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Post by krusader74 on Nov 14, 2013 4:41:52 GMT -6
There were four D&D B/X solo adventures that I know of... Unfortunately I don't think any of these are available yet as PDFs on dndclassics.com - M1 (or MSOLO1): Blizzard Pass by David Cook (1983) - The first D&D solo adventure AFAIK... for a Thief level 1-3
- MSOLO2: Maze of the Riddling Minotaur by Jeff Grubb (1983) - Any PC class, level 1-10
- BSOLO: Ghost of Lion Castle by Merle Rasmussen (1984)
- XSOLO: Lathan's Gold by Merle Rasmussen (1984)
There were also some solos published in Dragon magazine, detailed here.Myriador is a company that made d20 conversions of the Fighting Fantasy game books, starting with the Warlock of Firetop Mountain. Unfortunately, I think they're out-of-business. There are plenty of solo adventures for Tunnels and Trolls. These are great. Start here or here. Many free T&T solos in the free TrollZine fan magazine at DTRPG. You can play the first solo, Buffalo Castle, online. Lots of Fighting Fantasy game books. I'd also include interactive fiction (the Zork series, for example) into my list of favorite solo adventures. Many free online at the IF Archive. The computer games Rogue (1980) and NetHack (1987) took their inspiration of D&D. PCs have 6 abilities, etc. The dungeon is randomly generated. Updated variants use 2D or 3D graphic tiles rather than ASCII graphics. I've spent many hours blissfully playing NetHack. I'd rather play NetHack or IF games than 99.9% of modern console games or iOS/Android game apps. NetHack has a genuine old-school-gaming feel. This blog used to review game books, but hasn't been updated in a long time. Demian's Gamebook Web Page catalogs virtually every known game book ever, dating all the way back to 1929. It's a great resource for finding more solo adventures.
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Post by krusader74 on Nov 11, 2013 2:52:45 GMT -6
Thanks for the article link! It made perfect sense to me. The best chess player I knew had an eidetic memory. The guy simply memorized all the opening books, all solved end-games, and every famous historical game ever played. You would just mention a game to him, say Fischer vs Reshevsky 1961, and he'd replay it for you, step-by-step, lightning fast. One of the things I've noticed about Bobby Fischer's games is that he often takes his opponents out of their comfort zones by employing unusual openings. That's one way to deal with Chess's over-reliance on memorization. In this article, David Sirlin's uses a three-pronged solution to Chess's problem of over-reliance on memorization: - Pick 1-of-6 opening armies: This deals with the problem of memorized opening books.
- Mid-line invasion: You win if your King crosses the mid-line of the board. This new victory condition deals with the problem of memorized end-games.
- Dueling: Instead of simply capturing a piece, players use a double-blind bidding mechanic with a scarce resource called "stones" to decide the victor. This makes a good memory even less advantageous.
WRT dueling, it's noteworthy that Ken St. Andre, the inventor of Tunnels and Trolls, invented a chess variant called "Combat Chess" that also uses a form of dueling. He described it in his own words in a 1997 article called The Origins of Tunnels and Trolls: Ken said that "Combat Chess" was inspired by Edgar Rice Burroughs's The Chessmen of Mars, and the "exploding dice" mechanic was inspired by the board-game Monopoly. According to Monopoly's rules: Ken retained Combat Chess's exploding dice mechanic in Tunnels and Trolls, which calls it "DARO" (doubles add and roll-over) and "TARO" (triples add and roll-over). Getting back to the article on David Sirlin's chess variant, there is a brief write-up of it on the Chess Variants website: Chess 2. The complete rules to "Chess 2: The Sequel" are here. And there is also a discussion of it on Board Game Geek. Finally, it's worth pointing out that Gary Gygax invented his own chess variant, called Dragonchess, published in Dragon #100/August 1985. It uses 3 boards: Air, Land and Underworld. And it adds new pieces like the Thief, the Cleric, the Mage, and the Hero. There is a very detailed write-up for it on the Chess Variant webpage: Dragonchess. There's also a Wikipedia page devoted to it. Has anyone here played Dragonchess before?
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Post by krusader74 on Nov 11, 2013 1:25:36 GMT -6
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Post by krusader74 on Nov 9, 2013 21:28:53 GMT -6
Advanced Fighting Fantasy perhaps? It's a more involved version of the system used in the Fighting Fantasy choose your own adventure books. They are back in print now. I have the old versions from the 90s. I wanted to draw attention to the Advanced Fighting Fantasy Quickstart at DTRPG. It's free from Arion Games/Cubicle 7. It's only 17 pages. PCs have the following characteristics: SKILL (=to-hit), STAMINA (=HP), MAGIC (to-hit with spells), MAGIC POINTS, and LUCK (catch-all attribute). To fight an opponent you roll 2d6 and add your SKILL. (You may have a specialty skill for your weapon, in which case you add it too.) Your opponent does the same. In case of a tie, nobody gets hit. Otherwise, the one with the higher total hits. Damage is resolved by rolling 1d6 and using a lookup table based on the weapon type. Damage is subtracted from stamina. To cast a spell, 2d6 <= MAGIC succeeds. Either way, subtract the spell cost from your MAGIC POINTS. LUCK rolls are used where nothing else applies: 2d6 <= LUCK succeeds. Subtract 1 from your LUCK score each time you test your luck. When you reach 0, you've literally run out of luck. There's also a free fanzine for this system: Fighting Fantazine. There are currently 12 issues available. I like this system. It's very rules light. It keeps out of the way of roleplaying and story telling. The mechanics work great for solo adventures. Great recommendation!
