# The math of it all

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The Magician
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I like your thinking Mitch.

I like your thinking Mitch. Your catching on to where I'm going with this. Actually, I'm thinking of indefinate number of applications. I'm find the "AAG Principle" vary interesting. But, I just have to get it so cards don't have to only pair with one specific card. I find it.

Mitchell Allen
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AAG - Advanced Auto Glazing

Magician, AAG lead me off into the deep end.
I barely made it back to dry land. So, the rest of this post may be water-logged :)

If you combine sequences, then assign cards to multiple sequences, you might be able to create multiple applications.

I started to make an example, but got bogged down trying to make it work.

I got as far as starting an alphabetized word list with interesting properties:

Ark Bark Cardshark Dory Embark Foo Goo Hulk Igloo Jump Killed Lump Mark New Ostrich Pontoon Quark Rat Spark

The exponential sequence are water vehicles, and the prime number sequence was supposed to be words ending in -ark. Unfortunately my online references don't give me enough words. Unless you use proper nouns...sigh.

The gist is that you pre-arrange your set and use rules to control the re-ordering of that set (like AAG in the magic card tricks)

Cheers,

Mitch

The Magician
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Don't rush

I wouldn't rush it. I am deturmined there is lots that can be done with this but not to get burned out. I tend to hit a wall when I get burned out and creative idea stifled. I'm interested to see what you come up with but it's not worth burning out. The strategy I am going with is gathering all the magic tricks that I find that relate to sequences and math, try them out, and file the best ones away. Then contemplate what I want my game to do with it and let my subconscious do the rest.

Cheers,
D

The Magician
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First off, my visions for these mechanics, at least for my own application, ultimately are to have them be obscure and subtle to the player. I mean I'm not talking about for example a passage in the rule set saying "Unbenounced to your oponent, count out blah blah, and tell them "blah blah blah bla". Or, "(X) game is a unique adventure with magic like card play".

Anyway, what about this. I sort of got a seedling of an example using Gibonacci sequences mod 9:

Using the bracelet:
112358437189887641562819112....repeats it's self. Line up the first 12 on top and the proceeding 12 on bottom:

1 1 2 3 5 8 4 3 7 1 8 9
8 8 7 6 4 1 5 6 2 8 1 9

I give you (made up example) "Wizard vs. Wizard"

Each of the above numbers can represent a "spell" card. It's corresponding number in the sequence will be a value in the corner of the card or somewhere on it, representing the cost of the spell, it's money value. Notice each pair adds up to "9" besides the last pair of 9's. These spells would make up a spell deck.

So lets take the first pair 1, and 8. I buy a cheap spell for 1\$ and can cast it on you and it will put a lasting curs on you that does something irritating. It's effect don't go away until you use (Y) spell worth \$8, which despells it and cancels it out and both cards are discarded into a pile. You who dispelled the curse get \$9 or points. And so on with all the other pairs. The cards would say something like: "you get this curse, only (Y) spell can cure it. There would have to be more than that surelly. maybe something like there are two kinds of a number, one that casts a curse and one that dispells one. Or one spell has both effects. Maybe (Y)'s \$8 spell teleports money from your oponent to you, but your oponent can easily break it with (A) \$1.

I'm sure there's a lot more that can make this example worthwhile.

This is just a vary rough thought. I haven't spent much time with this example.

The Magician
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Is the illusionist reading

Is the illusionist reading this? Please man! Come to the table and help us with your tallents. We love tallented people! You could cause "Khonos" style ripple effects into the future with your posts. You could save mirrages with board games no doubt.

Now, my intent as far as mechanics go, are not to aply slights of hand or charming flurrish techniques. That's not the aspect of magic tricks I am looking at. Not to say that anyone else can't creat a game like that. I'm sure there's a hobby market for it. I want to see what we can do with math tricks. Will you join our investigation?

The Magician
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Please don't mind me

http://www.maa.org/columns/colm/cardcolm200810.html

I want to thank many of you who posted some great things on this thread. I am apreciating many of them more now, haveing more knowledge on sequences.

