The plane could crash down.

But all that dead weight is, itself, a risk. It is a much greater risk than that of mere individual failure.

If you haven't already, give Nassiim Nicholas Taleb's book, Antifragile: Things That Gain from Disorder, a try. I found it remarkably insightful about matters of risk.

Anonymous said...

Good food for thought. I'll throw a couple of my own ideas in. I find myself somewhat of a risk-taker. I do try to minimize my losses in personal endeavors as basic as driving a car, but when it comes to important things, such as, say, preparing to defend myself and perhaps others in public from some sort of potential attack, I think my mindset is distinctly weighted to take the risk. Not the stupid, careless risk, but simply the risk that doing "something" is more important than doing "nothing", but also inherently riskier.

I will also throw in that, for believers in a higher power, it may seem like a choice, to believe or to not believe. Perhaps you have your days of doubt, intermixed with your underlying belief. I am a non-believer, and unfortunately it is not a choice for me. At a very basic level, I simply can not believe. There's never a day where I think, hmm...maybe there IS a God. It's not a happy proposition. I'm not PROUD of it. It just is what it is. I recognize that there are very few downsides to believing, and that the upside is great. But my mind won't believe, can't believe. I don't let it bother me too much though, and I am aware of Noahic law. Thankfully, I've lived a life that mostly adheres to this code, and then some. So hopefully my downside risk is more limited. And in that way, perhaps I HAVE considered, "what if?"

The Colonel of Truth said...
This comment has been removed by the author.
The Colonel of Truth said...

Enjoyed your article Fran and the two comments...I am passionate about decision making and the military decision making process (MDMP). One of the things that drives our choice (what we decide to do), aside from known facts, is assumptions (about the future, our adversary, our capabilities, weather, market conditions, etc, etc.).

Understanding/writing our assumptions down can be useful in helping to see if we're being realistic. You alluded to a bunch of them...one of the assumptions I've been unable to shake is the eventual collapse of the dollar.(I'll just leave that there.)

To Anonymous: I would respectfully submit that faith comes by hearing, and hearing by the word of God (Romans 10:17).

The New Testament book of Hebrews describes faith this way:

11 Now faith is the substance of things hoped for, the evidence of things not seen. 2 For by it the elders obtained a good testimony.
3 By faith we understand that the worlds were framed by the word of God, so that the things which are seen were not made of things which are visible.

Please consider reading the rest of it. I promise you it is not beyond your grasp, but you do have to reach out for Him. (https://www.biblegateway.com/passage/?search=Hebrews%2011%20&version=NKJV)

Bless you all!

gamegetter II said...

Nooooo-not acey-duecy.
Lost on A-K,then later the same night,lost on A-2.
Cost me a weeks pay-that hurt,it also should have never happened twice in a couple hour period of time.
What's the odds of losing those two in the same night??

Anonymous said...

Colonel, I am anonymous, and thank you for the response. I'm certainly not here to further atheism, as I said, I don't think it helps our common cause, and I'm not offended by religion. But I will say, I can not seek God out, because I do not believe a higher power exists. I do believe underlying forces are at work, things we don't understand, but I definitely don't believe these are God or God-like. Space, time, particles, photons, forces, that's about it for me. I believe the answer to "where did these things come from" would be "God" from a believer, and "as yet unknown, but not likely a 'higher power' as such" from a disbeliever.

To give you a little more insight into where I'm coming from, and I don't mean any disrespect to your very nice response, but I did read the passages at the link you sent, and here are some of my thoughts. When I read: "Therefore God is not ashamed to be called their God, for He has prepared a city for them", the only thing I can think, vehemently, is: "I don't believe anyone has 'prepared a city' for me, and if on the off chance that God exists and HAS, I want nothing to do with that city, I'll make my own way". I wouldn't say I'm "angry with God", but when presented with the concept of a God who would do things on my behalf, it's frankly infuriating. I don't ask for anything, I don't expect or want anything, I just want to do my own thing, and success or failure, let the chips fall where they may. And if someone presumes to "go to bat" for me, without actively consulting with me about it, then I reject them outright. If my choices are Heaven or Hell, and I have to accept someone's sacrifices on my behalf in order to go to Heaven, then I truly deserve to go to Hell. And I don't believe I deserve to go to Hell, so that whole thing falls apart for me.

Anyway, again I thank you for directing part of your response to me, and I don't aim to be Anonymous the Atheist. I don't believe, but this is a personal conviction for me. I don't think it's the right viewpoint to hold, I hope others can avoid it, I'm just stuck with it.

Reg T said...

Priorities are indeed significant when choosing what actions to take. When suffering, years ago, from two cranial nerve neuralgias that caused excruciating pain, _not_ putting my wife through the pain and difficulties that would have attended self-termination was a higher priority than ending my pain, which wasn't responding to anything various doctors had tried (until the problems were finally, correctly diagnosed).

Conversely, I have often thought that I would gladly give my life to successfully remove one or more of the individuals causing so much damage to America, our Republic and the rule of law, if I had even a 50-50 chance of success. Alas, I know I possess neither the skill nor the resources, but that doesn't cheapen my willingness to place a higher priority on the _true_ state of our Union than upon my love for my wife (and less for love for my own life.

I, too, am a heathen, and have no thought of "going to a better world" when my life is ended, so I don't have that to fall back upon, to reduce the fear of dying. Nonetheless, _my_ priorities are such that living, while desirable and still mostly enjoyable, is not at the top of the list.

Giving my life for a loved one, for an innocent child or woman in harm's way, or for a significant attempt to return us to a country that values the rights of the individual, are all at or near the top of my list.