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Post by krusader74 on Nov 9, 2013 21:10:21 GMT -6
Just wanted to note that Melee/Wizard creator Steve Jackson and Fighting Fantasy creator Steve Jackson are two different guys. The former is American, the latter English. TFT may have been the first RPG I ever ran, back in the early 80s. Thanks for pointing this out! I edited my post to make the distinction between TFT's Steve Jackson (b. 1953 US) and FF's Steve Jackson (b. 1951 UK) clear. Also, I wanted to point out a current series of blog posts on TFT over at bigballofnofun @ blogspot.com So far there are 5 posts:
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Post by krusader74 on Nov 9, 2013 20:18:25 GMT -6
Try this: www.pbase.com/rpdoody/classic_american_cars_of_the_1920sThe first page is a gallery of thumbnails of cars from various American automobile manufacturers from the 20s. Drill down. For example, click :: Studebaker :: and you'll get 18 thumbnails of various Studebakers, from the 1925 model to the 1929 models. Click on a thumbnail, and you'll get a large image. There isn't any real info here, just a lot of great photos. Once you get a photo you like, you can Google for more info on that make/model/year. Hope this helps!
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Post by krusader74 on Oct 31, 2013 22:29:11 GMT -6
Steve Jackson's (b. 1953 US) The Fantasy Trip (TFT) is also an early entry in the FRPG market. It is extremely rules light. In the first edition, Melee (1977), PCs only had 2 attributes: Strength (ST) and Dexterity (DX). The second release, Wizard (1978), adds a third attribute, Intelligence (IQ). Combat is basically roll 3d6 <= DX to-hit. ST are hit-points. IQ is used for casting magic spells & using certain skills: roll 3d6 <= IQ to succeed. Only d6 are used; no funny dice. TFT's rules-lite approach resembles Microlite 74 (mentioned above by inkmeister) in that it too only uses the same 3 attributes (STR, DEX, MIND), but M74 uses the 3E/OGL d20 roll-over resolution mechanic, rather than TFT's 3d6 roll-under system. TFT's rules-light system also resembles the Fighting Fantasy (1982) solo adventures, created by Steve Jackson (b. 1951 UK). FF has only three attributes: STAMINA, SKILL and LUCK. I still play FF solo adventures, now published by Worldweaver as ebooks, on my Amazon Kindle. When TFT's publisher, Metagaming, went out of business, Jackson couldn't get the rights back, so he went on to create a more elaborate version of the rules--GURPS, which still uses the same 3 attributes and the 3d6 roll-under-attribute mechanic. You can find out a lot more about Melee & Wizard at this homage website. This site contains all the rules. Dark City Games publishes an 8-page retro-clone of TFT called Legends that you can get free here.
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Post by krusader74 on Oct 31, 2013 21:41:18 GMT -6
I second smokestackjones's nomination of Tunnels & Trolls. It's the world's second-oldest FRPG, published in 1975. It was conceived as an easier-to-understand D&D, and it definitely lives up to it's design goals. D6s only--no funny dice. Easy chargen--I keep my character sheet on an index card. Group-based combat (i.e., make a roll for each side; the difference is the damage divided among the losing side). Saving rolls cover everything else. T&T is well suited to solitaire adventures, and there are dozens available for it. I've played a number of these. You can play the first solo adventure, Buffalo Castle (1976), online at the publisher's website. There you will also find rules for chargen and combat. The game is well supported. In addition to online forums, there's also a free fanzine called TrollZine, that you can download from Flying Buffalo's page at DTRPG. The online store has many solo adventures, the free ruleset from Free RPG Day, and a copy of the 4th edition rules for $4. Besides the official publisher Flying Buffalo, Inc. (FBI), the game is supported by other publishers, including Peryton and Fiery Dragon, which published the 7.5 edition rules. I own several editions of the rules, including PDF and dead-tree versions of the latest 7.5 edition rules. Unlike D&D, the T&T rules have changed very little from edition-to-edition over the past 40 years!T&T's author, Ken St. Andre, known as the "Trollgod," maintains the Trollhala website. He is remarkably approachable, and I have exchanged several emails with him.
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Post by krusader74 on Oct 28, 2013 1:40:00 GMT -6
Hm, it seems strange to me to “solve,” in the context of a game, a real mystery which persists to this day. Unless the point were to do something utterly fantastic with it. Yes--fantastic--that's definitely the direction I would go. Here's what I was thinking:The Holy Fire is ignited by a fire imp. (Imps are described in the AD&D Monster Manual, p. 54. Fire imps are described on page 13 of White Dwarf #13, June/July 1979.) The fire imp calls himself Pyra (πυρά). He claims that he was a slave of Hades himself. On Holy Saturday, during the Harrowing of Hades, upon seeing the Lord, he had a conversion of the heart and begged the Lord for release from imprisonment, and the Lord mercifully released him ("The Lord sets free the prisoners" Psalm 146:7). He flew up into the Holy Sepulchre, where he has remained ever since. He admits he is evil but not unredeemable and that he must convert daily--renewing his option for the Lord each day. Each year, in recognition of his release from Hades, he ignites the Holy Fire for the monks. Pyra is the familiar of the Reverend Hieromonk Archemoros, an emaciated, pale man. Pyra has a telepathic link to Archemoros. Archemoros commanded Pyra not to light the Holy Fire in 1101 after Baldwin expelled the Greeks from the Holy Sepulchre. Archemoros has a deep grudge against the Frankish conquerors and the Roman Catholic clerics who kicked him out of the Holy Sepulchre. His vengeful thoughts are having a negative effect on Pyra. Like all imps, Pyra is able to polymorph into two animal forms. In this case, he can transform into (1) a black cat and (2) a giant toad. It is quite possible that Pyra is not altogether telling the truth, and that he and Archemoros have some ulterior motive. For example, Archemoros and Pyra may somehow be related to the "pale man" and "black cat/giant toad" in the Luciferian heresy, to be articulated later in the 1232 papal bull Vox in Rama (noted as the first official church document to condemn the black cat as an incarnation of Satan. That papal bull led to a "cat massacre" in Europe, which may have worsened the Black Death, which was spread by rats). Quoting from Wikipedia, Anyway, just brainstorming ideas for a campaign centered around Baldwin during the First Crusade. There's definitely a glut of fertile material in his Bio for numerous OD&D/Chainmail adventures! Illo of Pyra's "true form": For more info on the Harrowing of Hades, see
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Post by krusader74 on Oct 27, 2013 3:03:46 GMT -6
