ATRIUM MAP,
part of the Bod Library-On-Line’s
~~Inverse Annex for play research…
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~~~~~A Golden Balls Analysis
~~~~~How the Inverse Annex got its name
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ATRIUM FEATURES–
Atrium feature #1: A Golden Balls Epiphany/ Analysis
Atrium Feature #2: HOW THE INVERSE ANNEX GOT ITS NAME
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Atrium feature #1: A Golden Balls Epiphany/ Analysis
The Golden Balls Game Show–
The situation: In the final stage of the Golden Balls game-show, two players must each choose whether to play a split ball or a steal ball. (Outwardly the same, the choice inside.) Players choose & then reveal after having some discussion. If both choose split, they divide the grand prize half & half. If one reveals a steal ball while the other has split, the former ‘steals’ it all, the latter gets nothing. If both choose to steal, neither gets anything! Prizes at stake can range from a relatively few pounds to more than a hundred thousand, depending on earlier stages of the show’s play.
Statistical analyses of match results have been carried out by at least two research groups. I’ll share their fascinating findings in a follow-up, but first offer some comments on what’s been called “the most unusual Golden Balls match ever,” & “a brilliant solution.” Before reading it, however, take a moment to consider what your strategy might have been. Let’s say there’s $30,000 in the prize pot. Your “partner/adversary” presumably proposes that you agree to split, of course.
The Unusual Match: The pair included a dedicated game player who’d been on many game-shows, a young man who worked for a charitable organization benefitting children. His ‘partner/ potential opponent,’ about the same age, strongly advocated that they should agree to split the prize, pledging their word. He described how his father had taught him “one’s word is one’s life,” & “a man who doesn’t keep his word is not a man.”
Until this point, the game was developing as usual. The “master” player’s novel tack was to announce that he was going to be completely honest, itself not an unusual claim, except in his case, he then stated his intention to present the steal ball! “If you vote to steal also, neither of us will get anything,” he explained. “But if you vote to split, I’ll give you half afterwards.” No argument could shake him in his expressed intent, seemingly leaving the second player a choice between definitely getting nothing (by also presenting the steal ball) or going along with that plan (using the split ball, knowing he’d lose), on the hope (not legally binding) that he’d be given half (or at least something) after!
Result [available on YouTube]: The second player felt he had to go along, all the more ironic by the fact revealed after that, despite all his word-keeping rhetoric, he’d come intending to steal. All the business about his father’s teachings had been totally made up. (He’d never met his father.) Faced with the stark choice between what seemed like the certainty of getting nothing and some possibility his seemingly honest opponent would follow through with at least part of the promised reward, he changed his plan–and voted to split.
With a final twist that raised many new questions, the master gamer also revealed “split,” fulfilling his original promise to give the partner half, but one step earlier. [The original promise might have been problematical due to guest logistics designed to prevent subsequent contact.] By short-cutting to the split-split result, he raised the possibility that a future user of that approach would meet someone who would try to steal, turning the situation into a version of rock-paper-scissors. In a sense, the player introducing the strategy also sabotaged it.
He may have had to, given technicalities of the show, which might also have otherwise changed its rules to preserve its more usual dynamic. If the strategy in its pure form were to be used successfully, the audience would certainly need to know what happened in the follow-up–which players gave how much of what they’d pledged, for example. (Variations might also have arisen in which an announced “stealer” offers to share some portion less than half.) The game would no longer end at the conclusion of the show.
As far as I can tell, no one else has tried that approach since. There’s something unsettling about that final twist, besides, the supposedly “honest” master-gamer being dishonest about which ball he would play while remaining honest about his intent to split! To preserve the brilliant strategy in its pure form, one may argue, he should have followed through as stated, i.e., remained totally honest, including about which ball he was playing.
