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.

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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.

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“ 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.

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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?