Welcome to the Bod Library-On-Line's Inverse Wing for G.A.M.E.S. --Game theory & applications; --Adventures in understanding; --Master class in w-a-t ~~~(writing-awareness-thinking); --Educational explorations; --Surprise![Still going up, all in flux, along the following Page-plan.]
1. --Howdy, world (orientation & lobby features) ------This is it, folks! You're here now.
2. --Games & Their Applications ------A Golden Balls Analysis; ------The Ultimate Advantage Game --------(up soon, if asked)
3. --Adventures in understanding --------(intro to quest & challenge) ------Adventure #0 (figure password) ------Aha ! breakthroughs (ditto for entry)
4. --Master Class (w-a-t: writing, awareness, thinking)
5. --Enlightenment thoughts (after-thoughts & reflections)======================================== Welcome, friend. Here's the deal in a nutshell. This wing of the Bod is dedicated to the Game of WISING UP--yourself, your students, the seeker, would-be sage & accidental seer, starting with how we learn (by DOING, by PLAY, by ATTENTIVE DISCOVERY, by TRIAL & ERROR, by TRIAL & EXECUTION, by ACCIDENT, by WHAT WISE TEACHERS HAVE SHARED, by EXAMPLE, model, inspiration, course correction, REFLECTION & REVISION). "The proof is in the pudding--along with the lumps." --Yours Crudely ============================================ Special greetings to: # Game designers, enthusiasts, & theorists--whether linking from discussion of the Golden Balls TV show or elsewhere--may scroll down to our current LOBBY FEATURE, with discussion of the "most innovative strategy tried." # Adventurers who found their way here following their noses--keep it up. Scroll down far enough & you'll find footnotes to follow, e.g., How the Inverse Wing Got Its Name. # Members of the Mishugunah Order--the muse of play welcomes you with open mouth, arms, mop closet, mind, mu--now you see-um, now you don't. # Enlightenment seekers, reincarnated masters, beneficent guides of compassionate daycare, night-trippers for justice, fellow travelers--fools enter free (half-off exits, while they last). # Refuge friends following up on the "Nature Connect" challenge on the [no wold] "Aldo Zone" page (at www.bodlibrary.com) may continue on to the Nature-Connect page on this site. # Students (teachers) of writing, awareness, thinking, feeling, playing, sharing, & being skills--feel free to noodle around &/or go directly to the "Master Class" room for a more systematic guide to understanding & skill development, which integrates game-based doing & conceptual insight in a progressive sequence of light-shedding adventures. ===============================
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Lobby feature: Golden Balls Game ShowThe 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, they reveal which inside.) Players reveal together after 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 that day'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," for its brilliant solution. Before reading it, however, take a moment to consider what your strategy would be. Let's say there's $30,000 in the prize pot. Your "partner/adversary" proposes you agree to split. 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.] ================================================ "If the exception proves the rule is a rule, what proves (&/or disproves) it?" ~~~~-~Inspector 8, Uncracked Cases File ================================================= Back to YOU ARE HERE: Self-reference desk. Here's some deep background on the Inverse Wing itself, starting with-- ~~~~~~How the Inverse Wing got its name
The Inverse Wing (a.k.a. the Aha! Wing) is named for pioneer game-theorist John von Neumann's mentor, best friend, & dog--Inverse--, an influential presence in the neighborhood & at the Institute for Advanced Study. Click here for Inverse at Princeton, "lessons from the von Neumann dog."Lest there be any confusion, please note that neither Yours Crudely nor Inverse ever considered the idea of a pre-emptive nuclear strike against the Soviets circa 1950 anything short of flaming lunacy. Others may speculate on whether or not a brief window ever existed when the United States' nuclear monopoly, or early superiority, gave it the power to enforce a credibly cost-effective ultimatum on the Stalinist empire to free dominated countries, prevent the arms race, etc.. Nor do I have a clear sense of what Dr. von Neumann's strategic counsel was behind closed doors. His own thinking on the matter would have been considerably more complicated than is reflected here, in any case. We lack sufficient details to evaluate, except to note that, as a Hungarian Jew, he'd seen enough of Nazis & Soviets both to consider the post-war occupation of Eastern Europe reason for countervailing toughness. He was neither an ideologue, nor a maniacal Dr. Strangelove, however, but a strategist with a rigorous scientific approach, grounded in logic, math, & experiment--as well as on a bedrock of fundamentally civilized values. At least so I imagine. 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, with an ability to make connections across scales, as well as 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 the story above illustrates. He used abstractions as tools to create other tools--like the modern computers he helped invent to crunch Oppenheimer's Manhattan Project numbers. Nevertheless, 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--not how we think people might behave, but using game-based experiments to discover how they actually do behave, at least within the defined frameworks. As for why we didn't name the Wing for Johnny rather than Inverse: Not even the "father of game theory," with his notoriously perverse sense of humor, could match Inverse's good-natured sense of pure play. (Unlike John, Inverse never had a good laugh over having put Einstein, en route to New York, on a westbound train.)
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 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 (3 x fast). Being so transient, however, it could be gone before you're through. (Good riddance.)