That could have been the end of the show, however, at least changing it dramatically, with unknown results. In its pure form, it’s all too perfect, giving all the persuasive power to the player using it. The show had gone on daily for at least a couple of years with nothing of the kind beforehand. The drama was all in, first, which players got to the final match, then in the question of who would follow through with an agreement to split & who would not, with often surprising results–the most convincingly trustworthy taking the whole prize by their deception.
At first glance, I did not much like the idea of the game as I first heard it, mainly rewarding deceit, punishing the honest. By framing the exchange between players as a “game,” out of any real social context, the format encourages the concept of “winning,” and “winning as much as possible.” By eliminating consequences for false pledging, it raises the relative advantage given stealing, as well as the frequency of both players getting nothing, when even then, each could feel, “at least I didn’t get suckered–good thing I didn’t chose to split.”
It’s quite a different situation from the social reality–as well as from the Ultimate Advantage/ Prisoner’s Dilemma, where the social situation is more accurately simulated by virtue of “iteration,” playing repeated rounds with each player (also within a context in which information travels). In an iterated game, actions have consequences that loop back into subsequent actions, changing context & responses. The “Golden Balls” final match-up had none of that, no base for solid reasoning, nor reliable way of evaluating or appealing to “partners.”
Some players come committed to splitting, others plan to steal. Others try to base their choice on an assessment of the partner/adversary’s true (as distinct from expressed) intention, without another plan in advance. The evaluation of one’s ‘partner’ on the basis of the available information is an imperfect business at best. Those who consider it fundamental have a point, but also miss it. If in fact there is no reliable way to distinguish truth teller from liar on the basis of their words on this one question alone, that evaluation is no longer fundamental.
In the actual world, or in a game that has multiple rounds with the same players, one can adapt subsequent responses to actual play, the partner’s actions count–and provide an objective basis for evaluation. It’s not just “Trust, but verify” we go by, but then, “respond accordingly,” whether that’s “in kind,” in some useful way, or not at all.
In the “Golden Balls” game results, players are often emotionally deflated by having been snookered. There’s nothing they can do. They tend to respond as losers. Some find solace in having retained fidelity to principles of character applicable outside the game. Those who “win it all” mix their own emotional cocktails, x many parts glee in success, y many “sorries” in response to the reactions of their “victims” for having been taken in by their dishonesty in the verbal exchange. On the other hand, there’s the better feelings generated by split-splits, & the perverse satisfaction audiences must take in steal-steal outcomes, where each betrayer gets his/her comeuppance.
A great strategy should not be dependent on something one can’t necessarily do–whether this is a reliable evaluation of the partner’s honesty in this situation or one’s ability to convince a player to choose the split ball. Here, the master-gamer’s basic twist–indicating up front his intention to play the steal ball–not only leant weight to his claim of being honest, but took control of the match by collapsing the other player’s choices–eliminating any advantage the other player might try to gain from deception. It’s brilliance is highlighted by having changed the partner’s secret intention to go for the steal. If he’d agreed to split, in other words, he’d have lost it all (split-steal). Instead, he turned the results into an equal split in which each left with winnings. No other approach might have accomplished this.
[I’ll put a summary of the statistical studies from the full run of the show up ASAP, in conjunction with discussion of “The Ultimate Advantage Game.” Lots of samples from the “Golden Balls” show, including the match described, are available on YouTube.]
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“If the exception proves the rule is a rule, what disproves it?”
~~~~-~Inspector 8, Uncracked Cases File
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Atrium Feature #2: HOW THE INVERSE ANNEX GOT ITS NAME
The Inverse Wing (a.k.a. the Aha! Wing) is named for pioneer game-theorist John von Neumann’s mentor, canine companion & housemate, the dog he’d named Inverse, an influential presence in the neighborhood & at the Institute for Advanced Study.
Inverse-at-Princeton [Click to open Pdf. of “Inverse at Princeton,” which needs a new editing ASAP, although the facts & points made remain valid.]
