Zut-
That’s quite interesting, and also an elegant proof. Do you recommend the book you bought?
Yes and no. It discusses Morra, if that’s specifically what you’re interested in, and it gives lots of examples, and it gives pretty thorough coverage of basic theory. However, it was originally published in 1954, and the techniques demonstrated for solving problems are relatively cumbersome.
A better basic book, to my mind, is Game Theory: A Non-Technical Introduction by Morton D. Davis. This covers more ground (but a little less in depth), but it also demonstrates simpler problem-solving techniques, and has some really good real-life problems.
Although there is a lot of overlap, I thought having both of these books was useful; however, if you want just one, I felt that Davis’ was less mathematically laborious and more relevant to real life.
Alan? Veg’s report begins with the comment, “Geez, are there theories” and winds up with the the comment about his << sarcas-o-meter…swings wildly between “completely serious” and “total bunk.” >> There’s no deception here in terms of the suspiciousness of soi-disant data. The answer in the first paragraph of the Staff Report is, nobody knows.
The rest is amusement and embellishment, and clearly labelled so. Some reports are heavy with facts, some are lighter but make a fun report. I mean, c’mon, the simple answer “Nobody knows” wouldn’t make much of a Report, would it?
So what’s your complaint?
I certainly didn’t mean to imply that Veg was in any was dishonest or deceptive, but there seem to be serious questions about whether anything on the WRPSS site is completely serious or whether the theories he quotes are merely made up. I was able quite easily (thanks to a book that happened to already own) to find some information that was both interesting and to the point, and suggested some additional resources that he could (and, IMHO, should) have consulted as well.
I wish I could have written my last post to sound less critical. I know how hard you guys work, for no money and few thanks, and believe me, I think you do a great job. The Staff Reports are quite often more interesting than Cecil’s columns. (Shh…don’t tell him I said that!) That said, I think my criticisms were valid. Feel free to disagree, though.
Yes, Alan, this is indeed The Straight Dope. I’ll try to set the record straight.
[[ Woah ]]
Let’s not get into the long-standing Biblical debate about whether or not Noah’s uncle really existed.
[[ Are you saying that you based your answer on an interview with an obvious and admitted fraud and liar (is of a tounge-in-cheek and possibly scientific nature) because you “tend to think” he was only lying to the other guy? ]]
I never said anything even remotely like that. You seem to be reading things into my comment to WindFish. WindFish referred to a post on the bulletin board at the WRPSS website, and I commented on this post and a subsequent e-mail exchange I had with the author of the post, never mentioning a time frame. The fact is that I submitted my report prior to the post in question, and therefore prior to the e-mail exchange as well (Cecil is a busy man, and regardless, there’s no reason to assume that a Staff Report dated July 10th was penned on July 9th, especially since it was actually posted on July 5th or 6th). The fact is that I did not base my answer on one interview with the poster in question, and the interchanges that I did have with him and which I used in my report happened prior to the post referenced by WindFish.
Having said that, I’m also happy to say that, since my report hadn’t been posted yet when I read the post to which WindFish referred, I went back and re-read the report. Even after becoming more and more convinced that most of the information on the WRPSS website was for amusement only, I didn’t (and don’t) think that my report is in any way misleading about the origins of the game. Incomplete, perhaps, since I didn’t have a copy of the book you happened to have on your bookshelf, and since I was unable to find any more definitive information, but not misleading.
[[ You knew the website you used for research a joke, ]]
I knew no such thing. The fact is that I still don’t know it. Do I believe it? Yes, I now believe that most, if not all, of the WRPSS website is for amusement purposes only, but I don’t know this for a fact. If I were writing the report today, I’d probably indicate that my sarcas-o-meter was pegged at “total bunk” more often than “completely serious,” but I doubt that I’d actually take out any of what I included, especially the part about Rochambeau.
[[ but its mentions of made up laws and rules “sound good”? ]]
Well, they do to me, though you may disagree. I guess it depends on what you think “sounds good” in general, and whether or not you’re equating “sounding good” with “solid evidence” (I don’t, and I don’t believe I implied that I do).
[[ You “figured” it had “some facts scattered here and there”? ]]
Well, while “Think twice before using RPS for life-threatening decisions” isn’t technically a “fact,” it seems awfully reasonable to me. If you’d like to disprove it, as much as a not-technically-a-fact can be disproven, I invite you to let me know how your next encounter with a carjacker goes when you offer a friendly two-out-of-three RPS match as a way of deciding whether he does or does not get to take your car.
[[ I hope we can say more about your report! ]]
What I hope you, and everyone else, can say about my report is that it was an entertaining read, and that it pointed you to a website that was also entertaining. In addition, I hope it stirred up a few programming-type minds (based on k_i’s question, I appear to have succeeded there).