Continuing the ideas from the proposed Crusader-era OD&D scenarios here and here... Holy Fire, Pious FraudThe Church of the Holy Sepulchre is run by Greek Orthodox monks. The Holy Fire ceremony takes place every year on Holy Saturday, the day before Eastern Orthodox Easter. It routinely attracts thousands of pilgrims, who spend a lot of money and boost the local economy. Thirty-three candles are setup under the dome of the church. They spontaneously and spectacularly ignite. Pilgrims and clergy claim that the Holy Fire does not burn them. The Holy Fire is thought to be the miraculous descent of the Holy Spirit. But this Holy Fire is widely believed to be a pious fraud by the Roman Catholic Church.The Frankish warlord Baldwin became King of Jerusalem on December 25, 1100. Baldwin replaced the Greek Orthodox monks with his own Frankish clerics. In 1101, on the day before Easter, the Holy Fire failed to appear in the Church of the Holy Sepulchre. The failure of the fire to ignite led to street riots in Jerusalem (which may be played as a Chainmail scenario if desired). Worse for the local governments: No fire, no pilgrims, no revenue. So Baldwin acted quickly to reinstate the Orthodox monks. Next year, the Holy Fire returned, along with it the pilgrims, their cash, and the tax revenues. The PCs, traveling companions of Baldwin, but secretly procurators of the Holy Inquisition and curators of the Archivum Secretum Vaticanum, have been charged with investigating the rumors that the Holy Fire is a pious fraud.There are several theories: First, the Orthodox monks soak the 33 candles in white phosphorous and then set them up under the dome in the church. About 20 minutes later, the evaporating gases cause the candles to spontaneously and spectacularly self-combust. Second, a hidden zinc jar of naphtha is dripped down a chain onto the 33 candles by a monk hiding in the dome. But, it could also be the result of magic, monsters or a true miracle. This scenario is a detective mystery. Whatever the PCs find, they are to report their findings back to their handlers in Rome and await further instructions. Epilogue: In 1238, Pope Gregory IX denounced the Holy Fire as a fraud and forbade Franciscans from participating in the ceremony.
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Post by krusader74 on Oct 25, 2013 2:09:40 GMT -6
I found this article to be VERY fascinating. It’s an academic paper advancing the position that the Holy Grail legends were inspired by an artifact known as the Holy Mandylion, or the Icon “Not-made-by-hands” of Edessa. I find it fascinating because it combines (and enriches) two great interests of mine — Grail literature and Eastern Christianity — so I’m not sure how much the average reader will get out of it, but maybe it’s self-explanatory. Oh, also, the article SEEMS to presuppose that the Mandylion was the same as the artifact currently known as the Shroud of Turin (though it carefully skirts that theory, since it is a whole ’nother can of worms). Anyway, I thought of posting it here because it might provide some ideas of how to transpose the Grail adventures back to the Holy Land and the time of the Crusades. It's possible to tie Falconer's findings about the Holy Mandylion (AKA the Image of Edessa) to my proposed Chainmail scenario above. As a reminder, that scenario focuses on Baldwin and the First Battle of Ramla in 1101. Prior to this battle, Baldwin was "Count of Edssa." How this Frank came to rule Edessa is in itself very interesting. Edessa was conquered by the Seljuk emir Abu Sa'id Taj ad-Dawla Tutush I (brother of the Seljuk sultan Malik Shah I) in 1094. Although ruled by Sunni Turks, Edessa's population consisted mostly of Armenian Orthodox and some Greek Orthodox Christians. Tutush I installed Thoros as governor of Edessa. Thoros was ethnically Armenian but religiously Greek Orthodox. Thoros immediately tried to seize control of the city for himself. He fortified the city and survived a 2 month siege by the Seljuks. The Seljuks withdrew and Thoros was recognized as lord of the city. As a Greek Orthodox ruler, Thoros was not well liked by his Armenian Orthodox subjects. And Edessa was the frequent target of attacks by the Seljuks. In 1098, Thoros sought help from the Crusader armies laying siege to nearby Antioch. Baldwin answered Thoros's call for help. Baldwin convinced Thoros to adopt him as his son and hier. Thoros complied. No sooner had Thoros named Baldwin his successor than "Baldwin attacked Thoros' officers and besieged Thoros in the citadel... Thoros was assassinated by the Armenian inhabitants of the city, possibly at Baldwin's command, and Baldwin became the first count of Edessa" (quoted from here). Baldwin ruled Edessa until 1100, marrying Arda, the daughter of Thoros, and acting as an ambassador between the crusaders and Armenians. Getting back to how all this relates to the Holy Mandylion... The Holy Mandylion disappeared after the Sassanians conquered Edessa in 609. In 944 when Edessa was besieged by the Byzantine general John Kourkouas, the Muslims exchanged the Holy Mandylion for a group of Muslim prisoners. That same year, on August 16, 944, it was translated "to Constantinople where it was received amidst great celebration by emperor Romanos I Lekapenos, who deposited it in the Theotokos of the Pharos chapel in the Great Palace of Constantinople" (quoted from here).BUT...there is an alternative local legend that says the mendil of Jesus was thrown into a well in what is today Edessa's Great Mosque.So the premise of this proposed prequel scenario is that the Holy Mandylion in Constantinople is a pious fraud. The real one lies hidden at the bottom of a well in Edessa. The PCs, procurators of the Holy Inquisition and curators of the Archivum Secretum Vaticanum in Rome, have been charged with investigating the rumors that the real shroud is still in Edessa. Their mission is to find the cloth and return it safely to the Secret Vatican Archive. The PCs are traveling companions of Baldwin. But they must keep their mission secret from him. Should Baldwin discover the shroud, he will seize it for himself, and transport it back to France. (This is similar to what is thought to have happened with the actual shroud 100 years later: In 1204, during the 4th Crusade, after the Franks sacked Constantinople, the Holy Mandylion disappeared. Soon after, the shroud turned up in Lirey France. It was only translated from Chambéry (Southern France) to Turin (Northern Italy) in 1578. Now it is called the "Shroud of Turin.") Just as important as protecting the shroud from Baldwin, the PCs must not allow it to fall into the hands of the Armenians, the Greeks or the Seljuks. Beyond that, the PCs may wish to investigate the true origins of this relic: God-made, man-made, demonic or black magic? And what exactly are its miraculous properties? According to legend, the shroud may be used as a devastating weapon: In time of need, oil will flow from it. If this oil is poured onto an enemy army and lit on fire, it will destroy them. So it may prove invaluable to the Crusaders.
