I am utterly unfamiliar with magic with dice - apart from my Die Box and seeing a large die as a final load in a Cups and Balls routine.

I'm looking for a routine that would work well with a Monte Carlo simulation theme, so a routine that uses dice seems a natural fit.

Any ideas for routines that would work with this theme?

Thanks!

Dice stacking. Switching, magnetic dice, whip cup dice? Matrix? Poker Pot?

"Dr. Sack's Amazing Dice Trick." You'll find it (among other places) in Bruce Elliott's trusty "Classic Secrets of Magic"

If you're looking to do this:

1. Define a domain of possible inputs.
2. Generate inputs randomly from the domain, and perform a deterministic computation on them.
3. Aggregate the results of the individual computations into the final result.


1 would be the pips on a die (1-6)
2 inputs would come from a spectator
3 predict the number the spectator picks every single time

would that work?

The idea of Monte Carlo simulation is that instead of solving a problem analytically, you do a bunch of random trials and see if a solution materializes from the results. The name "Monte Carlo" comes from this idea of random trials: like rolling dice.

Here's a simple example, which came from a thread in the Magical equations forum:

Larry Barnowsky wanted to know the probability of getting at least four cards of the same color in a row in a randomly shuffled deck of cards. To try to count all possible arrangements of 52 cards that have at least four red cards in a row or at least four black cards in a row (without mistakenly counting the same arrangement more than once) is a very, very difficult problem. But it's easy to write a computer program to simulate a random shuffle. So you tell this program to generate, say, 100,000 random shuffles, count how many of those have at least four cards of the same color in a row, and that's probably a pretty good approximation to the real number.

Frank's thinking along the right lines: something that involves the randomness of the dice, but leads to a (magically) predictable result would be great!

As I say, I'm not familiar with dice magic, so while Dr. Sack's Amazing Dice Trick might be perfect, I haven't any idea, because I have no idea what the effect is.

Thanks for your help, guys! I know that it's a tall order.

After reading your explanation of Monte Carlo...
Isn't that how the 4 Color Theorem was "proven"?

If so, I prefer the proof of the 5 color theorem. Much more interesting.

Howie Schwarztman was trying to teach me a dice trick a couple days ago that might have suited you fine but he could not remember how to do it. If I figure out the solution to that one, I'll let you know. It's interesting.

Not exactly.

The proof of the Four Color Theorem comprised two parts. The first part was a general proof that a planar map could be colored with no more than four colors with no two adjacent regions being the same color, which covered all but a finite number of cases; unfortunately, that finite number was huge: several hundred billion cases or something like that. So these mathematicians wrote a computer progran to check all of the cases that the general proof didn't cover. They ran the program and it started ticking off all these cases:
1, check!;
2, check!;
3, check!;
and so on.

It got to the end and said, "They all work."

(Thus, the review of the proof consisted of trying to verify that the computer algorithm didn't miss any of the cases. How fun!)

It's interesting that for more complicated surfaces than a plane - the surface of a doughnut (a torus), for example - the general proof is comparatively easy.


Another possibility is a dice routine where the result is completely wrong - something along the lines of Topsy-Turvy Bottles - because occasionally the results of a Monte Carlo simulation are counterintuitive.

You can tell a story that makes pseudo scientific sense but is completely wrong, or highly implausible. Only a few will question you, even if they are engineers. There are so few scientists and mathematicians out there.

Marty, that made me smile. "There are so few scientists and mathematicians out there." you live between Harvard and MIT.

The proof actually went more this way:

It was proved that all planar maps could be reduced to a finite, although still relatively large, number of equivalent maps.

A computer program was created to examine all of these equivalent maps.

Many mathematicians don't accept the proof since there is no way to verify that the results of the program can be trusted. This requires that the program had no errors in it, that the computer system properly translated the program into something that the machine can execute. You also have to believe that there were no hardware errors.

So there are still mathematicians who are looking for a proof.

You can find more information on the map-coloring problem in Four Colors Suffice, by Robin Wilson. A quick trip to Amazon.com showed several used paperback copies available for under a dollar (before shipping).



Curt

Thanks for the clarification; I was trying to recall it from (an evidently slightly foggy) memory. For more details, check here.

Best of luck with it, Bill.

Well Bill, what did you discover....

Just today I got a package from Gambler's General Store: sleeves of dice in red, green, blue, pink, amber, black, and white.

I'm going with Chink-a-Chink from Stars of Magic. I can talk of Monte Carlo simulation having its origins at the dice table, use the dice to represent various risks that can arise, and explain that the purpose of using Monte Carlo simulation is to analyze the risks in combination: first one risk at a time, then two together, then three, then all four. I'd like to finish by pointing out that there are generally more than four risks to consider, and illustrate that by producing dozens of dice of various colors. I haven't settled on a method yet, so I'm going to put that off for a bit: I'm going to be taping the routine (along with two others) at the Castle on July 5.

Thanks for everyone's suggestions. Pete, ultimately, nailed it - matrix - but I'm going to be learning the Sachs (Sack's?)routine for my strolling magic.

Since you'll be studying matrix and Dice, I urge you to check out Charlie Frye's routine on one of his Eccentricks DVDs.

His Matrix is quite unique.

There's a clip of it toward the beginning of this video.
http://youtube.com/watch?v=JwRwKRhzKqk

Whew...... now that you fellers is done with all that scientifical stuff,there is a nice dice routine on No Jacket Required. It is his version ,I believe of the Sach routine

That's the Carl Andrews routine. Pretty standard sack's faire. A nice routine.

Also check out Bob Farrell's Four Dice Chink-A Chink on Daryl's Fooler Doolers Vol.3. The dice go in numerical order. There is also a decent into to the Sack's (Sach's ?) trick on there.

Both of those are also on the WGM DVD