P.S.: One of von Neumann’s most controversial positions–a potentially sufficient reason for naming our annex for Inverse rather than Johnny– was his reported support for the idea of a pre-emptive nuclear strike against the Soviet Union circa 1950. Although the idea initially seemed like flaming lunacy to me, thanks in part to some of its most notable advocates, I don’t really know von Neumann’s actual reasoning, not necessarily whatever was publicly reported at the time. Stated positions themselves become strategic tools that may carry weight with adversaries, as well as in domestic affairs more broadly.
Military historians may debate whether or not a brief window ever existed when the United States’ nuclear superiority gave it the power to enforce a credibly cost-effective ultimatum on the Stalinist empire, presumably establishing a true pax americana, freeing dominated peoples, &, arguably, preventing both the arms race & spread of WMD’s, the implications of the latter still to be determined. I have no clear sense of what Dr. von Neumann’s strategic counsel might have been behind closed doors, except no doubt considerably more nuanced & complicated than likely reflected in accessible accounts.
As a Hungarian Jew, von Neumann had seen enough of both Nazis & Soviets to consider the post-war occupation of Eastern Europe reason for countervailing toughness. As a strategist with a scientific approach to problems, grounded in logic, math, & experiment, however, he was neither ideologue, nor maniac (as per Dr. Strangelove), but committed to a bedrock of more enlightened values. At least so I imagine. There may be mixed evidence.
Given his experience, intelligence & knowledge of the most classified material, Von Neumann may have understood aspects of the clash of civilizations in that era as few others. His awareness covered some wide range of territory, making connections across scales & dimensions. Did he get trapped in some abstractions, as many strategists seem to? Possibly. He also drove wildly, often while drinking, and had a perverse sense of humor, as many stories illustrate.
He used abstractions as tools to create other tools–like the modern computers he helped invent to crunch Oppenheimer’s Manhattan Project numbers. His scientific commitment to discovering how things actually worked was what brought him to the development of game theory years before, using game situations to explore strategic & economic behavior–using game-based experiments to discover how people behave faced with alternatives, at least within the defined framework.
By definition, a game-framework will inevitably differ from real-world equivalents & applications in some key aspects, however. Play-fighting tiger cubs keep their claws retracted, for example, & are free to attack each other in ways adults would find imprudent. The fact that a game uses an imaginary currency can change the way players manage risk, for example. On the other hand, so can playing with (i.e., managing) other people’s money.
This may remind us that the translation between game behavior & represented reality is not always direct or literal. The game is still a game, a model or simulation, and although it has its own reality, it is not the same as action in the real-world, where combat differs from sparring, & bankruptcy differs from going bust in a single game, free to start a new game from scratch.
The translation may be there, but of a non-literal sort. For example, the simulated dynamics may teach a seat-of-the-pants sense of real-world dynamics in ways that save or make real money later from what was learned in play. In that case, going broke in a game might help save considerable real-world resources later–a functional translation.
Von Neumann’s original work was in using game-based situations experimentally to clarify our understanding of economic & strategic behavior: how people respond faced with particular choices in particular kinds of situations. That’s just the beginning, however, a first step, because in fact people respond to choices in different ways, not all the same, so subsequent steps try to determine relative effectiveness (value) of the various alternatives, as well as how equations may be affected by changing variables.
There is no set bet that is mandatory for any particular hand in poker, for example. There may be a generalized kind of “most rational” response, but even this will vary with many situational variables, including advantages that may be gained from mis-representing the hand one has. In addition, the concept of probability enters the picture from multiple directions, not just in terms of cards still to come. Aside from the possible disadvantages in being overly readable, the player who well plays the odds–like the house–will tend to have a longer term advantage.
Though it may seem so when playing with other people’s lives & money, real-world force & finance aren’t necessarily quite game-like–most notably in the matter of incomplete information. An essential element in poker, the bluff may be far less useful in business & international relations, where credibility of word & predictability of response may count for so much in fostering cooperative relations. The root of both diplomacy & contract law may be found in the advantages entities may gain by minimizing the uncertainties in their relations.