Mitchell Allen
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Doing the Wizard Shuffle

Heh, I don't mind at all. This is an inspiring thread.

I like the ideas in two of your previous posts: Wizard vs. Wizard and the Monge Shuffle.
Thank goodness for video! I had no idea what the written description was getting at!
The period and fixed points may help me to recreate that spelling trick! Thanks for sharing. :)

Anyway, the Wizard vs. Wizard gave me the idea that - even though you're thinking mechanic - it could also be an elegant way to balance your spells. It also helps you avoid feature creep, by limiting the spells to the length of the bracelet.

Actually, it could also lead to the double synchronicity! What if you created TWO bracelets and found a way to make them interact?

Rather than "burn out" on an example, I'll let that simmer in your sorting hat!

Cheers,

Mitch

The Magician
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Mitchell Allen wrote:Heh, I

Mitchell Allen wrote:
Heh, I don't mind at all. This is an inspiring thread.

I like the ideas in two of your previous posts: Wizard vs. Wizard and the Monge Shuffle.
Thank goodness for video! I had no idea what the written description was getting at!
The period and fixed points may help me to recreate that spelling trick! Thanks for sharing. :)

Anyway, the Wizard vs. Wizard gave me the idea that - even though you're thinking mechanic - it could also be an elegant way to balance your spells. It also helps you avoid feature creep, by limiting the spells to the length of the bracelet.

Actually, it could also lead to the double synchronicity! What if you created TWO bracelets and found a way to make them interact?

Rather than "burn out" on an example, I'll let that simmer in your sorting hat!

Cheers,

Mitch

Well, Mitch, I think there are other similar longer bracelets that go longer before repeating. I have yet to really break-in this new wrinkle in my brain. I need to really sit down and do some serious study on paper. And of course there's triple sums and what not.

All of this of cource has useful application in games. you know I like to start simple. Cool, if it creats some simple dandy ways of balance and stuff like that. I would like to get to a point where I'm using several combinations of math tricks and sequencing to create this interesting system of how cards play in the game. You know how in many games, in game set up, the decks have a certain place in relation to the board. It would even be cool if you could set it up, in such a sneakety deakety way that the player is making their own decisions, "and" the cards are shuffled, "but" because "you" design the cards, you could still pop in big "suprises" in the games. And the suprises change. It sounds like a tall order I know. But that is what motivates me.

Mitchell Allen
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Sneakety Deakety, Peekity Boo :)

You're funny.

One way I like to think about "control" is from the perspective of absolutes. Two quick examples:

Monopoly has no control over the dice. However, if you pick up the Go Back three Spaces card, you have no choice where you're going, depending upon which Chance square you're on.

Example #2: Abstract space flight. Rather than getting bogged down in the physics of space travel, games may simply say that, with the Buck Rogers 2000, it take 4 turns to get from planet a to planet b. (Doing a bit of simple algebra will ensure that the distances make sense) Once the base times are created, newer faster ships can be worked into the game with ease.

Cheers,

Mitch

The Magician
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hahahhah hah ahh you got me

hahahhah hah ahh you got me busting up laughing. (Dr. Evil grin)

The Magician
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suprises!

Guys I got something I really want to share. It's a card mechanic that I created from one of the math tricks I learned. I can't contain myself right now. I've been testing it and it validates exactly what I wanted to do with it. I'm pretty darn confident with this one. From what I've been working with, it creates electrifying suprises and unpredictable conflict. The concept has to do with building these little decks that you fight with. You take your little deck and play one card at a time with your oponent. That doesn't explain it well enough. I'm going to have to let this one hang for a day or two probably because I need to whip up some cards and create some clear examples.....whip up some photos. I don't promise anything but, when I have some kind of little presentation put together I would just love to share this mechanic. I know it's like why didn't I just wait before posting anything. The part that give me the Dr. Evil grin is that I think it can be explained in normal game rule language and made totally to just following a normal game rule procedure.

The Magician
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Rick-Holzgrafe wrote:Reiner

Rick-Holzgrafe wrote:
Reiner Knizia holds a doctorate in mathematics, but has said that his games are designed and tuned by doing lots of playtesting, not by mathematics.