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Post by krusader74 on Oct 13, 2013 18:06:00 GMT -6
Regarding copyrights, it's an important consideration that this is a worldwide forum and that copyright laws vary around the world. As Ynas Midgard noted, according to the US Copyright Office: This article goes on to say that elements like literary expression and art are copyrightable. Digging further, it seems that the typefaces used in a game aren't copyrightable, unless they constitute art. Game mechanics are patentable. Elements like names, brands and logos are subject to trademark. This post mentions that "Wizards was sued by Palladium simply for publishing a 'multi-system' book that presented a conversion to Palladium." The parties eventually settled. The suit nearly bankrupted Wizards. All that, even though "the idea for a game, its name" etc. theoretically aren't protected. Read more here. It's noteworthy that the tiny island of Antigua has become a copyright haven. Quoting this article, entitled " Where U.S. Copyrights Go To Die" dated 31 Jan 2013: (Similar articles about this here on Phys.org and here on Yahoo!)
In short, to make a legal retro clone, you'd need to consult with a legal expert in your jurisdiction. Regarding Chainmail, I'd like to see Wizards sell legal PDF copies of Chainmail on DnDclassics.com and also include a print copy of Chainmail in their upcoming (est. 17 Dec 2013) reprint, the Premium Original Dungeons & Dragons Fantasy Roleplaying Game. I'd also like to see a Chainmail retro clone. I thought about doing one. But, as shown above, the laws are murky, and even if you're legally in-the-right, the Palladium case proves you still might get the s**t sued out of you.
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Post by krusader74 on Sept 21, 2013 23:41:55 GMT -6
The square-cube law says that as a shape grows in size, its volume grows faster than its surface area. Specifically, volume grows with the cube of length while surface area only grows with the square of length. This has major repercussions for biomechanics: The article continues... "The giant monsters seen in horror movies (e.g., Godzilla or King Kong) are also unrealistic, as their sheer size would force them to collapse." Mythological dragons were originally conceived as water elementals (or sea serpents) as pointed out in this post: This makes 100% perfect sense in light of the square-cube law, because "the buoyancy of water negates to some extent the effects of gravity. Therefore, sea creatures can grow to very large sizes without the same musculoskeletal structures that would be required of similarly sized land creatures." (Quoted from Wikipedia, Square-cube law.)Therefore, aquatic dragons can be much, much larger than terrestrial or subterranean dragons. WRT flight, the Wikipedia article continues: "In the case of flying animals, the wing loading would be increased if they were scaled up, and they would therefore have to fly faster to gain the same amount of lift. Air resistance per unit mass is also higher for smaller animals, which is why a small animal like an ant cannot be crushed by falling from any height." So we'd expect the size of flying dragons to depend on the amount of thrust they can generate. The biggest flying dinosaurs were the Quetzalcoatlus with a wingspan of 30-33 feet and the Hatzegopteryx with a maximum estimated wingspan of 39 feet. Flying dragons could be even bigger, even as big as a jet, if they simply had jet propulsion. That's not as crazy as it sounds. Note that "cephalopods, sea hares, arthropods, and fish have convergently evolved jet propulsion mechanisms." (Quoted from Wikipedia, Jet propulsion.) Moreover, "In some dragonfly larvae, jet propulsion is achieved by the expulsion of water from a specialised cavity through the anus. Given the small size of the organism, a great speed is achieved." (Ibid.) This post mentions Turkish dragons, which "secrete flames from their tails, leaving a firey wake." Perhaps a form of jet propulsion?
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Post by krusader74 on Sept 18, 2013 2:00:57 GMT -6
"Dark life–-those organisms that thrive underground in the absence of sunlight–-comprises 50 percent of the earth's biomass, is responsible for many geological phenomena, degrades our wastes and produces some of our energy." (Quoted from " Dark Life: Biology.") Some of this "dark life" secretes sulfuric acid, which carves out huge caves and subterranean caverns. That's a key reason why the underworld exists. More importantly, dark life creates gold mines! They precipitate minerals, such as gold, iron and uranium. They also produce crude oil and natural gas. And they do this by consuming (what we consider) waste. In other words, chthonian life forms produce most of what we call "wealth." So, if you want to become wealthy, head underground.Dark life is studied by geomicrobiology, a mashup of the fields of geology, geophysics, hydrology, geochemistry, biochemistry, and microbiology. In the real world, dark life is microbial. But it's plausible that dark life could evolve into more complex life forms, like the monsters that inhabit the dungeons of D&D.