[[ I hope this isn’t coming across as a flame. ]]
Actually it is, but I don’t mind spraying a little friendly fire myself sometimes. I’m sure that if we have any lasting disagreements we can settle them over a beer and a three-out-of-five RPS match. I’ve been dying to try out “The Bureaucrat” when something’s actually at stake, and the price of a beer sounds just about right.
Incidentally. . .
[[ Google pulled up about ten hits for “games historian” that looked like they might be helpful in finding someone to contact (out of 33 hits total). ]]
Surely you jest. This web search produces results that are, on the surface at least, no more likely to provide a clue as to the origins of the game than a web search on “Kennedy’s assassin.” Based on the few most likely candidates – which weren’t part of the half that were clearly about Olympic Games historians – that I visited, I think it’s safe to say that none of them contains any data about this game in particular, and the likelihood that any of them would lead to someone who has some idea is minimal.
The suggestion about “Games” magazine is a good one, as is the reference to the book you own. I’ll keep them in mind if I ever take on another “game” question.
Rich
Sounds good to me, but you’d better be prepared for the devastating onslaught of my Toolbox! It’s a long way from Arkansas to California, but how about meeting me halfway? I’ll be driving to Colorado next month, and I’m sure I’ll be thirsty by the time I get there.
BTW, have you read this message on the World RBS Society BBS? (That would be the WRBSSBBS!)
Since my esteemed fellow Rush fans Coldfire and Falcon are MIA presently, and mars horizon hasn’t wandered in here yet, allow me to quote, please, from “Hand Over Fist”, on Presto (1989):
Thank you.
In an earlier post I mentioned that I learned a fourth option to RPS in Germany, but couldnt remember it.
Doesnt anyone know this? Im really curious!
RK
Well, I must say that I am shocked. How dare you people question the veracity of the WRPSS? In a troubled world the elegant simplicity of the eternal trinity of Rock, Paper and Scissors offers a rare and valuable place of calm and sanity. And the WRPPS, despite certain internal jurisdictional problems, remains the one true font of all things RPS.
I suspect that some of those casting aspersions on the WRPPS are indeed minions of the dreaded ITTTF (yes, the evil International Tic Tac Toe Federation itself) in their never-ending quest to discredit the WRPPS. I would think that adherents of The Straight Dope would be able to see through such a ruse, and would be willing -eager!- to expose such perfidy, but instead you seem to have bought into it. For shame, I say, for shame!
I see that the gremlins from ITTTF have even invaded my computer. I obviously meant to type WRPSS each time above. Though they try, the ITTTF shall never win in the end.
I refer to the post by regnad kcin, where it is asked about a fourth option in the game of RPS. This question obviously belongs on the WRPSS Bulletin Board and not here, but since I sense a certain hostility against WRPSS on this message board, at least some reluctance against taking us seriously, I choose to answer your question here.
Sure, adding a fourth element to RPS is very easy. In fact it is so easy that you can do it yourself. You do not have to rely on somebody from Germany. But I stress that this practice is not at all sanctioned by WRPSS which governs all forms of RPS play. I refer you to the Rule Governance section of the Official Rules of RPS Play which may be found on WRPSS’ homepage. I quote: “… must not include any variant throws beyond the basic trinity such as, but not limited to, dynamite, bird, well, spock, god, water, lightning, bomb, matchstick, water, and/or Texas longhorn.”
The topic is also thoroughly discussed on WRPSS Bulletin Board.
With that said I will discuss the theoretical sides about adding a fourth element to RPS and explain why it is totally ridiculous to do such a thing. Assume we start with the basic trinity, and since we study the abstract aspects of the game, we call the elements A, B and C, so that out discussion applies to both the traditional (Western) Rock-Paper-Scissors and the Indonesian, Elephant-Person-Ant, and any other variant consisting of exactly three throws. We let the three throws relate to each other the way that A beats B, B beats C and C beats A.
Then assume that we add a fourth element, D. Since we want our new game to be an interesting one, and not degenerating to the traditional three-throw game, we require that there be no throw that beats all the other three, and similarly no throw that is beaten by all the other three. We also require that all possible outcomes of a game be resolved - that is no tie, unless the two throws are actually equal to each other. Thus there is a throw, say A, which is beaten by D, and there is a throw, say B, which beats D. Then we can pick whichever outcome we want when C meets D. Say D beats C. We then have the following game:
A beats B.
B beats C and D.
C beats A.
D beats A and C.
The obvious question is: why would anyone throw C? Whenever you would like to throw C, you would do at least as good by throwing D, no matter what your opponent throws. Therefore we can assume that noone ever throws C, and the game degenerates into the following game, which is equivalent to the original three-throw game, except that D has replaced C.
A beats B.
B beats D.