I find math useful for some design purposes, but I don't do heavy probability studies. Occasionally a spreadsheet is useful. But the best thing you can do is just playtest the daylights out of your design, and make changes whenever you find something that isn't working as well as you'd like. Repeat until it's glorious.

This is an interesting point. One thing that strikes me though is that if Knizia holds a doctorate in mathematics....a doctorate, I'm sure a lot of the math is processed on a subconscious level by that point. But, your probably right about not requiring a lot of math. That was a thought that crossed my mind though. It's still a doctorate making the statement. He has a lot of playtesters I hear. Do you think that someone so skilled at something can simply say it was my playtesters? I mean if I were to paint a portrait of someone, I would be silly to say "Ohhhhhhh she told me how to paint her. She wispered in my ear, you can do the same thing I did just now. Look here, just let her wisper to you". I don't disagree with the knizia statement, but he does have a more than avorage math ability. How easy could it be to sluff that off?

Mitchell Allen
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Magic Mechanics

Sounds cool. Time's up. Details!

:)

Cheers,

Mitch

[edited] Doh! I saw the Journal entry after I hit save...This is going to take some reading offline :)

The Magician
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lol! Hey what's up Mitch?

lol! Hey what's up Mitch? How's you projects been going?

Mitchell Allen
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The Count of Monte Carlo

Magician, you are clever!
I only followed along with the text, declining to verify the actions, which I'm sure you've done already :)
Instead, I focused on the presentation and - depending on what you have in mind - it appears that you have an exciting mechanic.
The first and most obvious question is, when the deck is set up, must it be done "White-box" or "Black-box"?
In other words, must the dealer have foreknowledge of the intervals?

If so, I suppose this would work if the game employed a dungeon master. If not, then -as you stated - the other players will soon catch on. The mechanic may suffer the fate of Nim (once everyone knows the secret of Nim, the game becomes deterministic).

One interesting derivation I imagined is that the cards are replaced, rather than discarded. This could represent reinforcements or - more likely - multiple thrusts and parries by the warring party. I don't know how you can determine the effectiveness of intervals with such a replacement scheme.

Whatever comes of this mechanic, you've hit on a fascinating way to combine the humble shuffle with the very math you originally sought to down-play!

Cheers,

Mitch

The Magician
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Mitchell Allen wrote: The

Mitchell Allen wrote:

The first and most obvious question is, when the deck is set up, must it be done "White-box" or "Black-box"?
In other words, must the dealer have foreknowledge of the intervals?

If so, I suppose this would work if the game employed a dungeon master. If not, then -as you stated - the other players will soon catch on. The mechanic may suffer the fate of Nim (once everyone knows the secret of Nim, the game becomes deterministic).

One interesting derivation I imagined is that the cards are replaced, rather than discarded. This could represent reinforcements or - more likely - multiple thrusts and parries by the warring party. I don't know how you can determine the effectiveness of intervals with such a replacement scheme.

Cheers,

Mitch

Thank you Mitch! I post this stuff also to get fellow designers considering new possibilities.

Regarding the question of white boxes and black boxes, I will get back to you on that. What I've presented in the MS Word attachement, is the basic math of the mechanic. This is so a designer can look at it and understand the basics of what needs to be understood if she wants to create some variation or use this basic mechanism. On that writing, I don't say exactly how to execute it, being that it is open to the designers imagination on how to execute it. Like I said, I will get back to this question later.

As for the figureing out part, for one thing, I am confident that I can stream line this mechanic such that pretty much everything is explained on the cards that when you read them, you know what to do. And the complex system I think can be presenting as simple for a child to follow along. I am pretty sure it would not matter weather players actually catch on, because it still offers player choices that by design, would always be an unkown to the oponent.

No matter how ... "magical" or "clever" this mechanic tries to be or whatever anyone's perseption of it is, there are many advantages that this system has built into it for the game dynamics. I try to list as many of these advanteges that come to mind in my treatement.

Soon, I will make an effort to post some print-out cards to use to validate the mechanic.