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Post by krusader74 on Aug 19, 2013 20:54:52 GMT -6
If it's any reassurance, I got the same values as you, modeling the problem as a binomial distribution, as explained above.
Table 1. Probability of rolling exactly the number of face values on a certain # of dice. .......#of Individual Face Values #of d6 0 1 2 3 4 5 6 7 8 9 10 1 0.833333 0.166667 0. 0. 0. 0. 0. 0. 0. 0. 0. 2 0.694444 0.277778 0.0277778 0. 0. 0. 0. 0. 0. 0. 0. 3 0.578704 0.347222 0.0694444 0.00462963 0. 0. 0. 0. 0. 0. 0. 4 0.482253 0.385802 0.115741 0.0154321 0.000771605 0. 0. 0. 0. 0. 0. 5 0.401878 0.401878 0.160751 0.0321502 0.00321502 0.000128601 0. 0. 0. 0. 0. 6 0.334898 0.401878 0.200939 0.0535837 0.00803755 0.000643004 0.0000214335 0. 0. 0. 0. 7 0.279082 0.390714 0.234429 0.0781429 0.0156286 0.00187543 0.000125029 3.57225*10^-6 0. 0. 0. 8 0.232568 0.372109 0.260476 0.10419 0.0260476 0.00416762 0.000416762 0.000023815 5.95374*10^-7 0. 0. 9 0.193807 0.348852 0.279082 0.130238 0.0390714 0.00781429 0.0010419 0.0000893061 4.46531*10^-6 9.9229*10^-8 0. 10 0.161506 0.323011 0.29071 0.155045 0.0542659 0.0130238 0.00217064 0.000248073 0.0000186054 8.26909*10^-7 1.65382*10^-8
I've included a new column for 0. Row probabilities should sum to 1. This table was generated with the following Mathematica code: TableForm[Table[(Probability[x==#2, x\[Distributed]BinomialDistribution[#1,1/6]])&[i,j]//N,{i,10},{j,0,10}], TableHeadings-> {Range[10], Range[0,10]}]
Simply by changing "==" to ">=" in this code, you can compute the probability of rolling the exact number or greater...
Table 2. Probability of rolling the number of face values or greater on a certain # of dice. .......#of Individual Face Values #of d6 0 1 2 3 4 5 6 7 8 9 10 1 1. 0.166667 0. 0. 0. 0. 0. 0. 0. 0. 0. 2 1. 0.305556 0.0277778 0. 0. 0. 0. 0. 0. 0. 0. 3 1. 0.421296 0.0740741 0.00462963 0. 0. 0. 0. 0. 0. 0. 4 1. 0.517747 0.131944 0.0162037 0.000771605 0. 0. 0. 0. 0. 0. 5 1. 0.598122 0.196245 0.0354938 0.00334362 0.000128601 0. 0. 0. 0. 0. 6 1. 0.665102 0.263224 0.0622857 0.00870199 0.000664438 0.0000214335 0. 0. 0. 0. 7 1. 0.720918 0.330204 0.0957755 0.0176326 0.00200403 0.000128601 3.57225*10^-6 0. 0. 0. 8 1. 0.767432 0.395323 0.134847 0.0306564 0.00460879 0.000441172 0.0000244103 5.95374*10^-7 0. 0. 9 1. 0.806193 0.457341 0.17826 0.0480215 0.00895006 0.00113578 0.0000938707 4.56454*10^-6 9.9229*10^-8 0. 10 1. 0.838494 0.515483 0.224773 0.0697278 0.015462 0.00243816 0.000267521 0.0000194489 8.43447*10^-7 1.65382*10^-8
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Post by krusader74 on Aug 17, 2013 22:02:25 GMT -6
Let's say you roll 5 six-sided dice and you want to know the probability that you get exactly x of the dice with spots of one specific type. This is called the Binomial distribution with parameters-- - number of trials: n = 5
- success probability in each trial: p = 1/6
You can easily compute this distribution in WolframAlpha using the formula prob x for x binomial with n=5 and p=1/6Everything you want should be shown there... - This will show you the statistical properties (mean, standard deviation and higher moments).
- It will show you the formula using conventional math notation.
- It will show you a plot of the probabilities for x = 0 through 5.
- It can show you a table of probabilities for x-- Under the section labelled "Plots of PDF" click the button that says "Show table of values" and then click the "More" button to see x = 0 through 5.
