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nlokers Regular user Grand Rapids, MI 142 Posts |
I've been working on a new mathematical stack and was looking for patterns in it and comparing it to some randomly generated sequences, but since it is my stack I figure I am biased, and can't objectively look at it. I originally thought about posting it here and asking if anyone could find any patterns in it, but decided that it might be more interesting to see if you guys could pick it out from some randomly generated sequences.
What I did was take screen shots of 10 stacks, 9 of them were randomly generated and 1 is my new stack. I do swear that the 9 were the first 9 that I randomly generated, I didn't hand pick them in anyway, and they are in the order that I took them. Feel free to post your guesses here, however if you do figure it out, and find some patterns in it and/or completely reverse engineer the stack, I would prefer that you PM me as opposed to posting that info in the forum. https://dl.dropboxusercontent.com/u/9732......dex.html |
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landmark Inner circle within a triangle 5194 Posts |
I took about 20 minutes applying various tests for color, suit, and value. I couldn't come up with anything. Congratulations! You certainly don't have to worry about it being uncovered as a stack.
Now the next two things are: 1) Is it easy to memorize the algorithm(s)? 2)Is there a reason to use this stack more than another or a random memdeck? But well done.
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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Waterloophai Inner circle Belgium 1368 Posts |
Same here. I don't see "a stack" or a certain sequence.
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Bulla Special user Honolulu, HI 674 Posts |
First of all, what does the stack allow you to do?
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nlokers Regular user Grand Rapids, MI 142 Posts |
I would say that the main "feature" of the stack is like the BTCS, where if you know once card you can find the next one and it is cyclic. It also has the added feature of being able to jump a certain number of cards, for example jumping 7 cards, 10 cards or 26 cards is quite easy.
The algorithm is pretty straight forward, not a ton of math, but bigger numbers that you deal with in BTCS. There are also some shortcuts that have more steps, but deal with smaller numbers. Worth noting that there is a more abstract stack system that this stack is a part of. The system happens to work with Tarot cards as well, though is a bit more work than the playing card version. |
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yair61 New user Israel 55 Posts |
My guess is that the fake shuffled deck is number #1 or #6, most likely the first one.
My guess is based on a story of my university professor of the statistics course. The conclusion of the story is that if you try to fake results of a random 300 coin flips, you will not write more than 4 or 5 headtail in a row. but if you realy flip a coin 300 times you will probably get 7, 8 and even 9 times the same headtail in a row. that what I saw in the shuffled decks you sent. but even if I'm right here, I can guess it just because you asked us do find it. It's looks like a very good pattern. |
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nlokers Regular user Grand Rapids, MI 142 Posts |
I saw a video about the coin flip thing on youtube once, I'll have to try and find the video later. But the idea is you have someone create a sequence of 100 heads or tails from flipping a coin, and then you have them create one by hand, trying to make it seem as random as possible. If you go through and could the number of heads and tails in each sequence they usually come out to be pretty close. Then go through an count them up 2 at a time, so you would have a total for HH, HT, TH, and TT. Continue this process for 3 in a row, 4 in a row, and what you will find is that at some point, one of the sequences will have an even distribution, and the other will be totally skewed.
One lesson I learned from doing these random card sequences is how weird random stuff can be. If you do a simulation and count the average number of pairs in a shuffled deck you get a little over 3. Based on that knowledge I've complained about the Aronson stack having only 1 pair, and the BTCS having those clumps of court cards. However, after creating the sequences I went through and counted the pairs in each, and found that stuff that you wouldn't expect to be in a random sequence shows up quite often. Here are the results if you are interested #1: 5 pairs, #2: 6 pairs, #3: 4 pairs, #4: 4 pairs, #5: 3 pairs, #6: 1 pair, #7: 3 pairs, #8: 2 pairs, #9: 3 pairs, #10: 2 pairs This is why I wrote the thing about not hand picking the random sequences, because the fact that the first 4 sequences are over the average for the pairs. I also thought #10 looked pretty ridiculous. |
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nlokers Regular user Grand Rapids, MI 142 Posts |
I'm trying to figure out what to do with this thread.
Should I A: Just tell everyone which one it is B: Tell people which one it is if they PM, so as to not ruin it for people who are still trying to figure it out C: Try to reduce the task by eliminating some of the options D: Make some other web page or series of web pages that give hints, so that people can see them if they like, or avoid them if they want E. Let the thread die quick death Anybody have any feelings on this? |
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Robertology New user Michigan 55 Posts |
I imagine if someone is reading the thread they should expect to see which one it is at some point. So you can just put a big disclaimer then the answer.
Or post an easy but not completely simple math problem where the solution is the number of the deck. That way no one will accidentally see the number. Plus you like math, right?
- Robert
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landmark Inner circle within a triangle 5194 Posts |
I vote for a hint of some kind--although you already gave us some in your second post. I'm still flummoxed.
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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nlokers Regular user Grand Rapids, MI 142 Posts |
Alright, I'll combine the two ideas.
Here is a little math formula 8^x mod 11 you can plug in as many values between 0 and 8 as you want to. Each answer will tell you one that it is not. So if you want to reduce the choices by 3, you can calculate 8^0 mod 11 8^1 mod 11 8^2 mod 11 each will give you the number of one that isn't the stack You may be able to do the first few in your head, but then it starts to get out of hand and you'll need a calculator. |
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Robertology New user Michigan 55 Posts |
Ha! Nice. Now, some hints for the hints (for the non-math people).