I apreciate that you see value in this system. I welcome you and anyone else to use it in their own way. I would love to see your ideas Mitch relating to our discussions here and any other you may have.
Cheers,
Dustin

The Magician
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Oh, I forgot to emphisize

Oh, I forgot to emphisize something about this two part system. There's the "Beer Deal" and the "Magician's surprise". The battle is where the deal is executed. But why do I need "sixy alpha omegas" for my recruitment phase? Why not just the deal? Well the recruitemnt phase provides a structure of getting the deck set up for the beer deal. Also, lacing in it genuine player choice suprises. This I think provides some divertement from any sneakety deakety tricks-maybe not. But, it does several other things as well. Besides provideing a stucture for the players cards and how many they get in there court army or whatever you want to call it, I think it provides a fine way of stucturing in story and drama into the experince. By providing a story and context, like a double edged sword, I think it does just that and provides a divertement from the complicated trickery.

The Magician
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Holy mother of Shiva! Ther is

Holy mother of Shiva! Ther is a time traveler lurking in this forum....right here in this thread- in the box next to this post in the thread list "page views". Once the number got to (100) it went backwards in time. I couldn't beleave it at first, but I've been tracking the number for the past week and it confurms my suspicions. It's now at (82). I always knew numbers can time travel, but this confurms that numerical time travelers like BGDF. I think this agent is following me.

monica99
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math of it all

Sorry not really following the string...
But ultimately I think, the math should teeter on what a smart strategic player knows and what an impulsive player plays and that way an inexperience/experience player enjoys the game and plays again. What that number is I'm not sure I think though each play (even though not mathematical) should be considered "is this fun?" I think at a certain point you play like you are winning the lottery and a game needs to capture that feeling and even if it's an illusion the disaster should be swift and hilarious.

The Magician
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monica99 wrote:Sorry not

monica99 wrote:
Sorry not really following the string...
But ultimately I think, the math should teeter on what a smart strategic player knows and what an impulsive player plays and that way an inexperience/experience player enjoys the game and plays again. What that number is I'm not sure I think though each play (even though not mathematical) should be considered "is this fun?" I think at a certain point you play like you are winning the lottery and a game needs to capture that feeling and even if it's an illusion the disaster should be swift and hilarious.

Great point monica, and I hope to releave the player of the math. I intend to have the important information and numbers on the cards. Little math or none at all should be the burden of the player. Actually, in the mechanic that I shared, I beleave the players have plenty of choice and plenty room for strategy. As will be more developed in my battle procedures. The way I am working this mechanic, I will be saving the players a lot of stress and making it easier for them in my opinion. One of the things that I just love about the formula I am using is that I get to plug whatever values I want into the variables and it functions.

End of Time Games
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New Name

The Magician has a new name and profile. I will not use my other profile anymore. ET Games is resuming where "The Magician" left off. Thanks again my friends, I think I pretty much have finished addapting the new profile. I will delete the old when I found out whether or not Magician's content threads will disapear. Please don't think I am posting this to spoil or beef up this thread comment count.

End of Time Games
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Here's a simple way

@ Mitch

Okay man here's an easy alternative if you would like to do the demo. Since I don't have cards printed or uploaded yet, you can use playing cards and cards from any board game that you own. In the demo example in my post "The Magician's surprise", you see three basic catigories of card: snow wraiths, dark wraiths, and surprise cards. You can choose to have a single deck of playing cards represent the snow wraiths, another deck with a different back design or color to represent the dark wraith, and then take a series of cards from a game that you own and use them for the cards you will choose for the surprise. This is a simple way to use what you have to get the idea of the mechanic in action. Just a sugestion my friend.

End of Time Games
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Mitchell Allen wrote: A

Mitchell Allen wrote:

A college-level text on probability and statistics stays near me at all times. I failed the course, so I NEED that book.

I had six or seven of those S.O.B. college text books all different and from the same course over a period of a few years.....or more than a few. A few years ago I burned them in a sacred "I'm not doing that again" cerimony. Now I regret it because they actually could have come in handy by this time. Powels Books in Portland OR wouldn't take them (shaking head).