Furthermore, you can experiment by changing the parameters. For example, you want to roll 3 twenty-siders and see the likelihood of getting 0 through 3 dice showing one specific type of spots? Just change n to 3 and p to 1/20 in the formula above. For a thorough discussion of the Binomial distribution, I suggest Wikipedia-- en.wikipedia.org/wiki/Binomial_distributionIf you want to know how the formula was derived, here's a crash course...First use the "Multiplication Rule for Dependent Events" to get the probability that the first x of n dice show the desired number of spots and the rest don't: P(A and B) = P(A) * P(B|A)where - P(A) = (1/6)^x = probability of first rolling exactly x six-sided dice showing the given type of spots
- P(B|A) = (1 - 1/6)^(n-x) = probability of then rolling exactly (n-x) six-sided dice, *not* showing the given type of spots
Since we don't really care whether the x dice showing the given type of spots are the first x dice, the last x, or jumbled up any which way, we need to apply the "Addition Rule": If the events A and B are mutually exclusive, then P(A or B) = P(A) + P(B). The notation (n choose x) refers to the binomial coefficient-- the number of ways to choose x things out of n things. (What you've written above is the factorial form.) Since repeated addition is just multiplication, we simply multiply the previous formula by this binomial coefficient in order to get the desired probability: P(X=x) is (1/6)^x * (1 - 1/6)^(n-x) * (n choose x)where X ~ binomial with p = 1/6 and n given
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Post by krusader74 on Mar 22, 2013 14:45:47 GMT -6
The previous posters did a great job of quickly providing the correct answer. I wanted to offer a few tools for thinking about dice problems like this. Hopefully this information will aid others tackling similar problems in the future. But first a word on notation: "zN" means "a die labeled 0-N". This is called "zero-biased notation" and it comes from this post: forum.rpg.net/showthread.php?482860-Looking-for-a-new-dice-roll-shorthand-notation&p=11202182#post11202182Problem: Find the probability mass function for the sum of discrete uniform random variables d6+z9, where d6 = six-sided die z9 = ten-sided die labeled 0-9 Solution: Lots of different ways to think about this problem: #1 Use polynomials/generating functions...The generating functions G(x) of these dice are... d6: x^1+x^2+x^3+x^4+x^5+x^6 z9: x^0+x^1+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9 In these functions, the exponent k in the expression x^k represents the number of pips or spots on the die. The coefficient of x^k is the number of ways to get k pips; all the coefficients above are implicitly 1s. Read the plus sign (+) as an exclusive "or". So, the generating function for d6 says, "There's 1 way to get a 1; 1 way to get a 2; ...; or 1 way to get a 6." Apply the "product rule" from probability theory to get a representation of every outcome from throwing both dice and summing the results: (x^1+x^2+x^3+x^4+x^5+x^6) * (x^0+x^1+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9) = 1 x^1 + 2 x^2 + 3 x^3 + 4 x^4 + 5 x^5 + 6 x^6 + 6 x^7 + 6 x^8 + 6 x^9 + 6 x^10 + 5 x^11 + 4 x^12 + 3 x^13 + 2 x^14 + 1 x^15 This expression succinctly says: - There's one way (coefficient of x^1) to roll a 1 - There's two ways (coefficient of x^2) to roll a 2 - Etc. - There's 6 ways (coefficient of x^10) to roll a 10 - There's 5 ways (coefficient of x^11) to roll an 11 - Etc. Etc. In other words, the number of outcomes that sum to k is the coefficient of x^k. The total number of outcomes is 6*10=60. The probability that the sum is k is the number of outcomes that sum to k divided by the total outcomes (60). :. The probability that the sum of the dice = k is the coefficient of x^k divided by 60. In Mathematica, you could write all this in one line as... Table[{n,100*Coefficient[Expand[Sum[x^n,{n,1,6}]*Sum[x^n,{n,0,9}]],x^n]/60//N},{n,1,15}]//TableForm Outcome Percentage (%) chance 1 1.66667 2 3.33333 3 5. 4 6.66667 5 8.33333 6 10. 7 10. 8 10. 9 10. 10 10. 11 8.33333 12 6.66667 13 5. 14 3.33333 15 1.66667
As a check, the probabilities must sum to one: Fold[Plus, 0, (Coefficient[Expand[Sum[x^n,{n,1,6}]*Sum[x^n,{n,0,9}]],x^#])/60&/@range[1,15]] = 1 as required. #2 Use convolutions...The probability mass function of d6 is f(x) = 1/6 for x in 1..6, 0 otherwise. The probability mass function of z9 is g(x) = 1/10 for x in 0..9, 0 otherwise. The probability mass function of d6+z9 is the convolution h[n] = (f*g)[n] = Sum[f[m] g[n-m],{m,1,6}] where n in 1..15. Here the asterisk * is the convolution operator, and multiplication is represented by juxtaposition. You could write this in Mathematica as f[x_]:= If[x<1 || x > 6, 0, 1/6] g[x_]:=If[x<0||x>9,0,1/10] h[n_]:=Sum[f[m] g[n-m],{m,1,6}] Table[{n,h[n]},{n,1,15}]//TableForm
Here we express probabilities as exact fractions... 1 1/60 2 1/30 3 1/20 4 1/15 5 1/12 6 1/10 7 1/10 8 1/10 9 1/10 10 1/10 11 1/12 12 1/15 13 1/20 14 1/30 15 1/60And again we always check Sum[h[n],{n,1,15}] == 1. True. Once you have the probability mass function, its easy to compute statistics for this roll... Mean: Sum[n*h[n],{n,1,15}] = 8 Standard Deviation: Sqrt[Sum[n^2*h[n],{n,1,15}] - (Sum[n*h[n],{n,1,15}])^2] = Sqrt[67/6] ≈ 3.34166 #3 Use the Troll dice roller and probability calculator at topps.diku.dk/torbenm/troll.mspThe expression is: z9 + d6 Click the "Calculate probabilities" button. This confirms the above results. It also confirms the mean (8) and standard deviation (3.34165627596) we already got. Always pays to double check. Note that z9 == d10 - 1, so you could also have used the expression: d6 + d10 - 1 #4 Write a computer program to enumerate all the outcomes.Here's the Common Lisp code to solve this problem: ;; compute probabilities by enumerating all outcomes (setf h (make-hash-table)) ; h counts number of each outcome
