ins_akaa@jhunix.UUCP (Ken Arromdee) (03/20/86)
>>> A good way to confound a logical player is to make completely random >>> moves. The logic involved in strategic game playing generally involves >>> predicting the other player's moves; this is quite difficult if the >>> other player is random. Kirk's play was probably not random, but he >>> probably guessed every now and then, which was enough to throw Spock's >>> strategy off. >>In other words, this is a LOGICAL way to play against such a player, right? >You mean the logical thing to do is to play randomly, without logic? >Isn't that a contradiction in terms? (Where have I heard that before?) The point is that randomly does NOT mean "without logic", that in fact the most logical move can be a random decision. I am cross-posting this to net.math to see if any game theorists can confirm this... (can you?) -- "Father, they DO know what they are doing!" Kenneth Arromdee BITNET: G46I4701 at JHUVM and INS_AKAA at JHUVMS CSNET: ins_akaa@jhunix.CSNET ARPA: ins_akaa%jhunix@hopkins.ARPA UUCP: {allegra!hopkins, seismo!umcp-cs, ihnp4!whuxcc} !jhunix!ins_akaa
ins_apmj@jhunix.UUCP (Patrick M Juola) (03/20/86)
In article <2293@jhunix.UUCP> ins_akaa@jhunix.ARPA (Ken Arromdee) writes: >>>> A good way to confound a logical player is to make completely random >>>> moves. The logic involved in strategic game playing generally involves >>>> predicting the other player's moves; this is quite difficult if the >>>> other player is random. Kirk's play was probably not random, but he >>>> probably guessed every now and then, which was enough to throw Spock's >>>> strategy off. >>>In other words, this is a LOGICAL way to play against such a player, right? >>You mean the logical thing to do is to play randomly, without logic? >>Isn't that a contradiction in terms? (Where have I heard that before?) >The point is that randomly does NOT mean "without logic", that in fact >the most logical move can be a random decision. I am cross-posting this to >net.math to see if any game theorists can confirm this... (can you?) >-- >Kenneth Arromdee If I have to post another games theory article.... All right, guys -- in the *general* case, there are games that the *best*, read *most logical*, strategy is to play randomly. Read any games theory, finite mathematics, or linear algebra text to find examples. I'll mention just one -- you and your opponent set a penny down, either heads or tails. If you match, you win; otherwise your opponent wins. The best strategy is to play randomly. No matter what he does, you will at least break even. Now, on to the chess example. First of all -- let's get something straight. Spock is NOT infinitely intelligent -- he can be beaten (by the computer, by Kirk.) He is simply a damn good player, but Kirk can sometimes come up with an attack that Spock didn't expect. Heck, Spock may even make "blunders"! To those of you who think Spock is never wrong, just remember that he botched the acetylcholine test in "The Immunity Syndrome" or whatever the cosmic amoeba was called.... The next person who posts a games theory article will feel the full force of my wrath.... Pat Juola Hopkins Maths "Mr. Chekov, arm photon torpedoes!"
gwyn@brl-smoke.ARPA (Doug Gwyn ) (03/23/86)
> >>> A good way to confound a logical player is to make completely random > >>> moves. The logic involved in strategic game playing generally involves > >>> predicting the other player's moves; this is quite difficult if the > >>> other player is random. Kirk's play was probably not random, but he > >>> probably guessed every now and then, which was enough to throw Spock's > >>> strategy off. > >>In other words, this is a LOGICAL way to play against such a player, right? > >You mean the logical thing to do is to play randomly, without logic? > >Isn't that a contradiction in terms? (Where have I heard that before?) > The point is that randomly does NOT mean "without logic", that in fact > the most logical move can be a random decision. I am cross-posting this to > net.math to see if any game theorists can confirm this... (can you?) Yes, logical play in a two-player, zero-sum, discrete, finite, perfect-information, non-cooperative* game in general actually REQUIRES the use of a device for making a weighted random choice among several alternative pure strategies. A good, although rather dated, elementary introduction to this subject can be found in "The Compleat Strategist", written long ago by someone (whose name I have unfortunately forgotten) from the Rand Corp. * I wonder if I included enough qualifiers.
lambert@boring.UUCP (03/24/86)
> ... in "The Compleat Strategist", written long ago by someone > (whose name I have unfortunately forgotten) from the Rand Corp. J.D. Williams, The Compleat Strategyst, McGraw-Hill, 1954. -- Lambert Meertens ...!{seismo,okstate,garfield,decvax,philabs}!lambert@mcvax.UUCP CWI (Centre for Mathematics and Computer Science), Amsterdam
steve@jplgodo.UUCP (Steve Schlaifer x3171 156/224) (03/25/86)
In article <2014@brl-smoke.ARPA>, gwyn@brl-smoke.UUCP writes: > Yes, logical play in a two-player, zero-sum, discrete, finite, > perfect-information, non-cooperative* game in general actually > REQUIRES the use of a device for making a weighted random choice > among several alternative pure strategies. A good, although > rather dated, elementary introduction to this subject can be > found in "The Compleat Strategist", written long ago by someone > (whose name I have unfortunately forgotten) from the Rand Corp. > The revised edition of "The Compleat Strategyst" written by J. D. Williams was published by McGraw-Hill in 1966. It was from a RAND corporation research study. Copyright dates are given as 1954 and 1966 RAND corporation. -- ...smeagol\ Steve Schlaifer ......wlbr->!jplgodo!steve Advance Projects Group, Jet Propulsion Labs ....group3/ 4800 Oak Grove Drive, M/S 156/204 Pasadena, California, 91109 +1 818 354 3171
ark@alice.UucP (Andrew Koenig) (03/27/86)
Here is a very simple game in which it is logical to make random decisions. Each of us puts a penny on the table, covered by a hand so the other cannot see it. We then both remove our hands from the pennies. If they match, you win. If not, I win.
desj@brahms.BERKELEY.EDU (David desJardins) (03/29/86)
In article <768@hounx.UUCP> kort@hounx.UUCP (B.KORT) writes: >... In general, if someone is evidently following a nondeterministic >(hence unpredictible) strategy, is it decidable whether the person is >using a logical random strategy or merely behaving erratically? It >seems to me that it would be very difficult to decide the issue unless >one had many repetitions of the play upon which to cumulate statistics. A related point is: If God manipulates the universe by affecting random events (QM wavefunction collapse), it is impossible to prove that intervention is taking place. In fact, it is not clear if there is any distinction at all between intervention by an incomprehensible God and "true" randomness. -- David desJardins