End of Time Games
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Mitchell Allen

Mitchell Allen wrote:

Whatever comes of this mechanic, you've hit on a fascinating way to combine the humble shuffle with the very math you originally sought to down-play!

Cheers,

Mitch

Mitch, I never down played the math or the shuffle. I absolutely must clarefy this. I never down played either. I down played if anything the original purpose of the shuffle to predict cards. Not the shuffle though. I am the kind of magician no one ever hears or beleaves about and I chew these sorts of tricks up and spit them out into my own other creation.

As for the card trick, it doesn't just use these sorts of complex systems, it friken requires peeking at the card at the beginning anyway, then the illusionist goes into the system. I'm not impressed!!! I have had my time about these subjects in the past. I'm not saying another word about it.

I don't suspect that is the way you interpreted it. I just felt that I had to clarify what I was saying.

I love the math. I love the shuffle.

End of Time Games
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Game theory

Is anyone familiar with a branch of maththematics called "game theory"? I recently learned about it and strikes my curiosity. http://en.wikipedia.org/wiki/Game_theory

ReneWiersma
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Of course I'm familiar with

Of course I'm familiar with game theory :) I think you can't consider yourself a serious game designer if you don't know a thing or two about game theory.

Willi B
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I would say that there is room for others...

that have no great math skills and no study of game theory that can become serious designers as well.

I would consider these people the equivalent of "primitive" - "naive" - "outsider" artists by the newest definition. People that live outside of game study that accomplish great designs without the study and formal practice of games and those mathematics that bind their design.

Many designers start this way, making up rules to go with those army men or matchbox cars we got for Christmas.... I think you can sometimes find people like that that have never heard of many modern games or game theory that have been working independently of the culture and knowledge that have created wonderful works of fantasy and imagination.

I often wonder how much more creativity is lost to those of us who embrace the conformity that knowledge brings... the world needs more Willy Wonkas.

Katherine
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Thank you Willi B! Friends

Thank you Willi B!

Friends tell me that games have been around for thousands of years, but no-one seems to know when "theory" became a mandatory requirement for their developement.

End of Time Games
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ReneWiersma wrote:Of course

ReneWiersma wrote:
Of course I'm familiar with game theory :) I think you can't consider yourself a serious game designer if you don't know a thing or two about game theory.

Well good I'm glad that you do. Up until now, I just thought that there was the math side of things. This is a new turm for me. I don't consider myself a serious game designer. It's a hobby of mine. I must say though, having website for works in progress I think is going to help releave those auqward moments when I must tell people about my games in order to find testers. I can just make it short and point them to the website.

ReneWiersma
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Game theory is to game design

Game theory is to game design what chemistry is to alchemy. Sure, it is fun and all to try and combine various things, boil it together, and see what happens, but when you know a thing or two about the theory, you can also understand *why* things happen as they happen, and perhaps even predict them.

That's why I said you can't be a "serious" game designer if you don't know at least the basics of game theory. A creative person can come up with a combination of mechanics that make a brilliant game once, maybe twice in his lifetime, but I doubt they are able to come up with several "good" games a year, which is what it takes to become a professional in this field. It's the difference between art and craft, perhaps.

Also, knowing game theory doesn't mean you aren't able to think outside the box anymore. Game theory is just a tool. Just because a person knows the basics of architecture doesn't mean he cannot conjure up a great, new, inspiring idea for a building anymore. He just knows what will and won't work without constructing the building by trial and error and hope it doesn't fall down.

This reminds of a discussion I once had with one of the members of my band (a lefthanded guitarplayer). He told me that he didn't want to know any music theory, because he was afraid it would stifle his creativity. I think this is pure nonsense. Just because you know that the relative minor of the G-major chord is e-minor, doesn't hamper in anyway your creativity. In fact, I believe that knowing stuff such as the idea that you can transpose easily from any key to another by using diminished chords, gives you a lot more creative freedom.

Music theory doesn't tell you how to write songs, and game theory doesn't tell you how to make a game, they just desribe lessons learned in the past, theories tested and tried, and they help you to make that vision you have come true more easily. So don't be afraid of that wikipedia link. Click, read and be inspired.

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