(loop for x from 1 to 6 ; x = d6 do (loop for y from 0 to 9 ; y = z9 do (let* ((k (+ x y)) (v (gethash k h))) ; k = d6 + z9 (if v (setf (gethash k h) (1+ v)) ; increment outcome k count by 1 (setf (gethash k h) 1))))) ; initialize outcome k count to 1
; Print list of outcomes k and their probabilities 100%*v/60 (loop for k from 1 to 15 do (let ((v (gethash k h))) (format t "~d:~10t~f%~%" k (* 100 (/ v 60)))))
You can actually run this code at www.compileonline.com/execute_lisp_online.phpIt produces output like so: Executing the code.... $clisp /tmp/136391496511858.lisp 1: 1.6666666% 2: 3.3333333% 3: 5.0% 4: 6.6666665% 5: 8.333333% 6: 10.0% 7: 10.0% 8: 10.0% 9: 10.0% 10: 10.0% 11: 8.333333% 12: 6.6666665% 13: 5.0% 14: 3.3333333% 15: 1.6666666%
Which is exactly what we expect to see. #5 Write a computer program to simulate a large number of random variates.We can slightly modify the previous program to accomplish this: ;; simulate probabilities by generating two hundred fifty thousand random variates (setf h (make-hash-table)) (defvar iterations 250000) (loop for n from 1 to iterations do (let* ((x (1+ (random 6))) (y (random 10)) (k (+ x y)) (v (gethash k h))) (if v (setf (gethash k h) (1+ v)) (setf (gethash k h) 1)))) ; Print list of outcomes k and their probabilities 100%*v/iterations (loop for k from 1 to 15 do (let ((v (gethash k h))) (format t "~d:~10t~f%~%" k (* 100 (/ v iterations)))))
This produces the following results: 1: 1.6332% 2: 3.2772% 3: 5.0144% 4: 6.6868% 5: 8.414% 6: 10.0452% 7: 10.0404% 8: 10.0156% 9: 9.9716% 10: 9.9524% 11: 8.2184% 12: 6.7016% 13: 4.996% 14: 3.366% 15: 1.6672%
Increasing the number of iterations will increase your accuracy. I increased the number of random variates 40-fold to 10,000,000 and got the following results: 1: 1.6677% 2: 3.32552% 3: 4.98889% 4: 6.67127% 5: 8.33191% 6: 10.01302% 7: 9.99581% 8: 10.00938% 9: 9.99052% 10: 10.02067% 11: 8.32514% 12: 6.65458% 13: 5.00784% 14: 3.33027% 15: 1.66748%
That looks a little better For example, the error for outcome "3" improved by 3.29 thousandths.
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Post by krusader74 on Mar 14, 2013 18:42:10 GMT -6
I'm hesitant to post, after all the controversy, but I believe this thread still has potential, if it can elicit some useful materials for OD&D. Here's some practical OD&D advice on how to start a Crusader campaign.
Rules 1) Use Chainmail + 3LBBs only. If you don't own Chainmail, consider using Chainmail 2.0 (discussed on dragonsfoot).
2) Humans only. No demihumans.
3) Clerics are the pious saints of all three Abrahamic religions. Their "spells" are miracles from God.
4) Magic Users are Muslim alchemists; or Christian (or Jewish) cabalists. Their "spells" are just advanced knowledge of chemistry, physics and math.
5) Monsters: Decide whether or not to include monsters. If yes, consider using Djinn, Efreet, and Ghouls--all from Arabic folklore and listed in Monsters and Treasure (Volume 2). Also mummies and mummified animals. Griffons are from Egyptian legend. Dragons are mentioned in the Bible. You could create stats for golems (Jewish legend). All three religions have angels, demons and devils.
6) Make it a game of battle strategy and the exploration of the unknown. No religious/political BS.
Chainmail scenario Start by re-creating the first battle of Ramla, September 7, 1101. Crusaders won this. Ramla is in the middle of Israel. This basically secured Jerusalem for the Crusaders. Plus Ramla has three great historic places to explore after the battle. See below.
Use the Chainmail rules to recreate the battle. Historically, the Crusaders were vastly outnumbered 10:1. One third of the Crusaders perished before the tides of battle turned in their favor. Try to compensate for their numerical insufficiency by giving them more capable troops.
If you used tried to be 100% historically accurate in your setup, and you used the Chainmail 20:1 combat rules, you'd have about 500 Egyptian figures vs 65 Frankish figures. IMHO, that's too many too figures to manage, and it gives the Egyptians an overwhelming advantage, even if all the Egyptians were light forces and the Franks were heavy/armored. Instead try something like this (more like 66.6:1 scale):
Egyptians 30 Arab and Berber cavalry (Light Horse) 60 Sudanese bowmen (Light Foot/Archers) - These remained stationary during the actual battle 60 Light Foot 1 Hero - Saad el-Dawleh (D&D: Fighting Man/4 - Hero) -------------------------------------------------- 150 figures, 230 points
Franks 15 Heavy Horse 30 Armored Foot 1 Super Hero - King Baldwin I (D&D: Fighting Man/8 - Super Hero) 1 Hero-1 - Fulcher of Chartres (Baldwin's chaplain and chronicler) (D&D: Cleric/5 - Bishop). PCs are each 1 figure during the Chainmail battle (in terms of Chainmail, these figures could play as Heroes or Wizards). -------------------------------------------------- 47 figures, 220 points without the PCs
The Egyptians total 150 figures. 150 is roughly what Gary Gygax used per side in the Battle of Brown Hills in November 1971. So it should be manageable.
In this design, the Franks are only outnumbered 3:1, understating their disadvantage by a factor of 3 and 1/3 compared to history. But in terms of Point Values, there's balance: Each side is worth a little over 200 points without the PCs. Since I'd add one more figure for each PC, this shifts the balance slightly in favor of the Franks, which is what we want.
Victory conditions 1) The Franks will fight until the entire cavalry and infantry are all killed or routed off the battlefield. At this point, Baldwin will ride his horse, named "Gazala," to Jaffa to rendevouz with the English pirate and saint, Godric of Finchale, and attempt to get fresh troops from him for a rematch.