D beats A.
You can try all other possible configurations as well. No matter how you do it, one throw will be useless. So we see that the WRPSS has perfectly sensible reasons to rule out any kind of addition to the game. You may of course add two throws instead of one and get a sensible five-throw game. (This is left as an exercise.) However this would result in an unnecessarily complicated game.
I hope this is clearifying.
Senior Chancellor
Theoretical Throws Bureau
World RPS Society
It was only a matter of time.
But who knows, maybe board cross-pollination will be a good thing. . .
Rich
Indeed, Rich, a fertile cross-polination may result from your initial query on our fair board, a hybrid vigor of new outlooks. I myself have greatly appreciated Cecil’s column for some time (though my love for RPS has been a mainstay since childhood!) In the spirit of Outreach, I welcome any of this board’s regulars who would wish to investigate further the inner secrets of all things RPS (I hope this does not come across as “Witnessing”) I had no idea this board even existed until Rich contacted us asking for info. I doubt I will become a regular here, one board being quite enough for me, in addition to my duties in the hierarchy of the World RPS Society. But I do intend to drop by from time to time, see what’s going on, and offer any well intentioned and factually supported info I can on other subjects (I think now I’ll check on the Necronomicon thread). I have a remarkable memory for useless information.
Master Roshambollah
Director-Outreach, Fund Raising
and Spiritual Concerns
The World Rock Paper Scissors Society
Kris Rhodes wrote:
>>>I teach english to middle schoolers in Nagoya, Japan, and I’ve never heard it called anything but Janken. I’ve never heard it called “Jankenpon.” <<<
I’ve heard it called both, but “Jan-ken” is by far the most common term. And while I’ve never met anyone here (I teach university in Fukuoka, Japan) who knew the origin, I can easily believe it comes from Japan, since it is so ubiquitous. Japan’s “national cartoon,” Sazae-san (sort of a really boring “Father Knows Best/Leave It to Beaver” anime) actually ends with a round of Jan-ken every week.
Somebody once told me that Vietnam has a variation involving 15 (!) different hand signs. I am skeptical, as this would result in…well, a helluva lot of possible outcomes.
Another variation that intrigues me is Discordian Rock-Paper-Scissors-Spock-Lizard. Sadly, the webpage seems to be gone, but by increasing the number of hand signs to 5 (to conform to the Law of Fives, for the usual silly Discordian reasons), the number of outcomes increases greatly. Unfortunately, I can’t remember all of what beats what. The hand signs for the new ones are easy, though–“Spock” is, of course, that “Live long and prosper” sign, and Lizard is holding the hand palm-down with the fingers in a clawing shape.
Dave
A description of the game Rock-Paper-Scissors-Spock-Lizard may be found at http://www.vtiscan.com/~samkass/theories/RPSSL.html. However, I once again stress that this game is not in any way sanctioned by WRPSS.
As I mentioned in my previos post, there is no way to create an interesting RPS-like game with four throws. Interestingly, though, there are two such games consisting of five throws, one of which is desribed on the page mentioned above. If we represent the possible throws by the letters A, B, C, D and E, the two games are defined by the following
Game 1
A beats B and D.
B beats C and E.
C beats A and D.
D beats B and E.
E beats A and C.
Game 2
A beats B and E.
B beats C and E.
C beats A and E.
D beats A, B and C.
E beats D.
Now, those of you who presented the optimal strategy of RPS may amuse themselves by finding an optimal strategy to the second game described here. (Optimal strategy here means a strategy which will always break even in the long run against any opponent, even if your opponent is familiar with the strategy you are using.) Or you may find try to appropriate hand signs to substitute the letters A, B, C, D and E.
And remember: If these questions intrigue you, maybe Theoretical Throws Bureau (WRPSS) is the place you should be. We are always happy to receive new applicants.
Senior Chancellor
Theoretical Throws Bureau
World Rock Paper Scissors Society
The guaranteed break-even strategy for the second game mentioned is D 1/3, E 1/3, and A,B,C 1/9 each. It’s basically two nested games of standard RPS. First, you have to choose between {abc}, {d} or {e}. On average, a, b, and c perform equivalently, so we can lump them together here. By the standard reasoning, you should choose these three possibilities with equal probability, and if you choose {abc}, then you have to select from those.
Yes there is – if you relax your assumption that there are only two players.
For instance, if you had throws A, B, C, and D, you
can have the following chart:
A beats BC, BB, CC, DD
B beats CD, AA, CC, DD
C beats DA, AA, BB, DD
D beats AB, AA, BB, CC
And if all three people throw identically, it’s a tie.
OTOH, if we relax the assumption of only one set of moves, we could create pawns, knights, bishops, etc … maybe use a checkerboard to track them… and have a more interesting set of outcomes.