^ means "to the power of" so 8^2 is "8 to the power of 2" otherwise known as 8 squared. Any number to the power of zero is 1, and any number to the power of one is that number (in this case, eight). The "mod" is the remainder from division. Here you would do your "power of" then divide by 11 and look at the remainder. For example if we had 19 mod 5: 19 divided by 5 is 3 with a remainder of 4. So 4 would be our solution.
- Robert
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yair61 New user Israel 55 Posts |
Yes. Thus is the calculation. You can write it in Google: 8^5 mod 11, he know the answer.
And my guess was wrong, I need to work more about my statistics. |
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landmark Inner circle within a triangle 5194 Posts |
Wow, even when I know which stack it is, I'm still stumped. I think I know which direction to look in, but this is going to take some time.
Click here to get Gerald Deutsch's Perverse Magic: The First Sixteen Years
All proceeds to Open Heart Magic charity. |
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Bulla Special user Honolulu, HI 674 Posts |
Wow if the hint is anything like the math that you have to do to figure out the stack then that's too much calculation to do on the fly. I'll just stick with BTCS.
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nlokers Regular user Grand Rapids, MI 142 Posts |
There are no exponents involved. There are two methods for getting from one card to the next, the "straight-forward" one requires 2 basic operations (of the + - x / sort), however the number of digits you may have to deal with could be 3. The "shortcut" method requires memorizing 4 values, and requires 3 basic operations, but you never have to deal with more than 2 digits. Calculating 26 away is a single operation.
In general I would say that jumping to the next card takes a similar amount of thinking as the BTCS, though as we found out with the hints, what I consider to be super easy may not actually be for most people. Currently, I'm trying to put all my work together in some very plain language so that I can run it past some people to determine a few things. 1. How easy is it for a non math nerd to do the calculations 2. Does the system contain anything that could be applied elsewhere and should be published regardless of whether anyone actually uses the stack I made with it (not sure if I mentioned it or not, but the general system can be applied to tarot cards and quite a few other lengths in addition to 52 and 78) 3. Do the added features such as being a bit more random looking and being able to calculate cards at distances such as 7 away, 10 away, 26 away or 31 away, add enough value that anyone would choose it over BTCS. (One thing I think is that it would make a great memorized deck, so you could start with just using the next card feature, then you could choose to memorize a handful of cards, say if you memorized 12 or 13 cards, you would be able to get to any number with one or two calculations) I guess that is a little more than I was originally planning on spilling in this thread, but I guess now is as good a time as any. If anyone wants to be one of the people to given me feedback, I'm willing to start taking applications. I guess just PM me and tell me why you would be a good person to run this past. |
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BarryFernelius Inner circle Still learning, even though I've made 2537 Posts |
Several years ago, Steve Bryant published an interesting mathematical stack that was based on octal numbers. The stack was created by Richard Uhrich. Take a look here: http://littleegyptmagic.com/courses.htm
Look, it's an interesting idea for a stack. Bravo for using your mathematical skills to come up with it. But with that said, the calculations are faster and easier if you just memorize a stack. (This means that if someone names a card, you INSTANTLY know its stack number, the card before it, and the card after it. Similarly, if someone names a stack number, you INSTANTLY know the card. No calculations are required.) Most of the hard work required to memorize a stack can be done by most humans in about four hours. That's just one afternoon of concentrated work. (Juan Tamariz has done workshops that demonstrate that this is true.) I don't understand the advantages of your system. Why would you want to work this hard when you could solve the problem once and for all in less than one day?
"To achieve great things, two things are needed: a plan and not quite enough time."
-Leonard Bernstein |
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nlokers Regular user Grand Rapids, MI 142 Posts |
I've actually been using the Aronson stack that way for 8 or 9 years and continue to use it (and will until I know this stack as well as I know my current one).
This has just been something that I've been playing with for a few years after I figured out how BTCS worked. My interest in math made me admire its beauty, but I figured there had to be a more mathematically pure way to do it (I'm mainly referring to the figuring out of the suit, not that I think there is a problem with it, just that mathematically I wanted something cleaner so that I could do the same thing with non-playing cards, such as the Tarot). I do actually think that if anyone wants to use this, that they should do so with the goal of memorizing it. Knowing a stack cold does take a lot of work. For me to truly be comfortable with the Aronson stack I had to be able to do card->index, index->card, card->next card, card->previous card, and be able to just run through the stack forward and backward quickly. I think there are people out there that lurk here, intending to memorize a stack, but just don't out of some sort of fear. I think the mathematical stack is great for that, especially for someone like me who just seems to have no knack for actually visualizing things. Plus, like I said, I think that there may be some genius out there that can take the generic system and apply it to something that I haven't even thought of. |
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JanForster Inner circle Germany ... when not traveling... 4190 Posts |
You said it . Never understood why people invest so much time and work to invent a substitute for a MD instead of trying to learn one before. Actually it takes longer to invent a stack... Besides that there is no substitute for a MD what everybody will find out once they really start to work with it. You need your brain for other things, not for calculating where a card is now and at which position it is after one cut... Jan
Jan Forster
www.janforster.de |
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nlokers Regular user Grand Rapids, MI 142 Posts |
Something that Doug Dyment has pointed out at least twenty times on this forum (so I'm sure you guys have had to have read it at least once) is that you can memorize any stack. When it comes to choosing the stack that you want to memorize is what features you would like it to have.
Do you want it to look super random? Shuffle a deck and memorize that Do you want to have a bunch of poker hand tricks available? Memorize Aronson Do you want to be able to get into the deck from new deck order? Memorize Mneumonica Do you want to be able to have an easy to remember fallback in case you forget something? Memorize a mathematical stack Do you guys disagree with this? |
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