2) The Egyptians aren't going to sacrifice too much over Ramla. They already lost it in 1099. They'll only fight until 50% of their number are killed or routed off the battlefield, at which point they will attempt to withdraw in good order.
Additional notes 1) Re-match: There were also a second (1102) and third (1105) battle of Ramla. In the second battle, Baldwin rode with 500 knights into 30,000 Egyptians. Outnumbered 60:1, the Franks were massacred. Only Baldwin survived. He hid in the White Tower (see below) until nightfall, and then rode Gazala to Jaffa, to rendevouz with Godric of Finchale.
2) Baldwin I: Fulcher described Baldwin as a new Joshua. William of Tyre said that Baldwin "struggled in vain against the lustful sins of the flesh," and it was suspected that he was homosexual. Baldwin became the King of Jerusalem.
3) Rulers of Ramla: Ramla was part of the County of Jaffa and Ascalon. The Muslim's deserted it in 1099. Thereafter, it was left under the supervision of Robert of the diocese of Rouen, whom the crusaders installed as Bishop of Lydda and Ramla. It remained under control of the Church until 1106, when control passed to a secular ruler, Baldwin I, Castellan (not the same as our Baldwin), until 1134. It remained under the control of a succession of secular lords until it was recaptured by Saladin in 1187.
4) History of Ramla: It was founded in 716 AD by the Umayyad Caliph Sulayman ibn Abd al-Malik after the Arab conquest of the region. Its name derives from the Arabic word "Raml" meaning sand. The early residents came from nearby Ludd/Lydda/Lod. The White Mosque was completed in 720 AD. It was destroyed by an earthquake in 1034 and rebuilt in 1047.
OD&D scenarios After the battle, your PCs have three important places to explore in Ramla:
1) Ayalon Caves. Contains giant crustaceans/prehistoric monsters. And gems and precious metal deposits.
2) Jewish synagogue/cemetery/catacombs. Contains the bones of the Prophet Samuel. Important holy relic for all three Abrahamic religions. Maybe these relics have miraculous powers? Perhaps the cemetery has ghouls, a staple of Arabic folklore, eager to feed on the dead from the battle as well as hapless PCs exploring the cemetary? The catacombs below the cemetary contain: (a) war refuges, (b) smugglers' hideouts, and (c) a meeting place for a necromantic cult.
3) The White Mosque (a-Masjid al-Abyad). It is made from pure white marble. The minaret, The White Tower, is 89 ft tall. Google for maps and images of this complex. It contains the bones of the Islamic saint, Nabi Salih. There may have been a fountain in the central court. There are three giant underground cisterns that collect rainwater and water carried by an aqueduct from the springs in the hills east of Ramla. They provide storage for fresh drinking water and water for ablutions. Perhaps there's a dungeon underneath this complex to explore? And maybe there's even a Falak (fire-breathing dragon) in that dungeon? One idea is that a dragon is imprisoned in subterranean caverns. Feeding it water from the cisterns extinguishes its fire. It needs to drink oil to regain its power.
Raison d'etre In the campaign I'm planning, the PCs are acolytes, working for the inquisition. The twelfth century wasn't just the start of the Crusades, it was also a time numerous heresies arose, poisoning faith and morals, spreading like wildfire, and inciting rebellion against all authority, human and divine. The best known heretics of the time were the Petrobrusians, the Arnoldians, the Waldenses, and the Cathari. These heresies posed an existential threat to both the Church and the State. The PCs job is to investigate and shutdown heretics and sources of heresy. I'm a big Warhammer 40K fan, so that influences my ideas.
The real reason the PCs are tagging along with Baldwin is to investigate a rumor that an Arabic manuscript of the Kitab al-Azif, perhaps the original, is somewhere in Ramla. As a reminder: The Latin name for this book is The Necronomicon. The author, Abd al-Azrad, studied black magic under the Wizard Yakthoob in Memphis. He made pilgrimages from Egypt to the cursed city of Chorazin in Galilee. Jesus cursed Chorazin in the Bible: "Woe unto thee, Chorazin!..." (Matthew 11:20-24), Chorazin is thought to be the future birthplace of the Anti-Christ, and so it became a gathering place for black magicians. On one of these pilgrimages, circa 730 AD, al-Azrad went into a hallucinogenic trance for 8 years, and wrote the Kitab al-Azif. The experience reduced al-Azrad to a vegetative state. With help, he returned to his home in Damascus, only to be eaten alive by an invisible demon in the marketplace, while a fellow pilgrim and student of Yakthoob took the Kitab al-Azif back to his master in Memphis. While passing through Ramla, he was robbed by bandits, who killed him. The book was eventually sold to the scholars at the White Mosque. When the Muslims abandoned Ramla in 1099, the Kitab al-Azif may have been (1) stashed in the Ayalon Caves, (2) hidden in the catacombs beneath the Jewish cemetary, or (3) secured in the subterranean caverns under the White Mosque in the protection of the Falak. Roll a d3 to decide where it is.
The PCs mission is to retrieve the Kitab al-Azif, and return it to Vatican where it will be placed in the Archivum Secretum Vaticanum, before it becomes the source of heresy or mischief. The official position of the Church is that Abd al-Azrad wrote the Kitab al-Azif in a drug-fueled frenzy. There's nothing supernatural about it. But if it falls into the hands of the heretics, they will surely misuse it. If you like Cthulhu Mythos, then make the book the real deal--an extremely evil and powerful artifact that must be secured at all costs.
So in this campaign, Law is Church canon law, the Church hierarchy, and the inquisition; Chaos are heretics, rebels, satanists and anarchists opposed to Church rule. Neutrals are outsiders to this conflict, including Jews, Saracens and Pagans.
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