Whether used in war-games or economic modeling, simulations become serious business in the quest for both understanding & effective management in real-world translation. Games, too, can become quite serious, as the physical & financial effects of football & poker may remind us. If nothing else, real-world translation highlights the value that may be derived from understanding the games. Whether quantifiable, indirect or invisible, cross-discipline effects may be expected from playing–chess or the cello, baseball or ‘bean bazar” (our simplest trading game).
Where exercise develops muscular &/or neurological structures, it’s the playing that counts most, with awareness that intentionally tweaks the playing potentially fine-tuning the effort. Where abilities & effort are more or less equivalent, players with practical insight will tend to develop an edge, compounding over time. Others shlub along.
In the period immediately following WWII, the world experienced rapid change in the two main areas of strategic thinking–military & financial. One entered the new era with the introduction of nuclear weapons in the equation; the other, with the computer technology partly to facilitate the former. The one person who had the most advanced & creative understanding in both realms just happened to be Johnny von Neumann, pre-eminent pioneer in use of game-modeling to understand the interaction between psychology (behavior) & dynamic systems (political &/or economic orders). He served on high-level government advisory boards, and was an influence on activities of the Rand Corporation, a strategic think-tank at which many game-based studies & experiments were conducted–including some by his Princeton colleague, John Nash.
You might think all this might have been reason to name the Wing for Johnny rather than for his dog. Not even the “father of game theory,” with his notoriously perverse sense of humor, could match Inverse’s good-natured sense of pure play, however. Unlike John, Inverse never put Einstein on a westbound train to New York, or drove wildly while drinking. I suspect there are other reasons not clear or well enough established to cite. I also suspect Inverse inspired Johnny’s sense of play the way Johnny’s mathematical explorations inspired those who came after.
Bottom line: Inverse was not just more inherently playful, he seems more easily lovable. (Perhaps even the lovely & gracious Mrs. von Neumann would have agreed.) You can Google pictures of the three of them & see what I mean. Otherwise, Yours Crudely takes a perverse pleasure in naming a seriously playful site that’s not in verse the Inverse Annex.
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FOOTNOTES:
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1. See “This little piggy…:Games for Tots with Toes” for a time when play, rhyme, ditty, verse, sorcery & games were more or less one.
2. The source of the sorcery aspect may be seen in “Star light, star bright, first star I see tonight. I wish I may, I wish I might, have the wish I wish tonight–.” Learned in one’s mother’s arms, this is often the infant’s earliest introduction to the vast mystery of the starry-skied world, a lesson in focus, reminding us that for most of humanoid history, the stars at night were like the foot-trails by day, with signposts to orient us to where we were, a means of navigation.
3. Learning the lessons of the stars might once have been as basic as “look both ways before crossing the street” became to children like me, in other words.
~~~starry footnotes left–
~~~~~light in its passage across
~~~~~~~small animal tracks
4. Games & other forms of play have long been used to pass along foot-note know-how, practical lore, and skill sets–mental, emotional & physical. Sometimes, the game-board is laid out in the field; sometimes the field is represented on a game-board. Or the table becomes the “field,” with players seated facing each other &/or around.
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TMI Zone: Stop!
The Too Much Information Zone is currently closed to all but unauthorized personnel. Proceed at your own risk–or don’t, also on your own. Risk assessments are available from virtual actuaries at the Old Uncertainty Insurance Company’s Crystal Balls Headquarters for Improbability Studies, in Void, where “Nothing is as certain as Old Uncertainty.”
Meanwhile, the following not so witty “Trash Lit” ditty seems to be in a hybrid style created by mixing the Institute for Advanced Study’s Nobel mathematician Mad John Nash up in a page blender with Utah humorist Ogden Nash. The result is just what it’s called “Trash Lit” (3 x fast). Being so transient, however, it could be gone before you’re through. (Good riddance.)
~~~~~Trash Lit~~~~~